🕷️ Crawler Inspector

URL Lookup

Direct Parameter Lookup

Raw Queries and Responses

1. Shard Calculation

Query:

Response:

Calculated Shard: 0 (from laksa018)

2. Crawled Status Check

Query:

curl -X POST \
  'http://laksa000.int.ahrefs:8124/' \
  -H 'Content-Type: text/plain' \
  -H 'X-ClickHouse-Database: crawler3' \
  -H 'Authorization: Basic YXBpOg==' \
  -d 'SELECT getAhrefsURLFromUnparsed(src_unparsed) AS found_url, ifNull(toUnixTimestamp(download_stamp), 0) AS crawl_time, ifNull(toUnixTimestamp(props_url_first_seen), 0) AS first_indexed_time, download_http_code AS http_code, src_unparsed AS src_unparsed, src_root_hash AS src_root_hash, history_drop_reason AS history_drop_reason, meta_title AS meta_title, meta_descriptions AS meta_descriptions, attrs_boilerpipe_text AS attrs_boilerpipe_text, attrs_markdown AS attrs_markdown, attrs_readable_markdown AS attrs_readable_markdown, meta_canonical AS meta_canonical FROM crawler3.page_info_local FINAL PREWHERE (src_root_hash, src_unparsed) IN ((getAhrefsRootHashFromUnparsed(getAhrefsUnparsedNoserviceFromURL(\'https://www.statskingdom.com/\')), getAhrefsUnparsedNoserviceFromURL(\'https://www.statskingdom.com/\'))) FORMAT JSONEachRow'

Response:

{"found_url":"https:\/\/www.statskingdom.com\/","crawl_time":1775570578,"first_indexed_time":1556767050,"http_code":200,"src_unparsed":"com,statskingdom!www,\/ s443","src_root_hash":"18255949010202232800","history_drop_reason":null,"meta_title":"Statistics online - checks assumptions, interprets results","meta_descriptions":["Statistical tests, charts, probabilities and clear results. Automatically checks assumptions, interprets results and outputs graphs, histograms and other charts."],"attrs_boilerpipe_text":"Statistical tests, charts, probabilities and clear results. Automatically checks assumptions, interprets results and outputs graphs, histograms and other charts.\nThe statistics online calculators support not only the test statistic and the p-value but more results like effect size, test power, and the normality level.\nIf one of the validations fails, the tool recommends a solution.\nWhat statistical test should you use? the following link will help you choose:\nchoose a statistical test\n- decision questionnaire (\nTutorial\n).\nTest statistic calculators\nFind the test statistic calculator\nTest\nAssumptions\nRequired sample data\n#\nTest name\nCheck\nStatistic\nInd\nσ\nσ\n1\n=σ\n2\nd\nμ\/p\nx̄\/p̂;\nn\nS\n1\nOne Sample Z-Test\nMean\nz\n=\nx\n¯\n-\nμ\n0\nσ\n\/\nn\n✔\n✔\n✔\n✔\n✔\n✔\n2\nOne Sample T-Test\nMean\nt\n=\nx\n¯\n-\nμ\n0\nS\n\/\nn\n✔\n✔\n✘\n✔\n✔\n✔\n✔\n3\nTwo Sample Z-Test\nMean\nz\n=\nx\n1\n-\nx\n2\n-\nd\nσ\n2\nn\n1\n+\nσ\n2\nn\n2\n✔\n✔\n✔\n✔\n✔\n✔\n4\nTwo Sample T-Test (Pooled variance)\nMean\nt\n=\nx\n¯\n1\n-\nx\n¯\n2\n-\nd\ns\n1\nn\n1\n+\n1\nn\n2\n✔\n✔\n✘\n✔\n✔\n✔\n✔\n✔\n5\nTwo Sample T-Test (Welch's)\nMean\nt\n=\nx\n¯\n1\n-\nx\n¯\n2\n-\nd\ns\n1\n2\nn\n1\n+\ns\n2\n2\nn\n2\n✔\n✔\n✘\n✘\n✔\n✔\n✔\n✔\n6\nTwo Sample Mann-Whitney U Test\nRank\nz\n=\nU\n-\nμ\n+\nc\nσ\n✔\n✔\n✔\n7\nPaired T-Test\nMean\nt\n=\nx\n¯\nd\n-\nμ\n0\nS\nd\n\/\nn\n✔\nPaired\n✔\n8\nPaired Wilcoxon Sign Rank Test\nRank\nz\n=\nW\n-\nμ\n+\nc\nσ\nPaired\n✔\n9\nOne Way ANOVA Test\nMean\nF\n=\nMS\nBetween\nMS\nWithin\n✔\n✔\n✔\n✔\n10\nRepeated Measures ANOVA Test\nMean\nF\n=\nMS\nBetween\nMS\nWithin\n✔\nDependent\ngroups\nSphericity\n✔\n11\nFriedman Test\nMean\nχ²(df)\n=\n12\n∑\nj\n=\n1\nk\nR\nj\n2\n-\n3\nn\n2\nk\n(\nk\n+\n1\n)\n2\nn\nk\n(\nk\n+\n1\n)\n-\nC\nt\ni\ne\ns\nDependent\ngroups\n✔\n12\nKruskal-Wallis Test\nMean\nF\n=\nMS\nBetween\nMS\nWithin\n✔\n✔\n13\nTwo Way ANOVA Test\nFixed model, Mixed model, Random mode, Mixed model with repeats\nMean\nF\n=\nMS\nBetween\nMS\nWithin\n✔\n✔\n✔\n✔\n14\nOne Way MANOVA Test\nMean\nF\n=\nV\ns\n-\nV\n.\nd\nf\n2\nd\nf\n1\n✔\n✔\n✔\n✔\n15\nOne Sample Proportion Test\nProportion\nz\n=\n(\np\n^\n-\np\n0\n)\n+\nc\np\n0\n(\n1\n-\np\n0\n)\nn\nor\nX~\nB(\nn\n,\np\n0\n)\nBinomial\n✔\n✔\n✔\n✔\n16\nTwo Sample Proportion Test\nProportion\nz\n=\np\n^\n1\n-\np\n^\n2\n+\nCont\np\n^\n(\n1\n-\np\n^\n)\n(\n1\nn\n1\n+\n1\nn\n2\n)\nBinomial\n✔\n✔\n✔\n17\nChi-Squared Test For Variance\nσ\nχ\n2\n=\n(\nn\n-\n1\n)\nS\n2\nσ\n0\n2\n✔\n✔\n✔\n✔\n18\nF Test For Variances\nσ\nF\n=\nS\n1\n2\nS\n2\n2\n✔\n✔\n✔\n✔\n19\nLevene's Test For Variances\nσ\nF\n=\nMS\nBetween\nMS\nWithin\n✘\n✔\n✔\n20\nChi-Squared Test For Goodness Of Fit\nMcNemar test, Chi-squared test for association, Fisher test, Binomial test\nFit\nχ\n2\n=\n∑\ni\n=\n1\nn\n(\no\ni\n-\ne\ni\n)\n2\ne\ni\n✔\n✔\n21\nShapiro-Wilk Test\nFit\nW\n=\n(\n∑\ni\n=\n1\n⌊\nn\n\/\n2\n⌋\na\ni\n(\nx\nn+1-i\n-\nx\ni\n)\n)\n2\n∑\ni\n=\n1\nn\n(\nx\ni\n-\nx\n¯\n)\n2\n✔\n✔\n✔\n22\nKolmogorov Smirnov Test\nFit\nD\n= Max\n1≤i≤n\n(\nD\ni\n+\n,\nD\ni\n-\n)\n✔\n✔\n23\nTwo-Sample Kolmogorov Smirnov Test\nFit\nD\n= Max\n1≤i≤n\n(\nD\ni\n+\n,\nD\ni\n-\n)\n✔\n✔\n24\nKaplan Meier Survival Analysis\nSurvival\nχ\n2\n=\n∑\ni\n=\n1\nn\n(\no\ni\n-\ne\ni\n)\n2\ne\ni\n✔\n✔\n25\nDeLong test - Independent curves\nCompares the AUCs of two independent ROC curves\nAUC\nD\n=\nAUC\n1\n-\nAUC\n2\nVar\n1\n+\nVar\n1\n✔\n✔\n26\nDeLong test - Paired curves\nCompares the AUCs of two dependent ROC curves\nAUC\nZ\n=\nAUC\n1\n-\nAUC\n2\nVar\n₁\n+\nVar\n₂\n-\n2\n*\nCov\n(\nAUC\n₁\n,\nAUC\n₂\n)\nPaired\n✔\n**\n✔\n- Yes,\n✘\n- No, empty - irrelevant\nRegression calculator\n#\nRegression\nStatistic\n1\nSimple Linear Regression\nF\n=\nMS\nRegression\nMS\nError\n2\nMultiple Linear Regression\nF\n=\nMS\nRegression\nMS\nError\n3\n*Bulk Linear Regression\nF\n=\nMS\nRegression\nMS\nError\n4\nBinary Logistic Regression\nχ2 = 2(LL\n1\n-LL\n0\n)\n5\nMultinomial Logistic Regression\nχ2 = 2(LL\n1\n-LL\n0\n)\n6\nPropensity Score Matching\n*Bulk linear regression calculator for several dependent variables with the same predictors.\nConfidence interval, Sample size, Effect Size\n#\nCalculator\nImage\nSample size calculators\nTest power calculators\nEffect size calculators\nConfidence intervals calculators\nDistribution calculators\n#\nDistribution\nImage\nP-value\nDistributions\nNormal Distribution\nBinomial Distribution\nT Distribution (Student's)\nChi-Squared Distribution\nF Distribution (Fisher-Snedecor)\nPoisson Distribution\nWeibull Distribution\nExponential Distribution\nStatistical tables\n#\nTable\n1\nZ table\n2\nT table\nBasic statistics calculators\nEach statistics calculator contains step by step calculation.\nCalculator\nStatistic calculator\nImage\nStatistics calculator\nThe calculator computes statistics such as count, average and standard deviation for each\ncombination of the categorical variables\n.\nDescriptive statistics calculator\nThe calculator computes statistics such as count, average, and standard deviation for each\nvariable\n.\nPercentile calculator\nA percentile tells you the percentage of values below a given value in a data set.\nFor example, a value at the 75th percentile means that 75% of the data lies below that value.\nMean Median Mode calculator\nQ\n1\n, Q\n3\n, IRQ, Range\nMeasures Of Dispersion calculator\nMean, sample size, APA style\nStandard Deviation calculator\nMean, sample size, APA style\nS\n=\n∑\ni\n=\n1\nn\n(\nx\ni\n-\nx̄\n)\n2\nn\n-\n1\nVariance calculator\nVariance, Mean, SEM, MAD\nS\n2\n=\n∑\ni\n=\n1\nn\n(\nx\ni\n-\nx̄\n)\n2\nn\n-\n1\nCoefficient of Variation calculator\nCV\n=\ns\nx\n¯\nAverage calculator\nAverage, Sum, Count\nx\n¯\n=\nx\n1\n+\nx\n2\n+\n⋯\n+\nx\nn\nn\nSample Mean calculator\nSample mean, Sum, Count\nx\n¯\n=\nx\n1\n+\nx\n2\n+\n⋯\n+\nx\nn\nn\nGeometric Mean calculator\nProduct, n-th root\nG\nM\n=\nx\n1\nx\n2\n…\nx\nn\nn\nHarmonic Mean calculator\nThe harmonic mean is a type of average used for rates, for example average speed. It is found by dividing n by the sum of the reciprocals of the values.\nH\nn\n=\nn\n1\nx\n1\n+\n1\nx\n2\n+\n⋯\n+\n1\nx\nn\nProbability calculator\nProbability formula, Dependent events, Bayes' Theorem, Independent events\nP(A), P(A|B), P(A∩B), P(A∪B)\nCombinations calculator\nWith\/Without Repetitions\nC\nr\nn\n=\nn\n!\nr\n!\n(\nn\n−\nr\n)\n!\n,\nC\nr\nn + r - 1\n=\nn + r - 1\n!\nr\n!\n(\nn\n−\n1\n)\n!\nPermutation calculator\nWith\/Without Repetitions\nP\nr\nn\n=\nn\n!\n(\nn\n−\nr\n)\n!\n, n\nr\nCorrelation calculator\nPearson correlation, Spearman's rank correlation\nr\n=\n∑\ni\n=\n1\nn\n(\nx\ni\n−\nx\n¯\n)\n(\ny\ni\n−\ny\n¯\n)\n∑\ni\n=\n1\nn\n(\nx\n−\nx\n¯\n)\n2\n∑\ni\n=\n1\nn\n(\ny\ni\n−\ny\n¯\n)\n2\nOutliers\nTukey's Fences (Boxplot), Z-Score\nMarkov chain calculator\nnth step probability vector, steady-state vector\nOdds calculator\nOdds to probability, probability to odds\nBetting odds calculator\nFractional odds, decimal odds, American odds\nMean absolute deviation calculator\nMAD calculator\nμ\nMedian absolute deviation calculator\nMAD calculator\nMdn\nVisualization\n#\nChart\nImage\n1\nPrincipal component analysis\n2\nCluster analysis\n3\nHistogram maker\n4\nBox plot maker\n5\nBar graph maker\n6\nPie chart maker\n7\nLine chart maker\n8\nScatter chart maker\n9\nArea chart maker\n10\nViolin plot maker\n11\nVenn diagram maker\n12\nVenn diagram calculator\nVenn diagram calculator\n12\n3\n9\n13\nStem and Leaf plot\n14\nROC Calculator\nGuide\nGuide\nBonferroni correction\nCentral Limit Theorem\nConfidence interval\nLinear regression\nLogistic regression\nOutliers\nP-value\nSkewness and kurtosis\nStandard deviation\nTest power\nExams\nFree statistics exams with solution.\nStatistical Tests\nChi-squared test\nLevene's test\nMann-Whitney U Rank test\nOne Way ANOVA test\nProportion test\nShapiro Wilk test\nT-test\nT-test vs Z-Test\nTukey HSD test\nWilcoxon Sign Rank test\nGoal\nThe goal of this website is to make statistics accessible to anyone, converting complex statistical jargon into common everyday language.\nWe help everybody to calculate statistics.\nThe calculators also provide R codes for your convenience.\nWe started adding a step-by-step work-through for education purposes, an easy guide on how to calculate test statistics.\nTerms\nWe put in a lot of effort to provide accurate results and we automatically test every new page, The older pages were tested manually, but we slowly also automate the old pages.\nWe usually compare the results to the R results.\nThe information and tools on this website are given AS IS WITHOUT ANY WARRANTY OF ANY KIND.\nCalculate statistics\nThe best online calculator to calculate statistics.","attrs_markdown":"[Statistics Kingdom](https:\/\/www.statskingdom.com\/index.html)\n\n[Home](https:\/\/www.statskingdom.com\/index.html)\n\n- [Site Contents](https:\/\/www.statskingdom.com\/index.html)[Decision tree](https:\/\/www.statskingdom.com\/statistical-decision-tree.html)[Guide](https:\/\/www.statskingdom.com\/information.html)[About Us](https:\/\/www.statskingdom.com\/about.html)[Contact Us](https:\/\/www.statskingdom.com\/contact.html)[Privacy Policy](https:\/\/www.statskingdom.com\/privacy.html)[Terms of Use](https:\/\/www.statskingdom.com\/terms.html)\n\n- [Information](https:\/\/www.statskingdom.com\/)[Site Contents](https:\/\/www.statskingdom.com\/index.html)[Decision tree](https:\/\/www.statskingdom.com\/statistical-decision-tree.html)[Guide](https:\/\/www.statskingdom.com\/information.html)[Exams](https:\/\/www.statskingdom.com\/statistics-exam.html)[About Us](https:\/\/www.statskingdom.com\/about.html)[Contact Us](https:\/\/www.statskingdom.com\/contact.html)[Privacy Policy](https:\/\/www.statskingdom.com\/privacy.html)[Terms of Use](https:\/\/www.statskingdom.com\/terms.html)\n\n- [Basic Stats](https:\/\/www.statskingdom.com\/)[Statistics](https:\/\/www.statskingdom.com\/statistics-calculator.html)[Descriptive Statistics](https:\/\/www.statskingdom.com\/descriptive-statistics-calculator.html)[Median Mean Mode](https:\/\/www.statskingdom.com\/mean-median-mode-calculator.html)[Measures of dispersion](https:\/\/www.statskingdom.com\/measures-of-dispersion-calculator.html)[Standard Deviation](https:\/\/www.statskingdom.com\/standard-deviation-calculator.html)[Variance](https:\/\/www.statskingdom.com\/variance-calculator.html)[Coefficient of Variation](https:\/\/www.statskingdom.com\/coefficient-of-variation-calculator.html)[Pooled Variance](https:\/\/www.statskingdom.com\/pooled-variance-calculator.html)[Average](https:\/\/www.statskingdom.com\/average-calculator.html)[Sample Mean](https:\/\/www.statskingdom.com\/sample-mean-calculator.html)[Geometric Mean](https:\/\/www.statskingdom.com\/geometric-mean-calculator.html)[Harmonic Mean](https:\/\/www.statskingdom.com\/harmonic-mean-calculator.html)[Probability](https:\/\/www.statskingdom.com\/probability-calculator.html)[Combinations](https:\/\/www.statskingdom.com\/combinations-calculator.html)[Permutations](https:\/\/www.statskingdom.com\/permutations-calculator.html)[Combinations generator](https:\/\/www.statskingdom.com\/combinations-generator.html)[Correlation](https:\/\/www.statskingdom.com\/correlation-calculator.html)[Outliers](https:\/\/www.statskingdom.com\/outlier-calculator.html)[Markov Chain](https:\/\/www.statskingdom.com\/markov-chain-calculator.html)[Odds](https:\/\/www.statskingdom.com\/odds-calculator.html)[Betting odds](https:\/\/www.statskingdom.com\/betting-odds-calculator.html)[MAD](https:\/\/www.statskingdom.com\/mean-absolute-deviation-calculator.html)\n\n- [Distribution](https:\/\/www.statskingdom.com\/)[Critical Value](https:\/\/www.statskingdom.com\/critical-value-calculator.html)[P-value](https:\/\/www.statskingdom.com\/p_value.html)[All Distributions](https:\/\/www.statskingdom.com\/distribution-calculator.html)[Empirical Distribution](https:\/\/www.statskingdom.com\/ecdf.html)[Percentile](https:\/\/www.statskingdom.com\/percentile-calculator.html)[Probability](https:\/\/www.statskingdom.com\/probability-calculator.html)[Normal](https:\/\/www.statskingdom.com\/normal-distribution-calculator.html)[Binomial](https:\/\/www.statskingdom.com\/binomial-distribution-calculator.html)[T-Student](https:\/\/www.statskingdom.com\/distribution-calculator.html)[Chi-Squared](https:\/\/www.statskingdom.com\/distribution-calculator.html)[F-Fisher-Snedecor](https:\/\/www.statskingdom.com\/distribution-calculator.html)[Z table](https:\/\/www.statskingdom.com\/z_table.html)[Surprisal](https:\/\/www.statskingdom.com\/surprisal-calculator.html)\n\n- [Fit Tests](https:\/\/www.statskingdom.com\/)[Goodness of Fit](https:\/\/www.statskingdom.com\/310GoodnessChi.html)[Independence & Fisher](https:\/\/www.statskingdom.com\/310GoodnessChi.html)[Shapiro-Wilk](https:\/\/www.statskingdom.com\/shapiro-wilk-test-calculator.html)[Kolmogorov-Smirnov](https:\/\/www.statskingdom.com\/kolmogorov-smirnov-test-calculator.html)[Two Sample KS](https:\/\/www.statskingdom.com\/kolmogorov-smirnov-two-calculator.html)[D'Agostino-Pearson](https:\/\/www.statskingdom.com\/dagostino-pearson-test-calculator.html)[Survival Analysis (KM)](https:\/\/www.statskingdom.com\/kaplan-meier.html)\n\n- [Sample Size](https:\/\/www.statskingdom.com\/)[Sample Size](https:\/\/www.statskingdom.com\/sample_size_all.html)[Test Power](https:\/\/www.statskingdom.com\/statistical-power-calculators.html)[Effect Size](https:\/\/www.statskingdom.com\/effect-size-calculator.html)[Confidence Interval](https:\/\/www.statskingdom.com\/50_ci_sample_size.html)\n\n- [Conf Int](https:\/\/www.statskingdom.com\/)[Mean](https:\/\/www.statskingdom.com\/confidence-interval-calculator.html)[Mean Difference](https:\/\/www.statskingdom.com\/difference-confidence-interval-calculator.html)[Standard Deviation](https:\/\/www.statskingdom.com\/confidence-interval-calculator.html)[Two Variances](https:\/\/www.statskingdom.com\/variances-ratio-ci-calculator.html)[Proportion](https:\/\/www.statskingdom.com\/proportion-confidence-interval-calculator.html)[Two Proportions](https:\/\/www.statskingdom.com\/two-proportions-ci-calculator.html)[Correlation](https:\/\/www.statskingdom.com\/correlation-confidence-interval-calculator.html)[Confidence Level](https:\/\/www.statskingdom.com\/confidence-level-calculator.html)\n\n- [Mean Tests](https:\/\/www.statskingdom.com\/)[Mean Calculator](https:\/\/www.statskingdom.com\/sample-mean-calculator.html)[One Sample Z-test](https:\/\/www.statskingdom.com\/110MeanNormal1.html)[One Sample Proportion Z-test](https:\/\/www.statskingdom.com\/111proportion_normal1.html)[One Sample T-Test](https:\/\/www.statskingdom.com\/130MeanT1.html)[Two Sample Z-test](https:\/\/www.statskingdom.com\/120MeanNormal2.html)[Two Sample Proportions Z-test](https:\/\/www.statskingdom.com\/121proportion_normal2.html)[Two Sample T-test (Pooled-Variance)](https:\/\/www.statskingdom.com\/140MeanT2eq.html)[Two Sample T-test (Welch's)](https:\/\/www.statskingdom.com\/150MeanT2uneq.html)[Two Sample Mann–Whitney U test](https:\/\/www.statskingdom.com\/170median_mann_whitney.html)[Paired T-test](https:\/\/www.statskingdom.com\/paired-t-test-calculator.html)[Wilcoxon Signed Rank test](https:\/\/www.statskingdom.com\/175wilcoxon_signed_ranks.html)\n\n- [M\/ANOVA](https:\/\/www.statskingdom.com\/)[One Way ANOVA test](https:\/\/www.statskingdom.com\/180Anova1way.html)[Kruskal-Wallis Test](https:\/\/www.statskingdom.com\/kruskal-wallis-calculator.html)[Two Way ANOVA - Unbalanced](https:\/\/www.statskingdom.com\/unbalanced-two-way-anova.html)[Two Way ANOVA - Balanced](https:\/\/www.statskingdom.com\/two-way-anova-calculator.html)[Repeated Measures ANOVA](https:\/\/www.statskingdom.com\/repeated-anova-calculator.html)[Friedman test](https:\/\/www.statskingdom.com\/friedman-calculator.html)[One Way MANOVA test](https:\/\/www.statskingdom.com\/manova-calculator.html)\n\n- [Variance Tests](https:\/\/www.statskingdom.com\/)[χ2 Test for Variance](https:\/\/www.statskingdom.com\/210VarCHI1.html)[F Test for Variances](https:\/\/www.statskingdom.com\/220VarF2.html)[Levene's Equality of Variances](https:\/\/www.statskingdom.com\/230var_levenes.html)\n\n- [Regression](https:\/\/www.statskingdom.com\/)[Simple Linear Regression](https:\/\/www.statskingdom.com\/linear-regression-calculator.html)[Multiple Linear Regression](https:\/\/www.statskingdom.com\/410multi_linear_regression.html)[Binary Logistic Regression](https:\/\/www.statskingdom.com\/420logistic_regression.html)[Multinomial Logistic Regression](https:\/\/www.statskingdom.com\/430logistic_regression.html)[One Sample Correlation Test](https:\/\/www.statskingdom.com\/correlation-calculator.html)[Propensity Score Matching](https:\/\/www.statskingdom.com\/psm-calculator.html)[Neural Network](https:\/\/www.statskingdom.com\/neural-network.html)\n\n- [Visualization](https:\/\/www.statskingdom.com\/)[Histogram](https:\/\/www.statskingdom.com\/histogram-maker.html)[Box plot](https:\/\/www.statskingdom.com\/boxplot-maker.html)[Violin Plot](https:\/\/www.statskingdom.com\/violin-plot-maker.html)[Cluster Analysis](https:\/\/www.statskingdom.com\/cluster-analysis.html)[Charts](https:\/\/www.statskingdom.com\/chart-maker.html)[Bar Chart](https:\/\/www.statskingdom.com\/bar-chart-maker.html)[Pie Chart](https:\/\/www.statskingdom.com\/pie-chart-maker.html)[Scatter Chart](https:\/\/www.statskingdom.com\/scatter-chart-maker.html)[Line Chart](https:\/\/www.statskingdom.com\/line-chart-maker.html)[Area Chart](https:\/\/www.statskingdom.com\/area-chart-maker.html)[PCA](https:\/\/www.statskingdom.com\/pca-calculator.html)[Venn Maker](https:\/\/www.statskingdom.com\/venn-diagram-maker.html)[Venn Calculator](https:\/\/www.statskingdom.com\/venn-diagram-calculator.html)[Stem and Leaf](https:\/\/www.statskingdom.com\/stem-and-leaf.html)[ROC curve](https:\/\/www.statskingdom.com\/roc-calculator.html)[Palettes](https:\/\/www.statskingdom.com\/palettes.html)\n\n# Statistics online\nStatistical tests, charts, probabilities and clear results. Automatically checks assumptions, interprets results and outputs graphs, histograms and other charts.  \nThe statistics online calculators support not only the test statistic and the p-value but more results like effect size, test power, and the normality level.  \nIf one of the validations fails, the tool recommends a solution.  \nWhat statistical test should you use? the following link will help you choose: [**choose a statistical test**](https:\/\/www.statskingdom.com\/statistical-decision-tree.html) - decision questionnaire ([**Tutorial**](https:\/\/www.youtube.com\/embed\/QGZOBz_BXB4)).\n\n## Test statistic calculators\nFind the test statistic calculator\n\n| Test | Assumptions | Required sample data |   |   |   |   |   |   |   |   |   |   |   |\n|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n| \\# | Test name | Check | Statistic | ![Normal Distribution](https:\/\/www.statskingdom.com\/images\/Normal_trans.png) | Ind | σ | σ1\\=σ2 | d | μ\/p | x̄\/p̂; | n | S | ![data](https:\/\/www.statskingdom.com\/images\/data_icon2.png) |\n| 1 | [One Sample Z-Test](https:\/\/www.statskingdom.com\/110MeanNormal1.html) | Mean | z \\= x ¯ \\- μ 0 σ \/ n | ✔ | ✔ | ✔ |   |   | ✔ | ✔ | ✔ |   |   |\n| 2 | [One Sample T-Test](https:\/\/www.statskingdom.com\/130MeanT1.html) | Mean | t \\= x ¯ \\- μ 0 S \/ n | ✔ | ✔ | ✘ |   |   | ✔ | ✔ | ✔ | ✔ |   |\n| 3 | [Two Sample Z-Test](https:\/\/www.statskingdom.com\/120MeanNormal2.html) | Mean | z \\= x 1 \\- x 2 \\- d σ 2 n 1 \\+ σ 2 n 2 | ✔ | ✔ | ✔ |   | ✔ |   | ✔ | ✔ |   |   |\n| 4 | [Two Sample T-Test (Pooled variance)](https:\/\/www.statskingdom.com\/140MeanT2eq.html) | Mean | t \\= x ¯ 1 \\- x ¯ 2 \\- d s 1 n 1 \\+ 1 n 2 | ✔ | ✔ | ✘ | ✔ | ✔ |   | ✔ | ✔ | ✔ |   |\n| 5 | [Two Sample T-Test (Welch's)](https:\/\/www.statskingdom.com\/150MeanT2uneq.html) | Mean | t \\= x ¯ 1 \\- x ¯ 2 \\- d s 1 2 n 1 \\+ s 2 2 n 2 | ✔ | ✔ | ✘ | ✘ | ✔ |   | ✔ | ✔ | ✔ |   |\n| 6 | [Two Sample Mann-Whitney U Test](https:\/\/www.statskingdom.com\/170median_mann_whitney.html) | Rank | z \\= U \\- μ \\+ c σ |   | ✔ |   |   | ✔ |   |   |   |   | ✔ |\n| 7 | [Paired T-Test](https:\/\/www.statskingdom.com\/paired-t-test-calculator.html) | Mean | t \\= x ¯ d \\- μ 0 S d \/ n | ✔ | Paired |   |   |   |   |   |   |   | ✔ |\n| 8 | [Paired Wilcoxon Sign Rank Test](https:\/\/www.statskingdom.com\/175wilcoxon_signed_ranks.html) | Rank | z \\= W \\- μ \\+ c σ |   | Paired |   |   |   |   |   |   |   | ✔ |\n| 9 | [One Way ANOVA Test](https:\/\/www.statskingdom.com\/180Anova1way.html) | Mean | F \\= MS Between MS Within | ✔ | ✔ |   | ✔ |   |   |   |   |   | ✔ |\n| 10 | [Repeated Measures ANOVA Test](https:\/\/www.statskingdom.com\/repeated-anova-calculator.html) | Mean | F \\= MS Between MS Within | ✔ | Dependent groups |   | [Sphericity](https:\/\/www.statskingdom.com\/glossary.html#sp) |   |   |   |   |   | ✔ |\n| 11 | [Friedman Test](https:\/\/www.statskingdom.com\/friedman-calculator.html) | Mean | χ²(df) \\= 12 ∑ j \\= 1 k R j 2 \\- 3 n 2 k ( k \\+ 1 ) 2 n k ( k \\+ 1 ) \\- C t i e s |   | Dependent groups |   |   |   |   |   |   |   | ✔ |\n| 12 | [Kruskal-Wallis Test](https:\/\/www.statskingdom.com\/kruskal-wallis-calculator.html) | Mean | F \\= MS Between MS Within |   | ✔ |   |   |   |   |   |   |   | ✔ |\n| 13 | [Two Way ANOVA Test](https:\/\/www.statskingdom.com\/two-way-anova-calculator.html) Fixed model, Mixed model, Random mode, Mixed model with repeats | Mean | F \\= MS Between MS Within | ✔ | ✔ |   | ✔ |   |   |   |   |   | ✔ |\n| 14 | [One Way MANOVA Test](https:\/\/www.statskingdom.com\/manova-calculator.html) | Mean | F \\= V s \\- V . d f 2 d f 1 | ✔ | ✔ |   | ✔ |   |   |   |   |   | ✔ |\n| 15 | [One Sample Proportion Test](https:\/\/www.statskingdom.com\/111proportion_normal1.html) | Proportion | z \\= ( p ^ \\- p 0 ) \\+ c p 0 ( 1 \\- p 0 ) n or X~ B( n , p 0 ) | Binomial | ✔ |   |   |   | ✔ | ✔ | ✔ |   |   |\n| 16 | [Two Sample Proportion Test](https:\/\/www.statskingdom.com\/121proportion_normal2.html) | Proportion | z \\= p ^ 1 \\- p ^ 2 \\+ Cont p ^ ( 1 \\- p ^ ) ( 1 n 1 \\+ 1 n 2 ) | Binomial | ✔ |   |   |   |   | ✔ | ✔ |   |   |\n| 17 | [Chi-Squared Test For Variance](https:\/\/www.statskingdom.com\/210VarCHI1.html) | σ | χ 2 \\= ( n \\- 1 ) S 2 σ 0 2 | ✔ | ✔ |   |   |   |   |   | ✔ | ✔ |   |\n| 18 | [F Test For Variances](https:\/\/www.statskingdom.com\/220VarF2.html) | σ | F \\= S 1 2 S 2 2 | ✔ | ✔ |   |   |   |   |   | ✔ | ✔ |   |\n| 19 | [Levene's Test For Variances](https:\/\/www.statskingdom.com\/230var_levenes.html) | σ | F \\= MS Between MS Within | ✘ | ✔ |   |   |   |   |   |   |   | ✔ |\n| 20 | [Chi-Squared Test For Goodness Of Fit](https:\/\/www.statskingdom.com\/310GoodnessChi.html) McNemar test, Chi-squared test for association, Fisher test, Binomial test | Fit | χ 2 \\= ∑ i \\= 1 n ( o i \\- e i ) 2 e i |   | ✔ |   |   |   |   |   |   |   | ✔ |\n| 21 | [Shapiro-Wilk Test](https:\/\/www.statskingdom.com\/shapiro-wilk-test-calculator.html) | Fit | W \\= ( ∑ i \\= 1 ⌊ n \/ 2 ⌋ a i ( x n+1-i \\- x i ) ) 2 ∑ i \\= 1 n ( x i \\- x ¯ ) 2 | ✔ | ✔ |   |   |   |   |   |   |   | ✔ |\n| 22 | [Kolmogorov Smirnov Test](https:\/\/www.statskingdom.com\/kolmogorov-smirnov-test-calculator.html) | Fit | *D* = Max1≤i≤n(*D*i\\+,*D*i\\-) |   | ✔ |   |   |   |   |   |   |   | ✔ |\n| 23 | [Two-Sample Kolmogorov Smirnov Test](https:\/\/www.statskingdom.com\/kolmogorov-smirnov-two-calculator.html) | Fit | *D* = Max1≤i≤n(*D*i\\+,*D*i\\-) |   | ✔ |   |   |   |   |   |   |   | ✔ |\n| 24 | [Kaplan Meier Survival Analysis](https:\/\/www.statskingdom.com\/kaplan-meier.html) | Survival | χ 2 \\= ∑ i \\= 1 n ( o i \\- e i ) 2 e i |   | ✔ |   |   |   |   |   |   |   | ✔ |\n| 25 | [DeLong test - Independent curves](https:\/\/www.statskingdom.com\/roc-calculator.html) Compares the AUCs of two independent ROC curves | AUC | D \\= AUC 1 \\- AUC 2 Var 1 \\+ Var 1 |   | ✔ |   |   |   |   |   |   |   | ✔ |\n| 26 | [DeLong test - Paired curves](https:\/\/www.statskingdom.com\/roc-calculator.html) Compares the AUCs of two dependent ROC curves | AUC | Z \\= AUC 1 \\- AUC 2 Var ₁ \\+ Var ₂ \\- 2 \\* Cov ( AUC ₁ , AUC ₂ ) |   | Paired |   |   |   |   |   |   |   | ✔ |\n\n\\*\\* ✔ - Yes, ✘ - No, empty - irrelevant\n\n## Regression calculator\n| \\# | Regression | Statistic |\n|---|---|---|\n| 1 | [Simple Linear Regression](https:\/\/www.statskingdom.com\/linear-regression-calculator.html) | F \\= MS Regression MS Error |\n| 2 | [Multiple Linear Regression](https:\/\/www.statskingdom.com\/410multi_linear_regression.html) | F \\= MS Regression MS Error |\n| 3 | [\\*Bulk Linear Regression](https:\/\/www.statskingdom.com\/411list_linear_regression.html) | F \\= MS Regression MS Error |\n| 4 | [Binary Logistic Regression](https:\/\/www.statskingdom.com\/420logistic_regression.html) | χ2 = 2(LL1\\-LL0) |\n| 5 | [Multinomial Logistic Regression](https:\/\/www.statskingdom.com\/430logistic_regression.html) | χ2 = 2(LL1\\-LL0) |\n| 6 | [Propensity Score Matching](https:\/\/www.statskingdom.com\/psm-calculator.html) | ![Propensity Score Matching](https:\/\/www.statskingdom.com\/images\/psm.svg) |\n\n\\*Bulk linear regression calculator for several dependent variables with the same predictors.\n## Confidence interval, Sample size, Effect Size\n| \\# | Calculator | Image |\n|---|---|---|\n|   | [Sample size calculators](https:\/\/www.statskingdom.com\/sample_size_all.html) | ![sample size chart](https:\/\/www.statskingdom.com\/images\/sample_size.jpg) |\n|   | [Test power calculators](https:\/\/www.statskingdom.com\/statistical-power-calculators.html) | ![statistics power chart](https:\/\/www.statskingdom.com\/images\/small_t2_power2.jpg) |\n|   | [Effect size calculators](https:\/\/www.statskingdom.com\/effect-size-calculator.html) |   |\n|   | [Confidence intervals calculators](https:\/\/www.statskingdom.com\/confidence-interval-calculators.html) | ![statistics power chart](https:\/\/www.statskingdom.com\/images\/Normal1_t2_s.jpg) |\n## Distribution calculators\n| \\# | Distribution | Image |\n|---|---|---|\n|   | [P-value](https:\/\/www.statskingdom.com\/p_value.html) | ![p-value](https:\/\/www.statskingdom.com\/images\/p_value.jpg) |\n|   | [Distributions](https:\/\/www.statskingdom.com\/distribution-calculator.html) | ![Distribution Calculator](https:\/\/www.statskingdom.com\/images\/nrm_s.jpg) |\n|   | [Normal Distribution](https:\/\/www.statskingdom.com\/normal-distribution-calculator.html) | ![Normal Distribution](https:\/\/www.statskingdom.com\/images\/nrm_s.jpg) |\n|   | [Binomial Distribution](https:\/\/www.statskingdom.com\/binomial-distribution-calculator.html) | ![Binomial Distribution](https:\/\/www.statskingdom.com\/images\/binomial_s.jpg) |\n|   | [T Distribution (Student's)](https:\/\/www.statskingdom.com\/distribution-calculator.html) | ![T Distribution](https:\/\/www.statskingdom.com\/images\/t_s.jpg) |\n|   | [Chi-Squared Distribution](https:\/\/www.statskingdom.com\/distribution-calculator.html) | ![Chi squared Distribution](https:\/\/www.statskingdom.com\/images\/chi2_s.jpg) |\n|   | [F Distribution (Fisher-Snedecor)](https:\/\/www.statskingdom.com\/distribution-calculator.html) | ![F Distribution](https:\/\/www.statskingdom.com\/images\/f_s.jpg) |\n|   | [Poisson Distribution](https:\/\/www.statskingdom.com\/distribution-calculator.html) | ![Distribution](https:\/\/www.statskingdom.com\/images\/binomial_s.jpg) |\n|   | [Weibull Distribution](https:\/\/www.statskingdom.com\/distribution-calculator.html) |   |\n|   | [Exponential Distribution](https:\/\/www.statskingdom.com\/distribution-calculator.html) |   |\n## Statistical tables\n| \\# | Table |\n|---|---|\n| 1 | [Z table](https:\/\/www.statskingdom.com\/z_table.html) |\n| 2 | [T table](https:\/\/www.statskingdom.com\/t_table.html) |\n## Basic statistics calculators\nEach statistics calculator contains step by step calculation.\n\n| Calculator | Statistic calculator | Image |\n|---|---|---|\n| [Statistics calculator](https:\/\/www.statskingdom.com\/statistics-calculator.html) | The calculator computes statistics such as count, average and standard deviation for each combination of the categorical variables. | ![mean](https:\/\/www.statskingdom.com\/images\/statisticsCalc.svg) |\n| [Descriptive statistics calculator](https:\/\/www.statskingdom.com\/descriptive-statistics-calculator.html) | The calculator computes statistics such as count, average, and standard deviation for each variable. | ![mean](https:\/\/www.statskingdom.com\/images\/descriptive.svg) |\n| [Percentile calculator](https:\/\/www.statskingdom.com\/percentile-calculator.html) | A percentile tells you the percentage of values below a given value in a data set. For example, a value at the 75th percentile means that 75% of the data lies below that value. | ![percentile](https:\/\/www.statskingdom.com\/images\/percentile.svg) |\n| [Mean Median Mode calculator](https:\/\/www.statskingdom.com\/mean-median-mode-calculator.html) | Q1, Q3, IRQ, Range | ![mean](https:\/\/www.statskingdom.com\/images\/mean.svg) |\n| [Measures Of Dispersion calculator](https:\/\/www.statskingdom.com\/measures-of-dispersion-calculator.html) | Mean, sample size, APA style |   |\n| [Standard Deviation calculator](https:\/\/www.statskingdom.com\/standard-deviation-calculator.html) | Mean, sample size, APA style | S \\= ∑ i \\= 1 n ( x i \\- x̄ ) 2 n \\- 1 |\n| [Variance calculator](https:\/\/www.statskingdom.com\/variance-calculator.html) | Variance, Mean, SEM, MAD | S 2 \\= ∑ i \\= 1 n ( x i \\- x̄ ) 2 n \\- 1 |\n| [Coefficient of Variation calculator](https:\/\/www.statskingdom.com\/coefficient-of-variation-calculator.html) |   | CV \\= s x ¯ |\n| [Average calculator](https:\/\/www.statskingdom.com\/average-calculator.html) | Average, Sum, Count | x ¯ \\= x 1 \\+ x 2 \\+ ⋯ \\+ x n n |\n| [Sample Mean calculator](https:\/\/www.statskingdom.com\/sample-mean-calculator) | Sample mean, Sum, Count | x ¯ \\= x 1 \\+ x 2 \\+ ⋯ \\+ x n n |\n| [Geometric Mean calculator](https:\/\/www.statskingdom.com\/geometric-mean-calculator.html) | Product, n-th root | G M \\= x 1 x 2 … x n n |\n| [Harmonic Mean calculator](https:\/\/www.statskingdom.com\/harmonic-mean-calculator.html) | The harmonic mean is a type of average used for rates, for example average speed. It is found by dividing n by the sum of the reciprocals of the values. | H n \\= n 1 x 1 \\+ 1 x 2 \\+ ⋯ \\+ 1 x n |\n| [Probability calculator](https:\/\/www.statskingdom.com\/probability-calculator.html) | Probability formula, Dependent events, Bayes' Theorem, Independent events | P(A), P(A\\|B), P(A∩B), P(A∪B) |\n| [Combinations calculator](https:\/\/www.statskingdom.com\/combinations-calculator.html) | With\/Without Repetitions | ![Markov chain diagram](https:\/\/www.statskingdom.com\/images\/combinationsCalculator.svg) C r n \\= n \\! r \\! ( n − r ) \\! , C r n + r - 1 \\= n + r - 1 \\! r \\! ( n − 1 ) \\! |\n| [Permutation calculator](https:\/\/www.statskingdom.com\/permutations-calculator.html) | With\/Without Repetitions | ![Markov chain diagram](https:\/\/www.statskingdom.com\/images\/permutationsCalculator.svg) P r n \\= n \\! ( n − r ) \\! , nr |\n| [Correlation calculator](https:\/\/www.statskingdom.com\/correlation-calculator.html) | Pearson correlation, Spearman's rank correlation | r \\= ∑ i \\= 1 n ( x i − x ¯ ) ( y i − y ¯ ) ∑ i \\= 1 n ( x − x ¯ ) 2 ∑ i \\= 1 n ( y i − y ¯ ) 2 |\n| [Outliers](https:\/\/www.statskingdom.com\/outlier-calculator.html) | Tukey's Fences (Boxplot), Z-Score |   |\n| [Markov chain calculator](https:\/\/www.statskingdom.com\/markov-chain-calculator.html) | nth step probability vector, steady-state vector | ![Markov chain diagram](https:\/\/www.statskingdom.com\/images\/markov.svg) |\n| [Odds calculator](https:\/\/www.statskingdom.com\/odds-calculator.html) | Odds to probability, probability to odds | ![Odds calculator](https:\/\/www.statskingdom.com\/images\/odds.svg) |\n| [Betting odds calculator](https:\/\/www.statskingdom.com\/betting-odds-calculator.html) | Fractional odds, decimal odds, American odds | ![Odds calculator](https:\/\/www.statskingdom.com\/images\/betting-odds.svg) |\n| [Mean absolute deviation calculator](https:\/\/www.statskingdom.com\/mean-absolute-deviation-calculator.html) | MAD calculator | ![MAD diagram](https:\/\/www.statskingdom.com\/images\/mad.svg)μ |\n| [Median absolute deviation calculator](https:\/\/www.statskingdom.com\/Median-absolute-deviation-calculator.html) | MAD calculator | ![MAD diagram](https:\/\/www.statskingdom.com\/images\/mad.svg)Mdn |\n## Visualization\n| \\# | Chart | Image |\n|---|---|---|\n| 1 | [Principal component analysis](https:\/\/www.statskingdom.com\/pca-calculator.html) | ![Principal component analysis](https:\/\/www.statskingdom.com\/images\/i_pca.png) |\n| 2 | [Cluster analysis](https:\/\/www.statskingdom.com\/cluster-analysis.html) | ![Cluster analysis](https:\/\/www.statskingdom.com\/images\/i_cluster.png) |\n| 3 | [Histogram maker](https:\/\/www.statskingdom.com\/histogram-maker.html) | ![histogram](https:\/\/www.statskingdom.com\/images\/binomial_s.jpg) |\n| 4 | [Box plot maker](https:\/\/www.statskingdom.com\/boxplot-maker.html) | ![boxplot](https:\/\/www.statskingdom.com\/images\/i_boxplot.png) |\n| 5 | [Bar graph maker](https:\/\/www.statskingdom.com\/chart-maker.html) | ![bar graph](https:\/\/www.statskingdom.com\/images\/i_bar.png) |\n| 6 | [Pie chart maker](https:\/\/www.statskingdom.com\/pie-chart-maker.html) | ![pie chart](https:\/\/www.statskingdom.com\/images\/i_pie.png) |\n| 7 | [Line chart maker](https:\/\/www.statskingdom.com\/chart-maker.html) | ![line chart](https:\/\/www.statskingdom.com\/images\/i_line.png) |\n| 8 | [Scatter chart maker](https:\/\/www.statskingdom.com\/chart-maker.html) | ![scatter chart maker](https:\/\/www.statskingdom.com\/images\/i_scatter.png) |\n| 9 | [Area chart maker](https:\/\/www.statskingdom.com\/chart-maker.html) | ![area chart](https:\/\/www.statskingdom.com\/images\/i_area.png) |\n| 10 | [Violin plot maker](https:\/\/www.statskingdom.com\/violin-plot-maker.html) | ![violin plot](https:\/\/www.statskingdom.com\/images\/i_violin.png) |\n| 11 | [Venn diagram maker](https:\/\/www.statskingdom.com\/venn-diagram-maker.html) | ![Ven diagram](https:\/\/www.statskingdom.com\/images\/venn_two.png) |\n| 12 | [Venn diagram calculator](https:\/\/www.statskingdom.com\/venn-diagram-calculator.html) | 12 3 9 |\n| 13 | [Stem and Leaf plot](https:\/\/www.statskingdom.com\/stem-and-leaf.html) | ![Stem and Leaf plot maker](https:\/\/www.statskingdom.com\/images\/i_stem.png) |\n| 14 | [ROC Calculator](https:\/\/www.statskingdom.com\/roc-calculator.html) | ![roc curve](https:\/\/www.statskingdom.com\/images\/i_roc.png) |\n## Guide\n- [Guide](https:\/\/www.statskingdom.com\/information.html)\n- [Bonferroni correction](https:\/\/www.statskingdom.com\/doc_anova.html#bonferroni)\n- [Central Limit Theorem](https:\/\/www.statskingdom.com\/doc_clt.html)\n- [Confidence interval](https:\/\/www.statskingdom.com\/doc_confidence_interval.html)\n- [Linear regression](https:\/\/www.statskingdom.com\/doc_linear_regression.html)\n- [Logistic regression](https:\/\/www.statskingdom.com\/doc_logistic_regression.html)\n- [Outliers](https:\/\/www.statskingdom.com\/doc_outliers.html)\n- [P-value](https:\/\/www.statskingdom.com\/doc_pvalue.html)\n- [Skewness and kurtosis](https:\/\/www.statskingdom.com\/doc_skewness_kurtosis.html)\n- [Standard deviation](https:\/\/www.statskingdom.com\/doc_standard_deviation.html)\n- [Test power](https:\/\/www.statskingdom.com\/doc_test_power.html)\n### Exams\n[Free statistics exams with solution.](https:\/\/www.statskingdom.com\/statistics-exam.html)\n\n### Statistical Tests\n- [Chi-squared test](https:\/\/www.statskingdom.com\/doc_chi_squared.html)\n- [Levene's test](https:\/\/www.statskingdom.com\/doc_anova.html#levenes)\n- [Mann-Whitney U Rank test](https:\/\/www.statskingdom.com\/test_mann_whitney.html)\n- [One Way ANOVA test](https:\/\/www.statskingdom.com\/doc_anova.html)\n- [Proportion test](https:\/\/www.statskingdom.com\/doc_proportion_test.html)\n- [Shapiro Wilk test](https:\/\/www.statskingdom.com\/doc_shapiro_wilk.html)\n- [T-test](https:\/\/www.statskingdom.com\/t_test.html)\n- [T-test vs Z-Test](https:\/\/www.statskingdom.com\/doc_t_test_z_test.html)\n- [Tukey HSD test](https:\/\/www.statskingdom.com\/doc_anova.html#tukey)\n- [Wilcoxon Sign Rank test](https:\/\/www.statskingdom.com\/test_wilcoxon_signed_ranks.html)\n### Goal\nThe goal of this website is to make statistics accessible to anyone, converting complex statistical jargon into common everyday language.  \nWe help everybody to calculate statistics.  \nThe calculators also provide R codes for your convenience.  \nWe started adding a step-by-step work-through for education purposes, an easy guide on how to calculate test statistics.\n\n### [Terms](https:\/\/www.statskingdom.com\/terms.html)\nWe put in a lot of effort to provide accurate results and we automatically test every new page, The older pages were tested manually, but we slowly also automate the old pages.  \nWe usually compare the results to the R results.  \nThe information and tools on this website are given AS IS WITHOUT ANY WARRANTY OF ANY KIND.\n\n### Calculate statistics\nThe best online calculator to calculate statistics.","attrs_readable_markdown":"Statistical tests, charts, probabilities and clear results. Automatically checks assumptions, interprets results and outputs graphs, histograms and other charts.  \nThe statistics online calculators support not only the test statistic and the p-value but more results like effect size, test power, and the normality level.  \nIf one of the validations fails, the tool recommends a solution.  \nWhat statistical test should you use? the following link will help you choose: [**choose a statistical test**](https:\/\/www.statskingdom.com\/statistical-decision-tree.html) - decision questionnaire ([**Tutorial**](https:\/\/www.youtube.com\/embed\/QGZOBz_BXB4)).\n\n## Test statistic calculators\nFind the test statistic calculator\n\n| Test | Assumptions | Required sample data |   |   |   |   |   |   |   |   |   |   |   |\n|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n| \\# | Test name | Check | Statistic | ![Normal Distribution](https:\/\/www.statskingdom.com\/images\/Normal_trans.png) | Ind | σ | σ1\\=σ2 | d | μ\/p | x̄\/p̂; | n | S | ![data](https:\/\/www.statskingdom.com\/images\/data_icon2.png) |\n| 1 | [One Sample Z-Test](https:\/\/www.statskingdom.com\/110MeanNormal1.html) | Mean | z \\= x ¯ \\- μ 0 σ \/ n | ✔ | ✔ | ✔ |   |   | ✔ | ✔ | ✔ |   |   |\n| 2 | [One Sample T-Test](https:\/\/www.statskingdom.com\/130MeanT1.html) | Mean | t \\= x ¯ \\- μ 0 S \/ n | ✔ | ✔ | ✘ |   |   | ✔ | ✔ | ✔ | ✔ |   |\n| 3 | [Two Sample Z-Test](https:\/\/www.statskingdom.com\/120MeanNormal2.html) | Mean | z \\= x 1 \\- x 2 \\- d σ 2 n 1 \\+ σ 2 n 2 | ✔ | ✔ | ✔ |   | ✔ |   | ✔ | ✔ |   |   |\n| 4 | [Two Sample T-Test (Pooled variance)](https:\/\/www.statskingdom.com\/140MeanT2eq.html) | Mean | t \\= x ¯ 1 \\- x ¯ 2 \\- d s 1 n 1 \\+ 1 n 2 | ✔ | ✔ | ✘ | ✔ | ✔ |   | ✔ | ✔ | ✔ |   |\n| 5 | [Two Sample T-Test (Welch's)](https:\/\/www.statskingdom.com\/150MeanT2uneq.html) | Mean | t \\= x ¯ 1 \\- x ¯ 2 \\- d s 1 2 n 1 \\+ s 2 2 n 2 | ✔ | ✔ | ✘ | ✘ | ✔ |   | ✔ | ✔ | ✔ |   |\n| 6 | [Two Sample Mann-Whitney U Test](https:\/\/www.statskingdom.com\/170median_mann_whitney.html) | Rank | z \\= U \\- μ \\+ c σ |   | ✔ |   |   | ✔ |   |   |   |   | ✔ |\n| 7 | [Paired T-Test](https:\/\/www.statskingdom.com\/paired-t-test-calculator.html) | Mean | t \\= x ¯ d \\- μ 0 S d \/ n | ✔ | Paired |   |   |   |   |   |   |   | ✔ |\n| 8 | [Paired Wilcoxon Sign Rank Test](https:\/\/www.statskingdom.com\/175wilcoxon_signed_ranks.html) | Rank | z \\= W \\- μ \\+ c σ |   | Paired |   |   |   |   |   |   |   | ✔ |\n| 9 | [One Way ANOVA Test](https:\/\/www.statskingdom.com\/180Anova1way.html) | Mean | F \\= MS Between MS Within | ✔ | ✔ |   | ✔ |   |   |   |   |   | ✔ |\n| 10 | [Repeated Measures ANOVA Test](https:\/\/www.statskingdom.com\/repeated-anova-calculator.html) | Mean | F \\= MS Between MS Within | ✔ | Dependent groups |   | [Sphericity](https:\/\/www.statskingdom.com\/glossary.html#sp) |   |   |   |   |   | ✔ |\n| 11 | [Friedman Test](https:\/\/www.statskingdom.com\/friedman-calculator.html) | Mean | χ²(df) \\= 12 ∑ j \\= 1 k R j 2 \\- 3 n 2 k ( k \\+ 1 ) 2 n k ( k \\+ 1 ) \\- C t i e s |   | Dependent groups |   |   |   |   |   |   |   | ✔ |\n| 12 | [Kruskal-Wallis Test](https:\/\/www.statskingdom.com\/kruskal-wallis-calculator.html) | Mean | F \\= MS Between MS Within |   | ✔ |   |   |   |   |   |   |   | ✔ |\n| 13 | [Two Way ANOVA Test](https:\/\/www.statskingdom.com\/two-way-anova-calculator.html) Fixed model, Mixed model, Random mode, Mixed model with repeats | Mean | F \\= MS Between MS Within | ✔ | ✔ |   | ✔ |   |   |   |   |   | ✔ |\n| 14 | [One Way MANOVA Test](https:\/\/www.statskingdom.com\/manova-calculator.html) | Mean | F \\= V s \\- V . d f 2 d f 1 | ✔ | ✔ |   | ✔ |   |   |   |   |   | ✔ |\n| 15 | [One Sample Proportion Test](https:\/\/www.statskingdom.com\/111proportion_normal1.html) | Proportion | z \\= ( p ^ \\- p 0 ) \\+ c p 0 ( 1 \\- p 0 ) n or X~ B( n , p 0 ) | Binomial | ✔ |   |   |   | ✔ | ✔ | ✔ |   |   |\n| 16 | [Two Sample Proportion Test](https:\/\/www.statskingdom.com\/121proportion_normal2.html) | Proportion | z \\= p ^ 1 \\- p ^ 2 \\+ Cont p ^ ( 1 \\- p ^ ) ( 1 n 1 \\+ 1 n 2 ) | Binomial | ✔ |   |   |   |   | ✔ | ✔ |   |   |\n| 17 | [Chi-Squared Test For Variance](https:\/\/www.statskingdom.com\/210VarCHI1.html) | σ | χ 2 \\= ( n \\- 1 ) S 2 σ 0 2 | ✔ | ✔ |   |   |   |   |   | ✔ | ✔ |   |\n| 18 | [F Test For Variances](https:\/\/www.statskingdom.com\/220VarF2.html) | σ | F \\= S 1 2 S 2 2 | ✔ | ✔ |   |   |   |   |   | ✔ | ✔ |   |\n| 19 | [Levene's Test For Variances](https:\/\/www.statskingdom.com\/230var_levenes.html) | σ | F \\= MS Between MS Within | ✘ | ✔ |   |   |   |   |   |   |   | ✔ |\n| 20 | [Chi-Squared Test For Goodness Of Fit](https:\/\/www.statskingdom.com\/310GoodnessChi.html) McNemar test, Chi-squared test for association, Fisher test, Binomial test | Fit | χ 2 \\= ∑ i \\= 1 n ( o i \\- e i ) 2 e i |   | ✔ |   |   |   |   |   |   |   | ✔ |\n| 21 | [Shapiro-Wilk Test](https:\/\/www.statskingdom.com\/shapiro-wilk-test-calculator.html) | Fit | W \\= ( ∑ i \\= 1 ⌊ n \/ 2 ⌋ a i ( x n+1-i \\- x i ) ) 2 ∑ i \\= 1 n ( x i \\- x ¯ ) 2 | ✔ | ✔ |   |   |   |   |   |   |   | ✔ |\n| 22 | [Kolmogorov Smirnov Test](https:\/\/www.statskingdom.com\/kolmogorov-smirnov-test-calculator.html) | Fit | *D* = Max1≤i≤n(*D*i\\+,*D*i\\-) |   | ✔ |   |   |   |   |   |   |   | ✔ |\n| 23 | [Two-Sample Kolmogorov Smirnov Test](https:\/\/www.statskingdom.com\/kolmogorov-smirnov-two-calculator.html) | Fit | *D* = Max1≤i≤n(*D*i\\+,*D*i\\-) |   | ✔ |   |   |   |   |   |   |   | ✔ |\n| 24 | [Kaplan Meier Survival Analysis](https:\/\/www.statskingdom.com\/kaplan-meier.html) | Survival | χ 2 \\= ∑ i \\= 1 n ( o i \\- e i ) 2 e i |   | ✔ |   |   |   |   |   |   |   | ✔ |\n| 25 | [DeLong test - Independent curves](https:\/\/www.statskingdom.com\/roc-calculator.html) Compares the AUCs of two independent ROC curves | AUC | D \\= AUC 1 \\- AUC 2 Var 1 \\+ Var 1 |   | ✔ |   |   |   |   |   |   |   | ✔ |\n| 26 | [DeLong test - Paired curves](https:\/\/www.statskingdom.com\/roc-calculator.html) Compares the AUCs of two dependent ROC curves | AUC | Z \\= AUC 1 \\- AUC 2 Var ₁ \\+ Var ₂ \\- 2 \\* Cov ( AUC ₁ , AUC ₂ ) |   | Paired |   |   |   |   |   |   |   | ✔ |\n\n\\*\\* ✔ - Yes, ✘ - No, empty - irrelevant\n\n## Regression calculator\n| \\# | Regression | Statistic |\n|---|---|---|\n| 1 | [Simple Linear Regression](https:\/\/www.statskingdom.com\/linear-regression-calculator.html) | F \\= MS Regression MS Error |\n| 2 | [Multiple Linear Regression](https:\/\/www.statskingdom.com\/410multi_linear_regression.html) | F \\= MS Regression MS Error |\n| 3 | [\\*Bulk Linear Regression](https:\/\/www.statskingdom.com\/411list_linear_regression.html) | F \\= MS Regression MS Error |\n| 4 | [Binary Logistic Regression](https:\/\/www.statskingdom.com\/420logistic_regression.html) | χ2 = 2(LL1\\-LL0) |\n| 5 | [Multinomial Logistic Regression](https:\/\/www.statskingdom.com\/430logistic_regression.html) | χ2 = 2(LL1\\-LL0) |\n| 6 | [Propensity Score Matching](https:\/\/www.statskingdom.com\/psm-calculator.html) | ![Propensity Score Matching](https:\/\/www.statskingdom.com\/images\/psm.svg) |\n\n\\*Bulk linear regression calculator for several dependent variables with the same predictors.\n## Confidence interval, Sample size, Effect Size\n| \\# | Calculator | Image |\n|---|---|---|\n|   | [Sample size calculators](https:\/\/www.statskingdom.com\/sample_size_all.html) | ![sample size chart](https:\/\/www.statskingdom.com\/images\/sample_size.jpg) |\n|   | [Test power calculators](https:\/\/www.statskingdom.com\/statistical-power-calculators.html) | ![statistics power chart](https:\/\/www.statskingdom.com\/images\/small_t2_power2.jpg) |\n|   | [Effect size calculators](https:\/\/www.statskingdom.com\/effect-size-calculator.html) |   |\n|   | [Confidence intervals calculators](https:\/\/www.statskingdom.com\/confidence-interval-calculators.html) | ![statistics power chart](https:\/\/www.statskingdom.com\/images\/Normal1_t2_s.jpg) |\n## Distribution calculators\n| \\# | Distribution | Image |\n|---|---|---|\n|   | [P-value](https:\/\/www.statskingdom.com\/p_value.html) | ![p-value](https:\/\/www.statskingdom.com\/images\/p_value.jpg) |\n|   | [Distributions](https:\/\/www.statskingdom.com\/distribution-calculator.html) | ![Distribution Calculator](https:\/\/www.statskingdom.com\/images\/nrm_s.jpg) |\n|   | [Normal Distribution](https:\/\/www.statskingdom.com\/normal-distribution-calculator.html) | ![Normal Distribution](https:\/\/www.statskingdom.com\/images\/nrm_s.jpg) |\n|   | [Binomial Distribution](https:\/\/www.statskingdom.com\/binomial-distribution-calculator.html) | ![Binomial Distribution](https:\/\/www.statskingdom.com\/images\/binomial_s.jpg) |\n|   | [T Distribution (Student's)](https:\/\/www.statskingdom.com\/distribution-calculator.html) | ![T Distribution](https:\/\/www.statskingdom.com\/images\/t_s.jpg) |\n|   | [Chi-Squared Distribution](https:\/\/www.statskingdom.com\/distribution-calculator.html) | ![Chi squared Distribution](https:\/\/www.statskingdom.com\/images\/chi2_s.jpg) |\n|   | [F Distribution (Fisher-Snedecor)](https:\/\/www.statskingdom.com\/distribution-calculator.html) | ![F Distribution](https:\/\/www.statskingdom.com\/images\/f_s.jpg) |\n|   | [Poisson Distribution](https:\/\/www.statskingdom.com\/distribution-calculator.html) | ![Distribution](https:\/\/www.statskingdom.com\/images\/binomial_s.jpg) |\n|   | [Weibull Distribution](https:\/\/www.statskingdom.com\/distribution-calculator.html) |   |\n|   | [Exponential Distribution](https:\/\/www.statskingdom.com\/distribution-calculator.html) |   |\n## Statistical tables\n| \\# | Table |\n|---|---|\n| 1 | [Z table](https:\/\/www.statskingdom.com\/z_table.html) |\n| 2 | [T table](https:\/\/www.statskingdom.com\/t_table.html) |\n## Basic statistics calculators\nEach statistics calculator contains step by step calculation.\n\n| Calculator | Statistic calculator | Image |\n|---|---|---|\n| [Statistics calculator](https:\/\/www.statskingdom.com\/statistics-calculator.html) | The calculator computes statistics such as count, average and standard deviation for each combination of the categorical variables. | ![mean](https:\/\/www.statskingdom.com\/images\/statisticsCalc.svg) |\n| [Descriptive statistics calculator](https:\/\/www.statskingdom.com\/descriptive-statistics-calculator.html) | The calculator computes statistics such as count, average, and standard deviation for each variable. | ![mean](https:\/\/www.statskingdom.com\/images\/descriptive.svg) |\n| [Percentile calculator](https:\/\/www.statskingdom.com\/percentile-calculator.html) | A percentile tells you the percentage of values below a given value in a data set. For example, a value at the 75th percentile means that 75% of the data lies below that value. | ![percentile](https:\/\/www.statskingdom.com\/images\/percentile.svg) |\n| [Mean Median Mode calculator](https:\/\/www.statskingdom.com\/mean-median-mode-calculator.html) | Q1, Q3, IRQ, Range | ![mean](https:\/\/www.statskingdom.com\/images\/mean.svg) |\n| [Measures Of Dispersion calculator](https:\/\/www.statskingdom.com\/measures-of-dispersion-calculator.html) | Mean, sample size, APA style |   |\n| [Standard Deviation calculator](https:\/\/www.statskingdom.com\/standard-deviation-calculator.html) | Mean, sample size, APA style | S \\= ∑ i \\= 1 n ( x i \\- x̄ ) 2 n \\- 1 |\n| [Variance calculator](https:\/\/www.statskingdom.com\/variance-calculator.html) | Variance, Mean, SEM, MAD | S 2 \\= ∑ i \\= 1 n ( x i \\- x̄ ) 2 n \\- 1 |\n| [Coefficient of Variation calculator](https:\/\/www.statskingdom.com\/coefficient-of-variation-calculator.html) |   | CV \\= s x ¯ |\n| [Average calculator](https:\/\/www.statskingdom.com\/average-calculator.html) | Average, Sum, Count | x ¯ \\= x 1 \\+ x 2 \\+ ⋯ \\+ x n n |\n| [Sample Mean calculator](https:\/\/www.statskingdom.com\/sample-mean-calculator) | Sample mean, Sum, Count | x ¯ \\= x 1 \\+ x 2 \\+ ⋯ \\+ x n n |\n| [Geometric Mean calculator](https:\/\/www.statskingdom.com\/geometric-mean-calculator.html) | Product, n-th root | G M \\= x 1 x 2 … x n n |\n| [Harmonic Mean calculator](https:\/\/www.statskingdom.com\/harmonic-mean-calculator.html) | The harmonic mean is a type of average used for rates, for example average speed. It is found by dividing n by the sum of the reciprocals of the values. | H n \\= n 1 x 1 \\+ 1 x 2 \\+ ⋯ \\+ 1 x n |\n| [Probability calculator](https:\/\/www.statskingdom.com\/probability-calculator.html) | Probability formula, Dependent events, Bayes' Theorem, Independent events | P(A), P(A\\|B), P(A∩B), P(A∪B) |\n| [Combinations calculator](https:\/\/www.statskingdom.com\/combinations-calculator.html) | With\/Without Repetitions | ![Markov chain diagram](https:\/\/www.statskingdom.com\/images\/combinationsCalculator.svg) C r n \\= n \\! r \\! ( n − r ) \\! , C r n + r - 1 \\= n + r - 1 \\! r \\! ( n − 1 ) \\! |\n| [Permutation calculator](https:\/\/www.statskingdom.com\/permutations-calculator.html) | With\/Without Repetitions | ![Markov chain diagram](https:\/\/www.statskingdom.com\/images\/permutationsCalculator.svg) P r n \\= n \\! ( n − r ) \\! , nr |\n| [Correlation calculator](https:\/\/www.statskingdom.com\/correlation-calculator.html) | Pearson correlation, Spearman's rank correlation | r \\= ∑ i \\= 1 n ( x i − x ¯ ) ( y i − y ¯ ) ∑ i \\= 1 n ( x − x ¯ ) 2 ∑ i \\= 1 n ( y i − y ¯ ) 2 |\n| [Outliers](https:\/\/www.statskingdom.com\/outlier-calculator.html) | Tukey's Fences (Boxplot), Z-Score |   |\n| [Markov chain calculator](https:\/\/www.statskingdom.com\/markov-chain-calculator.html) | nth step probability vector, steady-state vector | ![Markov chain diagram](https:\/\/www.statskingdom.com\/images\/markov.svg) |\n| [Odds calculator](https:\/\/www.statskingdom.com\/odds-calculator.html) | Odds to probability, probability to odds | ![Odds calculator](https:\/\/www.statskingdom.com\/images\/odds.svg) |\n| [Betting odds calculator](https:\/\/www.statskingdom.com\/betting-odds-calculator.html) | Fractional odds, decimal odds, American odds | ![Odds calculator](https:\/\/www.statskingdom.com\/images\/betting-odds.svg) |\n| [Mean absolute deviation calculator](https:\/\/www.statskingdom.com\/mean-absolute-deviation-calculator.html) | MAD calculator | ![MAD diagram](https:\/\/www.statskingdom.com\/images\/mad.svg)μ |\n| [Median absolute deviation calculator](https:\/\/www.statskingdom.com\/Median-absolute-deviation-calculator.html) | MAD calculator | ![MAD diagram](https:\/\/www.statskingdom.com\/images\/mad.svg)Mdn |\n## Visualization\n| \\# | Chart | Image |\n|---|---|---|\n| 1 | [Principal component analysis](https:\/\/www.statskingdom.com\/pca-calculator.html) | ![Principal component analysis](https:\/\/www.statskingdom.com\/images\/i_pca.png) |\n| 2 | [Cluster analysis](https:\/\/www.statskingdom.com\/cluster-analysis.html) | ![Cluster analysis](https:\/\/www.statskingdom.com\/images\/i_cluster.png) |\n| 3 | [Histogram maker](https:\/\/www.statskingdom.com\/histogram-maker.html) | ![histogram](https:\/\/www.statskingdom.com\/images\/binomial_s.jpg) |\n| 4 | [Box plot maker](https:\/\/www.statskingdom.com\/boxplot-maker.html) | ![boxplot](https:\/\/www.statskingdom.com\/images\/i_boxplot.png) |\n| 5 | [Bar graph maker](https:\/\/www.statskingdom.com\/chart-maker.html) | ![bar graph](https:\/\/www.statskingdom.com\/images\/i_bar.png) |\n| 6 | [Pie chart maker](https:\/\/www.statskingdom.com\/pie-chart-maker.html) | ![pie chart](https:\/\/www.statskingdom.com\/images\/i_pie.png) |\n| 7 | [Line chart maker](https:\/\/www.statskingdom.com\/chart-maker.html) | ![line chart](https:\/\/www.statskingdom.com\/images\/i_line.png) |\n| 8 | [Scatter chart maker](https:\/\/www.statskingdom.com\/chart-maker.html) | ![scatter chart maker](https:\/\/www.statskingdom.com\/images\/i_scatter.png) |\n| 9 | [Area chart maker](https:\/\/www.statskingdom.com\/chart-maker.html) | ![area chart](https:\/\/www.statskingdom.com\/images\/i_area.png) |\n| 10 | [Violin plot maker](https:\/\/www.statskingdom.com\/violin-plot-maker.html) | ![violin plot](https:\/\/www.statskingdom.com\/images\/i_violin.png) |\n| 11 | [Venn diagram maker](https:\/\/www.statskingdom.com\/venn-diagram-maker.html) | ![Ven diagram](https:\/\/www.statskingdom.com\/images\/venn_two.png) |\n| 12 | [Venn diagram calculator](https:\/\/www.statskingdom.com\/venn-diagram-calculator.html) | 12 3 9 |\n| 13 | [Stem and Leaf plot](https:\/\/www.statskingdom.com\/stem-and-leaf.html) | ![Stem and Leaf plot maker](https:\/\/www.statskingdom.com\/images\/i_stem.png) |\n| 14 | [ROC Calculator](https:\/\/www.statskingdom.com\/roc-calculator.html) | ![roc curve](https:\/\/www.statskingdom.com\/images\/i_roc.png) |\n## Guide\n- [Guide](https:\/\/www.statskingdom.com\/information.html)\n- [Bonferroni correction](https:\/\/www.statskingdom.com\/doc_anova.html#bonferroni)\n- [Central Limit Theorem](https:\/\/www.statskingdom.com\/doc_clt.html)\n- [Confidence interval](https:\/\/www.statskingdom.com\/doc_confidence_interval.html)\n- [Linear regression](https:\/\/www.statskingdom.com\/doc_linear_regression.html)\n- [Logistic regression](https:\/\/www.statskingdom.com\/doc_logistic_regression.html)\n- [Outliers](https:\/\/www.statskingdom.com\/doc_outliers.html)\n- [P-value](https:\/\/www.statskingdom.com\/doc_pvalue.html)\n- [Skewness and kurtosis](https:\/\/www.statskingdom.com\/doc_skewness_kurtosis.html)\n- [Standard deviation](https:\/\/www.statskingdom.com\/doc_standard_deviation.html)\n- [Test power](https:\/\/www.statskingdom.com\/doc_test_power.html)\n### Exams\n[Free statistics exams with solution.](https:\/\/www.statskingdom.com\/statistics-exam.html)\n\n### Statistical Tests\n- [Chi-squared test](https:\/\/www.statskingdom.com\/doc_chi_squared.html)\n- [Levene's test](https:\/\/www.statskingdom.com\/doc_anova.html#levenes)\n- [Mann-Whitney U Rank test](https:\/\/www.statskingdom.com\/test_mann_whitney.html)\n- [One Way ANOVA test](https:\/\/www.statskingdom.com\/doc_anova.html)\n- [Proportion test](https:\/\/www.statskingdom.com\/doc_proportion_test.html)\n- [Shapiro Wilk test](https:\/\/www.statskingdom.com\/doc_shapiro_wilk.html)\n- [T-test](https:\/\/www.statskingdom.com\/t_test.html)\n- [T-test vs Z-Test](https:\/\/www.statskingdom.com\/doc_t_test_z_test.html)\n- [Tukey HSD test](https:\/\/www.statskingdom.com\/doc_anova.html#tukey)\n- [Wilcoxon Sign Rank test](https:\/\/www.statskingdom.com\/test_wilcoxon_signed_ranks.html)\n### Goal\nThe goal of this website is to make statistics accessible to anyone, converting complex statistical jargon into common everyday language.  \nWe help everybody to calculate statistics.  \nThe calculators also provide R codes for your convenience.  \nWe started adding a step-by-step work-through for education purposes, an easy guide on how to calculate test statistics.\n\n### [Terms](https:\/\/www.statskingdom.com\/terms.html)\nWe put in a lot of effort to provide accurate results and we automatically test every new page, The older pages were tested manually, but we slowly also automate the old pages.  \nWe usually compare the results to the R results.  \nThe information and tools on this website are given AS IS WITHOUT ANY WARRANTY OF ANY KIND.\n\n### Calculate statistics\nThe best online calculator to calculate statistics.","meta_canonical":null}

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Boilerpipe Text	Statistical tests, charts, probabilities and clear results. Automatically checks assumptions, interprets results and outputs graphs, histograms and other charts. The statistics online calculators support not only the test statistic and the p-value but more results like effect size, test power, and the normality level. If one of the validations fails, the tool recommends a solution. What statistical test should you use? the following link will help you choose: choose a statistical test - decision questionnaire ( Tutorial ). Test statistic calculators Find the test statistic calculator Test Assumptions Required sample data # Test name Check Statistic Ind σ σ 1 =σ 2 d μ/p x̄/p̂; n S 1 One Sample Z-Test Mean z = x ¯ - μ 0 σ / n ✔ ✔ ✔ ✔ ✔ ✔ 2 One Sample T-Test Mean t = x ¯ - μ 0 S / n ✔ ✔ ✘ ✔ ✔ ✔ ✔ 3 Two Sample Z-Test Mean z = x 1 - x 2 - d σ 2 n 1 + σ 2 n 2 ✔ ✔ ✔ ✔ ✔ ✔ 4 Two Sample T-Test (Pooled variance) Mean t = x ¯ 1 - x ¯ 2 - d s 1 n 1 + 1 n 2 ✔ ✔ ✘ ✔ ✔ ✔ ✔ ✔ 5 Two Sample T-Test (Welch's) Mean t = x ¯ 1 - x ¯ 2 - d s 1 2 n 1 + s 2 2 n 2 ✔ ✔ ✘ ✘ ✔ ✔ ✔ ✔ 6 Two Sample Mann-Whitney U Test Rank z = U - μ + c σ ✔ ✔ ✔ 7 Paired T-Test Mean t = x ¯ d - μ 0 S d / n ✔ Paired ✔ 8 Paired Wilcoxon Sign Rank Test Rank z = W - μ + c σ Paired ✔ 9 One Way ANOVA Test Mean F = MS Between MS Within ✔ ✔ ✔ ✔ 10 Repeated Measures ANOVA Test Mean F = MS Between MS Within ✔ Dependent groups Sphericity ✔ 11 Friedman Test Mean χ²(df) = 12 ∑ j = 1 k R j 2 - 3 n 2 k ( k + 1 ) 2 n k ( k + 1 ) - C t i e s Dependent groups ✔ 12 Kruskal-Wallis Test Mean F = MS Between MS Within ✔ ✔ 13 Two Way ANOVA Test Fixed model, Mixed model, Random mode, Mixed model with repeats Mean F = MS Between MS Within ✔ ✔ ✔ ✔ 14 One Way MANOVA Test Mean F = V s - V . d f 2 d f 1 ✔ ✔ ✔ ✔ 15 One Sample Proportion Test Proportion z = ( p ^ - p 0 ) + c p 0 ( 1 - p 0 ) n or X~ B( n , p 0 ) Binomial ✔ ✔ ✔ ✔ 16 Two Sample Proportion Test Proportion z = p ^ 1 - p ^ 2 + Cont p ^ ( 1 - p ^ ) ( 1 n 1 + 1 n 2 ) Binomial ✔ ✔ ✔ 17 Chi-Squared Test For Variance σ χ 2 = ( n - 1 ) S 2 σ 0 2 ✔ ✔ ✔ ✔ 18 F Test For Variances σ F = S 1 2 S 2 2 ✔ ✔ ✔ ✔ 19 Levene's Test For Variances σ F = MS Between MS Within ✘ ✔ ✔ 20 Chi-Squared Test For Goodness Of Fit McNemar test, Chi-squared test for association, Fisher test, Binomial test Fit χ 2 = ∑ i = 1 n ( o i - e i ) 2 e i ✔ ✔ 21 Shapiro-Wilk Test Fit W = ( ∑ i = 1 ⌊ n / 2 ⌋ a i ( x n+1-i - x i ) ) 2 ∑ i = 1 n ( x i - x ¯ ) 2 ✔ ✔ ✔ 22 Kolmogorov Smirnov Test Fit D = Max 1≤i≤n ( D i + , D i - ) ✔ ✔ 23 Two-Sample Kolmogorov Smirnov Test Fit D = Max 1≤i≤n ( D i + , D i - ) ✔ ✔ 24 Kaplan Meier Survival Analysis Survival χ 2 = ∑ i = 1 n ( o i - e i ) 2 e i ✔ ✔ 25 DeLong test - Independent curves Compares the AUCs of two independent ROC curves AUC D = AUC 1 - AUC 2 Var 1 + Var 1 ✔ ✔ 26 DeLong test - Paired curves Compares the AUCs of two dependent ROC curves AUC Z = AUC 1 - AUC 2 Var ₁ + Var ₂ - 2 * Cov ( AUC ₁ , AUC ₂ ) Paired ✔ ** ✔ - Yes, ✘ - No, empty - irrelevant Regression calculator # Regression Statistic 1 Simple Linear Regression F = MS Regression MS Error 2 Multiple Linear Regression F = MS Regression MS Error 3 Bulk Linear Regression F = MS Regression MS Error 4 Binary Logistic Regression χ2 = 2(LL 1 -LL 0 ) 5 Multinomial Logistic Regression χ2 = 2(LL 1 -LL 0 ) 6 Propensity Score Matching Bulk linear regression calculator for several dependent variables with the same predictors. Confidence interval, Sample size, Effect Size # Calculator Image Sample size calculators Test power calculators Effect size calculators Confidence intervals calculators Distribution calculators # Distribution Image P-value Distributions Normal Distribution Binomial Distribution T Distribution (Student's) Chi-Squared Distribution F Distribution (Fisher-Snedecor) Poisson Distribution Weibull Distribution Exponential Distribution Statistical tables # Table 1 Z table 2 T table Basic statistics calculators Each statistics calculator contains step by step calculation. Calculator Statistic calculator Image Statistics calculator The calculator computes statistics such as count, average and standard deviation for each combination of the categorical variables . Descriptive statistics calculator The calculator computes statistics such as count, average, and standard deviation for each variable . Percentile calculator A percentile tells you the percentage of values below a given value in a data set. For example, a value at the 75th percentile means that 75% of the data lies below that value. Mean Median Mode calculator Q 1 , Q 3 , IRQ, Range Measures Of Dispersion calculator Mean, sample size, APA style Standard Deviation calculator Mean, sample size, APA style S = ∑ i = 1 n ( x i - x̄ ) 2 n - 1 Variance calculator Variance, Mean, SEM, MAD S 2 = ∑ i = 1 n ( x i - x̄ ) 2 n - 1 Coefficient of Variation calculator CV = s x ¯ Average calculator Average, Sum, Count x ¯ = x 1 + x 2 + ⋯ + x n n Sample Mean calculator Sample mean, Sum, Count x ¯ = x 1 + x 2 + ⋯ + x n n Geometric Mean calculator Product, n-th root G M = x 1 x 2 … x n n Harmonic Mean calculator The harmonic mean is a type of average used for rates, for example average speed. It is found by dividing n by the sum of the reciprocals of the values. H n = n 1 x 1 + 1 x 2 + ⋯ + 1 x n Probability calculator Probability formula, Dependent events, Bayes' Theorem, Independent events P(A), P(A\|B), P(A∩B), P(A∪B) Combinations calculator With/Without Repetitions C r n = n ! r ! ( n − r ) ! , C r n + r - 1 = n + r - 1 ! r ! ( n − 1 ) ! Permutation calculator With/Without Repetitions P r n = n ! ( n − r ) ! , n r Correlation calculator Pearson correlation, Spearman's rank correlation r = ∑ i = 1 n ( x i − x ¯ ) ( y i − y ¯ ) ∑ i = 1 n ( x − x ¯ ) 2 ∑ i = 1 n ( y i − y ¯ ) 2 Outliers Tukey's Fences (Boxplot), Z-Score Markov chain calculator nth step probability vector, steady-state vector Odds calculator Odds to probability, probability to odds Betting odds calculator Fractional odds, decimal odds, American odds Mean absolute deviation calculator MAD calculator μ Median absolute deviation calculator MAD calculator Mdn Visualization # Chart Image 1 Principal component analysis 2 Cluster analysis 3 Histogram maker 4 Box plot maker 5 Bar graph maker 6 Pie chart maker 7 Line chart maker 8 Scatter chart maker 9 Area chart maker 10 Violin plot maker 11 Venn diagram maker 12 Venn diagram calculator Venn diagram calculator 12 3 9 13 Stem and Leaf plot 14 ROC Calculator Guide Guide Bonferroni correction Central Limit Theorem Confidence interval Linear regression Logistic regression Outliers P-value Skewness and kurtosis Standard deviation Test power Exams Free statistics exams with solution. Statistical Tests Chi-squared test Levene's test Mann-Whitney U Rank test One Way ANOVA test Proportion test Shapiro Wilk test T-test T-test vs Z-Test Tukey HSD test Wilcoxon Sign Rank test Goal The goal of this website is to make statistics accessible to anyone, converting complex statistical jargon into common everyday language. We help everybody to calculate statistics. The calculators also provide R codes for your convenience. We started adding a step-by-step work-through for education purposes, an easy guide on how to calculate test statistics. Terms We put in a lot of effort to provide accurate results and we automatically test every new page, The older pages were tested manually, but we slowly also automate the old pages. We usually compare the results to the R results. The information and tools on this website are given AS IS WITHOUT ANY WARRANTY OF ANY KIND. Calculate statistics The best online calculator to calculate statistics.
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[Mean Tests](https://www.statskingdom.com/)[Mean Calculator](https://www.statskingdom.com/sample-mean-calculator.html)[One Sample Z-test](https://www.statskingdom.com/110MeanNormal1.html)[One Sample Proportion Z-test](https://www.statskingdom.com/111proportion_normal1.html)[One Sample T-Test](https://www.statskingdom.com/130MeanT1.html)[Two Sample Z-test](https://www.statskingdom.com/120MeanNormal2.html)[Two Sample Proportions Z-test](https://www.statskingdom.com/121proportion_normal2.html)[Two Sample T-test (Pooled-Variance)](https://www.statskingdom.com/140MeanT2eq.html)[Two Sample T-test (Welch's)](https://www.statskingdom.com/150MeanT2uneq.html)[Two Sample Mann–Whitney U test](https://www.statskingdom.com/170median_mann_whitney.html)[Paired T-test](https://www.statskingdom.com/paired-t-test-calculator.html)[Wilcoxon Signed Rank test](https://www.statskingdom.com/175wilcoxon_signed_ranks.html) - [M/ANOVA](https://www.statskingdom.com/)[One Way ANOVA test](https://www.statskingdom.com/180Anova1way.html)[Kruskal-Wallis Test](https://www.statskingdom.com/kruskal-wallis-calculator.html)[Two Way ANOVA - Unbalanced](https://www.statskingdom.com/unbalanced-two-way-anova.html)[Two Way ANOVA - Balanced](https://www.statskingdom.com/two-way-anova-calculator.html)[Repeated Measures ANOVA](https://www.statskingdom.com/repeated-anova-calculator.html)[Friedman test](https://www.statskingdom.com/friedman-calculator.html)[One Way MANOVA test](https://www.statskingdom.com/manova-calculator.html) - [Variance Tests](https://www.statskingdom.com/)[χ2 Test for Variance](https://www.statskingdom.com/210VarCHI1.html)[F Test for Variances](https://www.statskingdom.com/220VarF2.html)[Levene's Equality of Variances](https://www.statskingdom.com/230var_levenes.html) - [Regression](https://www.statskingdom.com/)[Simple Linear Regression](https://www.statskingdom.com/linear-regression-calculator.html)[Multiple Linear Regression](https://www.statskingdom.com/410multi_linear_regression.html)[Binary Logistic Regression](https://www.statskingdom.com/420logistic_regression.html)[Multinomial Logistic Regression](https://www.statskingdom.com/430logistic_regression.html)[One Sample Correlation Test](https://www.statskingdom.com/correlation-calculator.html)[Propensity Score Matching](https://www.statskingdom.com/psm-calculator.html)[Neural Network](https://www.statskingdom.com/neural-network.html) - [Visualization](https://www.statskingdom.com/)[Histogram](https://www.statskingdom.com/histogram-maker.html)[Box plot](https://www.statskingdom.com/boxplot-maker.html)[Violin Plot](https://www.statskingdom.com/violin-plot-maker.html)[Cluster Analysis](https://www.statskingdom.com/cluster-analysis.html)[Charts](https://www.statskingdom.com/chart-maker.html)[Bar Chart](https://www.statskingdom.com/bar-chart-maker.html)[Pie Chart](https://www.statskingdom.com/pie-chart-maker.html)[Scatter Chart](https://www.statskingdom.com/scatter-chart-maker.html)[Line Chart](https://www.statskingdom.com/line-chart-maker.html)[Area Chart](https://www.statskingdom.com/area-chart-maker.html)[PCA](https://www.statskingdom.com/pca-calculator.html)[Venn Maker](https://www.statskingdom.com/venn-diagram-maker.html)[Venn Calculator](https://www.statskingdom.com/venn-diagram-calculator.html)[Stem and Leaf](https://www.statskingdom.com/stem-and-leaf.html)[ROC curve](https://www.statskingdom.com/roc-calculator.html)[Palettes](https://www.statskingdom.com/palettes.html) # Statistics online Statistical tests, charts, probabilities and clear results. Automatically checks assumptions, interprets results and outputs graphs, histograms and other charts. The statistics online calculators support not only the test statistic and the p-value but more results like effect size, test power, and the normality level. If one of the validations fails, the tool recommends a solution. What statistical test should you use? the following link will help you choose: [choose a statistical test](https://www.statskingdom.com/statistical-decision-tree.html) - decision questionnaire ([Tutorial](https://www.youtube.com/embed/QGZOBz_BXB4)). ## Test statistic calculators Find the test statistic calculator \| Test \| Assumptions \| Required sample data \| \| \| \| \| \| \| \| \| \| \| \| \|---\|---\|---\|---\|---\|---\|---\|---\|---\|---\|---\|---\|---\|---\| \| \# \| Test name \| Check \| Statistic \| ![Normal Distribution](https://www.statskingdom.com/images/Normal_trans.png) \| Ind \| σ \| σ1\=σ2 \| d \| μ/p \| x̄/p̂; \| n \| S \| ![data](https://www.statskingdom.com/images/data_icon2.png) \| \| 1 \| [One Sample Z-Test](https://www.statskingdom.com/110MeanNormal1.html) \| Mean \| z \= x ¯ \- μ 0 σ / n \| ✔ \| ✔ \| ✔ \| \| \| ✔ \| ✔ \| ✔ \| \| \| \| 2 \| [One Sample T-Test](https://www.statskingdom.com/130MeanT1.html) \| Mean \| t \= x ¯ \- μ 0 S / n \| ✔ \| ✔ \| ✘ \| \| \| ✔ \| ✔ \| ✔ \| ✔ \| \| \| 3 \| [Two Sample Z-Test](https://www.statskingdom.com/120MeanNormal2.html) \| Mean \| z \= x 1 \- x 2 \- d σ 2 n 1 \+ σ 2 n 2 \| ✔ \| ✔ \| ✔ \| \| ✔ \| \| ✔ \| ✔ \| \| \| \| 4 \| [Two Sample T-Test (Pooled variance)](https://www.statskingdom.com/140MeanT2eq.html) \| Mean \| t \= x ¯ 1 \- x ¯ 2 \- d s 1 n 1 \+ 1 n 2 \| ✔ \| ✔ \| ✘ \| ✔ \| ✔ \| \| ✔ \| ✔ \| ✔ \| \| \| 5 \| [Two Sample T-Test (Welch's)](https://www.statskingdom.com/150MeanT2uneq.html) \| Mean \| t \= x ¯ 1 \- x ¯ 2 \- d s 1 2 n 1 \+ s 2 2 n 2 \| ✔ \| ✔ \| ✘ \| ✘ \| ✔ \| \| ✔ \| ✔ \| ✔ \| \| \| 6 \| [Two Sample Mann-Whitney U Test](https://www.statskingdom.com/170median_mann_whitney.html) \| Rank \| z \= U \- μ \+ c σ \| \| ✔ \| \| \| ✔ \| \| \| \| \| ✔ \| \| 7 \| [Paired T-Test](https://www.statskingdom.com/paired-t-test-calculator.html) \| Mean \| t \= x ¯ d \- μ 0 S d / n \| ✔ \| Paired \| \| \| \| \| \| \| \| ✔ \| \| 8 \| [Paired Wilcoxon Sign Rank Test](https://www.statskingdom.com/175wilcoxon_signed_ranks.html) \| Rank \| z \= W \- μ \+ c σ \| \| Paired \| \| \| \| \| \| \| \| ✔ \| \| 9 \| [One Way ANOVA Test](https://www.statskingdom.com/180Anova1way.html) \| Mean \| F \= MS Between MS Within \| ✔ \| ✔ \| \| ✔ \| \| \| \| \| \| ✔ \| \| 10 \| [Repeated Measures ANOVA Test](https://www.statskingdom.com/repeated-anova-calculator.html) \| Mean \| F \= MS Between MS Within \| ✔ \| Dependent groups \| \| [Sphericity](https://www.statskingdom.com/glossary.html#sp) \| \| \| \| \| \| ✔ \| \| 11 \| [Friedman Test](https://www.statskingdom.com/friedman-calculator.html) \| Mean \| χ²(df) \= 12 ∑ j \= 1 k R j 2 \- 3 n 2 k ( k \+ 1 ) 2 n k ( k \+ 1 ) \- C t i e s \| \| Dependent groups \| \| \| \| \| \| \| \| ✔ \| \| 12 \| [Kruskal-Wallis Test](https://www.statskingdom.com/kruskal-wallis-calculator.html) \| Mean \| F \= MS Between MS Within \| \| ✔ \| \| \| \| \| \| \| \| ✔ \| \| 13 \| [Two Way ANOVA Test](https://www.statskingdom.com/two-way-anova-calculator.html) Fixed model, Mixed model, Random mode, Mixed model with repeats \| Mean \| F \= MS Between MS Within \| ✔ \| ✔ \| \| ✔ \| \| \| \| \| \| ✔ \| \| 14 \| [One Way MANOVA Test](https://www.statskingdom.com/manova-calculator.html) \| Mean \| F \= V s \- V . d f 2 d f 1 \| ✔ \| ✔ \| \| ✔ \| \| \| \| \| \| ✔ \| \| 15 \| [One Sample Proportion Test](https://www.statskingdom.com/111proportion_normal1.html) \| Proportion \| z \= ( p ^ \- p 0 ) \+ c p 0 ( 1 \- p 0 ) n or X~ B( n , p 0 ) \| Binomial \| ✔ \| \| \| \| ✔ \| ✔ \| ✔ \| \| \| \| 16 \| [Two Sample Proportion Test](https://www.statskingdom.com/121proportion_normal2.html) \| Proportion \| z \= p ^ 1 \- p ^ 2 \+ Cont p ^ ( 1 \- p ^ ) ( 1 n 1 \+ 1 n 2 ) \| Binomial \| ✔ \| \| \| \| \| ✔ \| ✔ \| \| \| \| 17 \| [Chi-Squared Test For Variance](https://www.statskingdom.com/210VarCHI1.html) \| σ \| χ 2 \= ( n \- 1 ) S 2 σ 0 2 \| ✔ \| ✔ \| \| \| \| \| \| ✔ \| ✔ \| \| \| 18 \| [F Test For Variances](https://www.statskingdom.com/220VarF2.html) \| σ \| F \= S 1 2 S 2 2 \| ✔ \| ✔ \| \| \| \| \| \| ✔ \| ✔ \| \| \| 19 \| [Levene's Test For Variances](https://www.statskingdom.com/230var_levenes.html) \| σ \| F \= MS Between MS Within \| ✘ \| ✔ \| \| \| \| \| \| \| \| ✔ \| \| 20 \| [Chi-Squared Test For Goodness Of Fit](https://www.statskingdom.com/310GoodnessChi.html) McNemar test, Chi-squared test for association, Fisher test, Binomial test \| Fit \| χ 2 \= ∑ i \= 1 n ( o i \- e i ) 2 e i \| \| ✔ \| \| \| \| \| \| \| \| ✔ \| \| 21 \| [Shapiro-Wilk Test](https://www.statskingdom.com/shapiro-wilk-test-calculator.html) \| Fit \| W \= ( ∑ i \= 1 ⌊ n / 2 ⌋ a i ( x n+1-i \- x i ) ) 2 ∑ i \= 1 n ( x i \- x ¯ ) 2 \| ✔ \| ✔ \| \| \| \| \| \| \| \| ✔ \| \| 22 \| [Kolmogorov Smirnov Test](https://www.statskingdom.com/kolmogorov-smirnov-test-calculator.html) \| Fit \| D = Max1≤i≤n(Di\+,Di\-) \| \| ✔ \| \| \| \| \| \| \| \| ✔ \| \| 23 \| [Two-Sample Kolmogorov Smirnov Test](https://www.statskingdom.com/kolmogorov-smirnov-two-calculator.html) \| Fit \| D = Max1≤i≤n(Di\+,Di\-) \| \| ✔ \| \| \| \| \| \| \| \| ✔ \| \| 24 \| [Kaplan Meier Survival Analysis](https://www.statskingdom.com/kaplan-meier.html) \| Survival \| χ 2 \= ∑ i \= 1 n ( o i \- e i ) 2 e i \| \| ✔ \| \| \| \| \| \| \| \| ✔ \| \| 25 \| [DeLong test - Independent curves](https://www.statskingdom.com/roc-calculator.html) Compares the AUCs of two independent ROC curves \| AUC \| D \= AUC 1 \- AUC 2 Var 1 \+ Var 1 \| \| ✔ \| \| \| \| \| \| \| \| ✔ \| \| 26 \| [DeLong test - Paired curves](https://www.statskingdom.com/roc-calculator.html) Compares the AUCs of two dependent ROC curves \| AUC \| Z \= AUC 1 \- AUC 2 Var ₁ \+ Var ₂ \- 2 \* Cov ( AUC ₁ , AUC ₂ ) \| \| Paired \| \| \| \| \| \| \| \| ✔ \| \\ ✔ - Yes, ✘ - No, empty - irrelevant ## Regression calculator \| \# \| Regression \| Statistic \| \|---\|---\|---\| \| 1 \| [Simple Linear Regression](https://www.statskingdom.com/linear-regression-calculator.html) \| F \= MS Regression MS Error \| \| 2 \| [Multiple Linear Regression](https://www.statskingdom.com/410multi_linear_regression.html) \| F \= MS Regression MS Error \| \| 3 \| [\Bulk Linear Regression](https://www.statskingdom.com/411list_linear_regression.html) \| F \= MS Regression MS Error \| \| 4 \| [Binary Logistic Regression](https://www.statskingdom.com/420logistic_regression.html) \| χ2 = 2(LL1\-LL0) \| \| 5 \| [Multinomial Logistic Regression](https://www.statskingdom.com/430logistic_regression.html) \| χ2 = 2(LL1\-LL0) \| \| 6 \| [Propensity Score Matching](https://www.statskingdom.com/psm-calculator.html) \| ![Propensity Score Matching](https://www.statskingdom.com/images/psm.svg) \| \Bulk linear regression calculator for several dependent variables with the same predictors. ## Confidence interval, Sample size, Effect Size \| \# \| Calculator \| Image \| \|---\|---\|---\| \| \| [Sample size calculators](https://www.statskingdom.com/sample_size_all.html) \| ![sample size chart](https://www.statskingdom.com/images/sample_size.jpg) \| \| \| [Test power calculators](https://www.statskingdom.com/statistical-power-calculators.html) \| ![statistics power chart](https://www.statskingdom.com/images/small_t2_power2.jpg) \| \| \| [Effect size calculators](https://www.statskingdom.com/effect-size-calculator.html) \| \| \| \| [Confidence intervals calculators](https://www.statskingdom.com/confidence-interval-calculators.html) \| ![statistics power chart](https://www.statskingdom.com/images/Normal1_t2_s.jpg) \| ## Distribution calculators \| \# \| Distribution \| Image \| \|---\|---\|---\| \| \| [P-value](https://www.statskingdom.com/p_value.html) \| ![p-value](https://www.statskingdom.com/images/p_value.jpg) \| \| \| [Distributions](https://www.statskingdom.com/distribution-calculator.html) \| ![Distribution Calculator](https://www.statskingdom.com/images/nrm_s.jpg) \| \| \| [Normal Distribution](https://www.statskingdom.com/normal-distribution-calculator.html) \| ![Normal Distribution](https://www.statskingdom.com/images/nrm_s.jpg) \| \| \| [Binomial Distribution](https://www.statskingdom.com/binomial-distribution-calculator.html) \| ![Binomial Distribution](https://www.statskingdom.com/images/binomial_s.jpg) \| \| \| [T Distribution (Student's)](https://www.statskingdom.com/distribution-calculator.html) \| ![T Distribution](https://www.statskingdom.com/images/t_s.jpg) \| \| \| [Chi-Squared Distribution](https://www.statskingdom.com/distribution-calculator.html) \| ![Chi squared Distribution](https://www.statskingdom.com/images/chi2_s.jpg) \| \| \| [F Distribution (Fisher-Snedecor)](https://www.statskingdom.com/distribution-calculator.html) \| ![F Distribution](https://www.statskingdom.com/images/f_s.jpg) \| \| \| [Poisson Distribution](https://www.statskingdom.com/distribution-calculator.html) \| ![Distribution](https://www.statskingdom.com/images/binomial_s.jpg) \| \| \| [Weibull Distribution](https://www.statskingdom.com/distribution-calculator.html) \| \| \| \| [Exponential Distribution](https://www.statskingdom.com/distribution-calculator.html) \| \| ## Statistical tables \| \# \| Table \| \|---\|---\| \| 1 \| [Z table](https://www.statskingdom.com/z_table.html) \| \| 2 \| [T table](https://www.statskingdom.com/t_table.html) \| ## Basic statistics calculators Each statistics calculator contains step by step calculation. \| Calculator \| Statistic calculator \| Image \| \|---\|---\|---\| \| [Statistics calculator](https://www.statskingdom.com/statistics-calculator.html) \| The calculator computes statistics such as count, average and standard deviation for each combination of the categorical variables. \| ![mean](https://www.statskingdom.com/images/statisticsCalc.svg) \| \| [Descriptive statistics calculator](https://www.statskingdom.com/descriptive-statistics-calculator.html) \| The calculator computes statistics such as count, average, and standard deviation for each variable. \| ![mean](https://www.statskingdom.com/images/descriptive.svg) \| \| [Percentile calculator](https://www.statskingdom.com/percentile-calculator.html) \| A percentile tells you the percentage of values below a given value in a data set. For example, a value at the 75th percentile means that 75% of the data lies below that value. \| ![percentile](https://www.statskingdom.com/images/percentile.svg) \| \| [Mean Median Mode calculator](https://www.statskingdom.com/mean-median-mode-calculator.html) \| Q1, Q3, IRQ, Range \| ![mean](https://www.statskingdom.com/images/mean.svg) \| \| [Measures Of Dispersion calculator](https://www.statskingdom.com/measures-of-dispersion-calculator.html) \| Mean, sample size, APA style \| \| \| [Standard Deviation calculator](https://www.statskingdom.com/standard-deviation-calculator.html) \| Mean, sample size, APA style \| S \= ∑ i \= 1 n ( x i \- x̄ ) 2 n \- 1 \| \| [Variance calculator](https://www.statskingdom.com/variance-calculator.html) \| Variance, Mean, SEM, MAD \| S 2 \= ∑ i \= 1 n ( x i \- x̄ ) 2 n \- 1 \| \| [Coefficient of Variation calculator](https://www.statskingdom.com/coefficient-of-variation-calculator.html) \| \| CV \= s x ¯ \| \| [Average calculator](https://www.statskingdom.com/average-calculator.html) \| Average, Sum, Count \| x ¯ \= x 1 \+ x 2 \+ ⋯ \+ x n n \| \| [Sample Mean calculator](https://www.statskingdom.com/sample-mean-calculator) \| Sample mean, Sum, Count \| x ¯ \= x 1 \+ x 2 \+ ⋯ \+ x n n \| \| [Geometric Mean calculator](https://www.statskingdom.com/geometric-mean-calculator.html) \| Product, n-th root \| G M \= x 1 x 2 … x n n \| \| [Harmonic Mean calculator](https://www.statskingdom.com/harmonic-mean-calculator.html) \| The harmonic mean is a type of average used for rates, for example average speed. It is found by dividing n by the sum of the reciprocals of the values. \| H n \= n 1 x 1 \+ 1 x 2 \+ ⋯ \+ 1 x n \| \| [Probability calculator](https://www.statskingdom.com/probability-calculator.html) \| Probability formula, Dependent events, Bayes' Theorem, Independent events \| P(A), P(A\\|B), P(A∩B), P(A∪B) \| \| [Combinations calculator](https://www.statskingdom.com/combinations-calculator.html) \| With/Without Repetitions \| ![Markov chain diagram](https://www.statskingdom.com/images/combinationsCalculator.svg) C r n \= n \! r \! ( n − r ) \! , C r n + r - 1 \= n + r - 1 \! r \! ( n − 1 ) \! \| \| [Permutation calculator](https://www.statskingdom.com/permutations-calculator.html) \| With/Without Repetitions \| ![Markov chain diagram](https://www.statskingdom.com/images/permutationsCalculator.svg) P r n \= n \! ( n − r ) \! , nr \| \| [Correlation calculator](https://www.statskingdom.com/correlation-calculator.html) \| Pearson correlation, Spearman's rank correlation \| r \= ∑ i \= 1 n ( x i − x ¯ ) ( y i − y ¯ ) ∑ i \= 1 n ( x − x ¯ ) 2 ∑ i \= 1 n ( y i − y ¯ ) 2 \| \| [Outliers](https://www.statskingdom.com/outlier-calculator.html) \| Tukey's Fences (Boxplot), Z-Score \| \| \| [Markov chain calculator](https://www.statskingdom.com/markov-chain-calculator.html) \| nth step probability vector, steady-state vector \| ![Markov chain diagram](https://www.statskingdom.com/images/markov.svg) \| \| [Odds calculator](https://www.statskingdom.com/odds-calculator.html) \| Odds to probability, probability to odds \| ![Odds calculator](https://www.statskingdom.com/images/odds.svg) \| \| [Betting odds calculator](https://www.statskingdom.com/betting-odds-calculator.html) \| Fractional odds, decimal odds, American odds \| ![Odds calculator](https://www.statskingdom.com/images/betting-odds.svg) \| \| [Mean absolute deviation calculator](https://www.statskingdom.com/mean-absolute-deviation-calculator.html) \| MAD calculator \| ![MAD diagram](https://www.statskingdom.com/images/mad.svg)μ \| \| [Median absolute deviation calculator](https://www.statskingdom.com/Median-absolute-deviation-calculator.html) \| MAD calculator \| ![MAD diagram](https://www.statskingdom.com/images/mad.svg)Mdn \| ## Visualization \| \# \| Chart \| Image \| \|---\|---\|---\| \| 1 \| [Principal component analysis](https://www.statskingdom.com/pca-calculator.html) \| ![Principal component analysis](https://www.statskingdom.com/images/i_pca.png) \| \| 2 \| [Cluster analysis](https://www.statskingdom.com/cluster-analysis.html) \| ![Cluster analysis](https://www.statskingdom.com/images/i_cluster.png) \| \| 3 \| [Histogram maker](https://www.statskingdom.com/histogram-maker.html) \| ![histogram](https://www.statskingdom.com/images/binomial_s.jpg) \| \| 4 \| [Box plot maker](https://www.statskingdom.com/boxplot-maker.html) \| ![boxplot](https://www.statskingdom.com/images/i_boxplot.png) \| \| 5 \| [Bar graph maker](https://www.statskingdom.com/chart-maker.html) \| ![bar graph](https://www.statskingdom.com/images/i_bar.png) \| \| 6 \| [Pie chart maker](https://www.statskingdom.com/pie-chart-maker.html) \| ![pie chart](https://www.statskingdom.com/images/i_pie.png) \| \| 7 \| [Line chart maker](https://www.statskingdom.com/chart-maker.html) \| ![line chart](https://www.statskingdom.com/images/i_line.png) \| \| 8 \| [Scatter chart maker](https://www.statskingdom.com/chart-maker.html) \| ![scatter chart maker](https://www.statskingdom.com/images/i_scatter.png) \| \| 9 \| [Area chart maker](https://www.statskingdom.com/chart-maker.html) \| ![area chart](https://www.statskingdom.com/images/i_area.png) \| \| 10 \| [Violin plot maker](https://www.statskingdom.com/violin-plot-maker.html) \| ![violin plot](https://www.statskingdom.com/images/i_violin.png) \| \| 11 \| [Venn diagram maker](https://www.statskingdom.com/venn-diagram-maker.html) \| ![Ven diagram](https://www.statskingdom.com/images/venn_two.png) \| \| 12 \| [Venn diagram calculator](https://www.statskingdom.com/venn-diagram-calculator.html) \| 12 3 9 \| \| 13 \| [Stem and Leaf plot](https://www.statskingdom.com/stem-and-leaf.html) \| ![Stem and Leaf plot maker](https://www.statskingdom.com/images/i_stem.png) \| \| 14 \| [ROC Calculator](https://www.statskingdom.com/roc-calculator.html) \| ![roc curve](https://www.statskingdom.com/images/i_roc.png) \| ## Guide - [Guide](https://www.statskingdom.com/information.html) - [Bonferroni correction](https://www.statskingdom.com/doc_anova.html#bonferroni) - [Central Limit Theorem](https://www.statskingdom.com/doc_clt.html) - [Confidence interval](https://www.statskingdom.com/doc_confidence_interval.html) - [Linear regression](https://www.statskingdom.com/doc_linear_regression.html) - [Logistic regression](https://www.statskingdom.com/doc_logistic_regression.html) - [Outliers](https://www.statskingdom.com/doc_outliers.html) - [P-value](https://www.statskingdom.com/doc_pvalue.html) - [Skewness and kurtosis](https://www.statskingdom.com/doc_skewness_kurtosis.html) - [Standard deviation](https://www.statskingdom.com/doc_standard_deviation.html) - [Test power](https://www.statskingdom.com/doc_test_power.html) ### Exams [Free statistics exams with solution.](https://www.statskingdom.com/statistics-exam.html) ### Statistical Tests - [Chi-squared test](https://www.statskingdom.com/doc_chi_squared.html) - [Levene's test](https://www.statskingdom.com/doc_anova.html#levenes) - [Mann-Whitney U Rank test](https://www.statskingdom.com/test_mann_whitney.html) - [One Way ANOVA test](https://www.statskingdom.com/doc_anova.html) - [Proportion test](https://www.statskingdom.com/doc_proportion_test.html) - [Shapiro Wilk test](https://www.statskingdom.com/doc_shapiro_wilk.html) - [T-test](https://www.statskingdom.com/t_test.html) - [T-test vs Z-Test](https://www.statskingdom.com/doc_t_test_z_test.html) - [Tukey HSD test](https://www.statskingdom.com/doc_anova.html#tukey) - [Wilcoxon Sign Rank test](https://www.statskingdom.com/test_wilcoxon_signed_ranks.html) ### Goal The goal of this website is to make statistics accessible to anyone, converting complex statistical jargon into common everyday language. We help everybody to calculate statistics. The calculators also provide R codes for your convenience. We started adding a step-by-step work-through for education purposes, an easy guide on how to calculate test statistics. ### [Terms](https://www.statskingdom.com/terms.html) We put in a lot of effort to provide accurate results and we automatically test every new page, The older pages were tested manually, but we slowly also automate the old pages. We usually compare the results to the R results. The information and tools on this website are given AS IS WITHOUT ANY WARRANTY OF ANY KIND. ### Calculate statistics The best online calculator to calculate statistics.
Readable Markdown	Statistical tests, charts, probabilities and clear results. Automatically checks assumptions, interprets results and outputs graphs, histograms and other charts. The statistics online calculators support not only the test statistic and the p-value but more results like effect size, test power, and the normality level. If one of the validations fails, the tool recommends a solution. What statistical test should you use? the following link will help you choose: [choose a statistical test](https://www.statskingdom.com/statistical-decision-tree.html) - decision questionnaire ([Tutorial](https://www.youtube.com/embed/QGZOBz_BXB4)). ## Test statistic calculators Find the test statistic calculator \| Test \| Assumptions \| Required sample data \| \| \| \| \| \| \| \| \| \| \| \| \|---\|---\|---\|---\|---\|---\|---\|---\|---\|---\|---\|---\|---\|---\| \| \# \| Test name \| Check \| Statistic \| ![Normal Distribution](https://www.statskingdom.com/images/Normal_trans.png) \| Ind \| σ \| σ1\=σ2 \| d \| μ/p \| x̄/p̂; \| n \| S \| ![data](https://www.statskingdom.com/images/data_icon2.png) \| \| 1 \| [One Sample Z-Test](https://www.statskingdom.com/110MeanNormal1.html) \| Mean \| z \= x ¯ \- μ 0 σ / n \| ✔ \| ✔ \| ✔ \| \| \| ✔ \| ✔ \| ✔ \| \| \| \| 2 \| [One Sample T-Test](https://www.statskingdom.com/130MeanT1.html) \| Mean \| t \= x ¯ \- μ 0 S / n \| ✔ \| ✔ \| ✘ \| \| \| ✔ \| ✔ \| ✔ \| ✔ \| \| \| 3 \| [Two Sample Z-Test](https://www.statskingdom.com/120MeanNormal2.html) \| Mean \| z \= x 1 \- x 2 \- d σ 2 n 1 \+ σ 2 n 2 \| ✔ \| ✔ \| ✔ \| \| ✔ \| \| ✔ \| ✔ \| \| \| \| 4 \| [Two Sample T-Test (Pooled variance)](https://www.statskingdom.com/140MeanT2eq.html) \| Mean \| t \= x ¯ 1 \- x ¯ 2 \- d s 1 n 1 \+ 1 n 2 \| ✔ \| ✔ \| ✘ \| ✔ \| ✔ \| \| ✔ \| ✔ \| ✔ \| \| \| 5 \| [Two Sample T-Test (Welch's)](https://www.statskingdom.com/150MeanT2uneq.html) \| Mean \| t \= x ¯ 1 \- x ¯ 2 \- d s 1 2 n 1 \+ s 2 2 n 2 \| ✔ \| ✔ \| ✘ \| ✘ \| ✔ \| \| ✔ \| ✔ \| ✔ \| \| \| 6 \| [Two Sample Mann-Whitney U Test](https://www.statskingdom.com/170median_mann_whitney.html) \| Rank \| z \= U \- μ \+ c σ \| \| ✔ \| \| \| ✔ \| \| \| \| \| ✔ \| \| 7 \| [Paired T-Test](https://www.statskingdom.com/paired-t-test-calculator.html) \| Mean \| t \= x ¯ d \- μ 0 S d / n \| ✔ \| Paired \| \| \| \| \| \| \| \| ✔ \| \| 8 \| [Paired Wilcoxon Sign Rank Test](https://www.statskingdom.com/175wilcoxon_signed_ranks.html) \| Rank \| z \= W \- μ \+ c σ \| \| Paired \| \| \| \| \| \| \| \| ✔ \| \| 9 \| [One Way ANOVA Test](https://www.statskingdom.com/180Anova1way.html) \| Mean \| F \= MS Between MS Within \| ✔ \| ✔ \| \| ✔ \| \| \| \| \| \| ✔ \| \| 10 \| [Repeated Measures ANOVA Test](https://www.statskingdom.com/repeated-anova-calculator.html) \| Mean \| F \= MS Between MS Within \| ✔ \| Dependent groups \| \| [Sphericity](https://www.statskingdom.com/glossary.html#sp) \| \| \| \| \| \| ✔ \| \| 11 \| [Friedman Test](https://www.statskingdom.com/friedman-calculator.html) \| Mean \| χ²(df) \= 12 ∑ j \= 1 k R j 2 \- 3 n 2 k ( k \+ 1 ) 2 n k ( k \+ 1 ) \- C t i e s \| \| Dependent groups \| \| \| \| \| \| \| \| ✔ \| \| 12 \| [Kruskal-Wallis Test](https://www.statskingdom.com/kruskal-wallis-calculator.html) \| Mean \| F \= MS Between MS Within \| \| ✔ \| \| \| \| \| \| \| \| ✔ \| \| 13 \| [Two Way ANOVA Test](https://www.statskingdom.com/two-way-anova-calculator.html) Fixed model, Mixed model, Random mode, Mixed model with repeats \| Mean \| F \= MS Between MS Within \| ✔ \| ✔ \| \| ✔ \| \| \| \| \| \| ✔ \| \| 14 \| [One Way MANOVA Test](https://www.statskingdom.com/manova-calculator.html) \| Mean \| F \= V s \- V . d f 2 d f 1 \| ✔ \| ✔ \| \| ✔ \| \| \| \| \| \| ✔ \| \| 15 \| [One Sample Proportion Test](https://www.statskingdom.com/111proportion_normal1.html) \| Proportion \| z \= ( p ^ \- p 0 ) \+ c p 0 ( 1 \- p 0 ) n or X~ B( n , p 0 ) \| Binomial \| ✔ \| \| \| \| ✔ \| ✔ \| ✔ \| \| \| \| 16 \| [Two Sample Proportion Test](https://www.statskingdom.com/121proportion_normal2.html) \| Proportion \| z \= p ^ 1 \- p ^ 2 \+ Cont p ^ ( 1 \- p ^ ) ( 1 n 1 \+ 1 n 2 ) \| Binomial \| ✔ \| \| \| \| \| ✔ \| ✔ \| \| \| \| 17 \| [Chi-Squared Test For Variance](https://www.statskingdom.com/210VarCHI1.html) \| σ \| χ 2 \= ( n \- 1 ) S 2 σ 0 2 \| ✔ \| ✔ \| \| \| \| \| \| ✔ \| ✔ \| \| \| 18 \| [F Test For Variances](https://www.statskingdom.com/220VarF2.html) \| σ \| F \= S 1 2 S 2 2 \| ✔ \| ✔ \| \| \| \| \| \| ✔ \| ✔ \| \| \| 19 \| [Levene's Test For Variances](https://www.statskingdom.com/230var_levenes.html) \| σ \| F \= MS Between MS Within \| ✘ \| ✔ \| \| \| \| \| \| \| \| ✔ \| \| 20 \| [Chi-Squared Test For Goodness Of Fit](https://www.statskingdom.com/310GoodnessChi.html) McNemar test, Chi-squared test for association, Fisher test, Binomial test \| Fit \| χ 2 \= ∑ i \= 1 n ( o i \- e i ) 2 e i \| \| ✔ \| \| \| \| \| \| \| \| ✔ \| \| 21 \| [Shapiro-Wilk Test](https://www.statskingdom.com/shapiro-wilk-test-calculator.html) \| Fit \| W \= ( ∑ i \= 1 ⌊ n / 2 ⌋ a i ( x n+1-i \- x i ) ) 2 ∑ i \= 1 n ( x i \- x ¯ ) 2 \| ✔ \| ✔ \| \| \| \| \| \| \| \| ✔ \| \| 22 \| [Kolmogorov Smirnov Test](https://www.statskingdom.com/kolmogorov-smirnov-test-calculator.html) \| Fit \| D = Max1≤i≤n(Di\+,Di\-) \| \| ✔ \| \| \| \| \| \| \| \| ✔ \| \| 23 \| [Two-Sample Kolmogorov Smirnov Test](https://www.statskingdom.com/kolmogorov-smirnov-two-calculator.html) \| Fit \| D = Max1≤i≤n(Di\+,Di\-) \| \| ✔ \| \| \| \| \| \| \| \| ✔ \| \| 24 \| [Kaplan Meier Survival Analysis](https://www.statskingdom.com/kaplan-meier.html) \| Survival \| χ 2 \= ∑ i \= 1 n ( o i \- e i ) 2 e i \| \| ✔ \| \| \| \| \| \| \| \| ✔ \| \| 25 \| [DeLong test - Independent curves](https://www.statskingdom.com/roc-calculator.html) Compares the AUCs of two independent ROC curves \| AUC \| D \= AUC 1 \- AUC 2 Var 1 \+ Var 1 \| \| ✔ \| \| \| \| \| \| \| \| ✔ \| \| 26 \| [DeLong test - Paired curves](https://www.statskingdom.com/roc-calculator.html) Compares the AUCs of two dependent ROC curves \| AUC \| Z \= AUC 1 \- AUC 2 Var ₁ \+ Var ₂ \- 2 \* Cov ( AUC ₁ , AUC ₂ ) \| \| Paired \| \| \| \| \| \| \| \| ✔ \| \\ ✔ - Yes, ✘ - No, empty - irrelevant ## Regression calculator \| \# \| Regression \| Statistic \| \|---\|---\|---\| \| 1 \| [Simple Linear Regression](https://www.statskingdom.com/linear-regression-calculator.html) \| F \= MS Regression MS Error \| \| 2 \| [Multiple Linear Regression](https://www.statskingdom.com/410multi_linear_regression.html) \| F \= MS Regression MS Error \| \| 3 \| [\Bulk Linear Regression](https://www.statskingdom.com/411list_linear_regression.html) \| F \= MS Regression MS Error \| \| 4 \| [Binary Logistic Regression](https://www.statskingdom.com/420logistic_regression.html) \| χ2 = 2(LL1\-LL0) \| \| 5 \| [Multinomial Logistic Regression](https://www.statskingdom.com/430logistic_regression.html) \| χ2 = 2(LL1\-LL0) \| \| 6 \| [Propensity Score Matching](https://www.statskingdom.com/psm-calculator.html) \| ![Propensity Score Matching](https://www.statskingdom.com/images/psm.svg) \| \Bulk linear regression calculator for several dependent variables with the same predictors. ## Confidence interval, Sample size, Effect Size \| \# \| Calculator \| Image \| \|---\|---\|---\| \| \| [Sample size calculators](https://www.statskingdom.com/sample_size_all.html) \| ![sample size chart](https://www.statskingdom.com/images/sample_size.jpg) \| \| \| [Test power calculators](https://www.statskingdom.com/statistical-power-calculators.html) \| ![statistics power chart](https://www.statskingdom.com/images/small_t2_power2.jpg) \| \| \| [Effect size calculators](https://www.statskingdom.com/effect-size-calculator.html) \| \| \| \| [Confidence intervals calculators](https://www.statskingdom.com/confidence-interval-calculators.html) \| ![statistics power chart](https://www.statskingdom.com/images/Normal1_t2_s.jpg) \| ## Distribution calculators \| \# \| Distribution \| Image \| \|---\|---\|---\| \| \| [P-value](https://www.statskingdom.com/p_value.html) \| ![p-value](https://www.statskingdom.com/images/p_value.jpg) \| \| \| [Distributions](https://www.statskingdom.com/distribution-calculator.html) \| ![Distribution Calculator](https://www.statskingdom.com/images/nrm_s.jpg) \| \| \| [Normal Distribution](https://www.statskingdom.com/normal-distribution-calculator.html) \| ![Normal Distribution](https://www.statskingdom.com/images/nrm_s.jpg) \| \| \| [Binomial Distribution](https://www.statskingdom.com/binomial-distribution-calculator.html) \| ![Binomial Distribution](https://www.statskingdom.com/images/binomial_s.jpg) \| \| \| [T Distribution (Student's)](https://www.statskingdom.com/distribution-calculator.html) \| ![T Distribution](https://www.statskingdom.com/images/t_s.jpg) \| \| \| [Chi-Squared Distribution](https://www.statskingdom.com/distribution-calculator.html) \| ![Chi squared Distribution](https://www.statskingdom.com/images/chi2_s.jpg) \| \| \| [F Distribution (Fisher-Snedecor)](https://www.statskingdom.com/distribution-calculator.html) \| ![F Distribution](https://www.statskingdom.com/images/f_s.jpg) \| \| \| [Poisson Distribution](https://www.statskingdom.com/distribution-calculator.html) \| ![Distribution](https://www.statskingdom.com/images/binomial_s.jpg) \| \| \| [Weibull Distribution](https://www.statskingdom.com/distribution-calculator.html) \| \| \| \| [Exponential Distribution](https://www.statskingdom.com/distribution-calculator.html) \| \| ## Statistical tables \| \# \| Table \| \|---\|---\| \| 1 \| [Z table](https://www.statskingdom.com/z_table.html) \| \| 2 \| [T table](https://www.statskingdom.com/t_table.html) \| ## Basic statistics calculators Each statistics calculator contains step by step calculation. \| Calculator \| Statistic calculator \| Image \| \|---\|---\|---\| \| [Statistics calculator](https://www.statskingdom.com/statistics-calculator.html) \| The calculator computes statistics such as count, average and standard deviation for each combination of the categorical variables. \| ![mean](https://www.statskingdom.com/images/statisticsCalc.svg) \| \| [Descriptive statistics calculator](https://www.statskingdom.com/descriptive-statistics-calculator.html) \| The calculator computes statistics such as count, average, and standard deviation for each variable. \| ![mean](https://www.statskingdom.com/images/descriptive.svg) \| \| [Percentile calculator](https://www.statskingdom.com/percentile-calculator.html) \| A percentile tells you the percentage of values below a given value in a data set. For example, a value at the 75th percentile means that 75% of the data lies below that value. \| ![percentile](https://www.statskingdom.com/images/percentile.svg) \| \| [Mean Median Mode calculator](https://www.statskingdom.com/mean-median-mode-calculator.html) \| Q1, Q3, IRQ, Range \| ![mean](https://www.statskingdom.com/images/mean.svg) \| \| [Measures Of Dispersion calculator](https://www.statskingdom.com/measures-of-dispersion-calculator.html) \| Mean, sample size, APA style \| \| \| [Standard Deviation calculator](https://www.statskingdom.com/standard-deviation-calculator.html) \| Mean, sample size, APA style \| S \= ∑ i \= 1 n ( x i \- x̄ ) 2 n \- 1 \| \| [Variance calculator](https://www.statskingdom.com/variance-calculator.html) \| Variance, Mean, SEM, MAD \| S 2 \= ∑ i \= 1 n ( x i \- x̄ ) 2 n \- 1 \| \| [Coefficient of Variation calculator](https://www.statskingdom.com/coefficient-of-variation-calculator.html) \| \| CV \= s x ¯ \| \| [Average calculator](https://www.statskingdom.com/average-calculator.html) \| Average, Sum, Count \| x ¯ \= x 1 \+ x 2 \+ ⋯ \+ x n n \| \| [Sample Mean calculator](https://www.statskingdom.com/sample-mean-calculator) \| Sample mean, Sum, Count \| x ¯ \= x 1 \+ x 2 \+ ⋯ \+ x n n \| \| [Geometric Mean calculator](https://www.statskingdom.com/geometric-mean-calculator.html) \| Product, n-th root \| G M \= x 1 x 2 … x n n \| \| [Harmonic Mean calculator](https://www.statskingdom.com/harmonic-mean-calculator.html) \| The harmonic mean is a type of average used for rates, for example average speed. It is found by dividing n by the sum of the reciprocals of the values. \| H n \= n 1 x 1 \+ 1 x 2 \+ ⋯ \+ 1 x n \| \| [Probability calculator](https://www.statskingdom.com/probability-calculator.html) \| Probability formula, Dependent events, Bayes' Theorem, Independent events \| P(A), P(A\\|B), P(A∩B), P(A∪B) \| \| [Combinations calculator](https://www.statskingdom.com/combinations-calculator.html) \| With/Without Repetitions \| ![Markov chain diagram](https://www.statskingdom.com/images/combinationsCalculator.svg) C r n \= n \! r \! ( n − r ) \! , C r n + r - 1 \= n + r - 1 \! r \! ( n − 1 ) \! \| \| [Permutation calculator](https://www.statskingdom.com/permutations-calculator.html) \| With/Without Repetitions \| ![Markov chain diagram](https://www.statskingdom.com/images/permutationsCalculator.svg) P r n \= n \! ( n − r ) \! , nr \| \| [Correlation calculator](https://www.statskingdom.com/correlation-calculator.html) \| Pearson correlation, Spearman's rank correlation \| r \= ∑ i \= 1 n ( x i − x ¯ ) ( y i − y ¯ ) ∑ i \= 1 n ( x − x ¯ ) 2 ∑ i \= 1 n ( y i − y ¯ ) 2 \| \| [Outliers](https://www.statskingdom.com/outlier-calculator.html) \| Tukey's Fences (Boxplot), Z-Score \| \| \| [Markov chain calculator](https://www.statskingdom.com/markov-chain-calculator.html) \| nth step probability vector, steady-state vector \| ![Markov chain diagram](https://www.statskingdom.com/images/markov.svg) \| \| [Odds calculator](https://www.statskingdom.com/odds-calculator.html) \| Odds to probability, probability to odds \| ![Odds calculator](https://www.statskingdom.com/images/odds.svg) \| \| [Betting odds calculator](https://www.statskingdom.com/betting-odds-calculator.html) \| Fractional odds, decimal odds, American odds \| ![Odds calculator](https://www.statskingdom.com/images/betting-odds.svg) \| \| [Mean absolute deviation calculator](https://www.statskingdom.com/mean-absolute-deviation-calculator.html) \| MAD calculator \| ![MAD diagram](https://www.statskingdom.com/images/mad.svg)μ \| \| [Median absolute deviation calculator](https://www.statskingdom.com/Median-absolute-deviation-calculator.html) \| MAD calculator \| ![MAD diagram](https://www.statskingdom.com/images/mad.svg)Mdn \| ## Visualization \| \# \| Chart \| Image \| \|---\|---\|---\| \| 1 \| [Principal component analysis](https://www.statskingdom.com/pca-calculator.html) \| ![Principal component analysis](https://www.statskingdom.com/images/i_pca.png) \| \| 2 \| [Cluster analysis](https://www.statskingdom.com/cluster-analysis.html) \| ![Cluster analysis](https://www.statskingdom.com/images/i_cluster.png) \| \| 3 \| [Histogram maker](https://www.statskingdom.com/histogram-maker.html) \| ![histogram](https://www.statskingdom.com/images/binomial_s.jpg) \| \| 4 \| [Box plot maker](https://www.statskingdom.com/boxplot-maker.html) \| ![boxplot](https://www.statskingdom.com/images/i_boxplot.png) \| \| 5 \| [Bar graph maker](https://www.statskingdom.com/chart-maker.html) \| ![bar graph](https://www.statskingdom.com/images/i_bar.png) \| \| 6 \| [Pie chart maker](https://www.statskingdom.com/pie-chart-maker.html) \| ![pie chart](https://www.statskingdom.com/images/i_pie.png) \| \| 7 \| [Line chart maker](https://www.statskingdom.com/chart-maker.html) \| ![line chart](https://www.statskingdom.com/images/i_line.png) \| \| 8 \| [Scatter chart maker](https://www.statskingdom.com/chart-maker.html) \| ![scatter chart maker](https://www.statskingdom.com/images/i_scatter.png) \| \| 9 \| [Area chart maker](https://www.statskingdom.com/chart-maker.html) \| ![area chart](https://www.statskingdom.com/images/i_area.png) \| \| 10 \| [Violin plot maker](https://www.statskingdom.com/violin-plot-maker.html) \| ![violin plot](https://www.statskingdom.com/images/i_violin.png) \| \| 11 \| [Venn diagram maker](https://www.statskingdom.com/venn-diagram-maker.html) \| ![Ven diagram](https://www.statskingdom.com/images/venn_two.png) \| \| 12 \| [Venn diagram calculator](https://www.statskingdom.com/venn-diagram-calculator.html) \| 12 3 9 \| \| 13 \| [Stem and Leaf plot](https://www.statskingdom.com/stem-and-leaf.html) \| ![Stem and Leaf plot maker](https://www.statskingdom.com/images/i_stem.png) \| \| 14 \| [ROC Calculator](https://www.statskingdom.com/roc-calculator.html) \| ![roc curve](https://www.statskingdom.com/images/i_roc.png) \| ## Guide - [Guide](https://www.statskingdom.com/information.html) - [Bonferroni correction](https://www.statskingdom.com/doc_anova.html#bonferroni) - [Central Limit Theorem](https://www.statskingdom.com/doc_clt.html) - [Confidence interval](https://www.statskingdom.com/doc_confidence_interval.html) - [Linear regression](https://www.statskingdom.com/doc_linear_regression.html) - [Logistic regression](https://www.statskingdom.com/doc_logistic_regression.html) - [Outliers](https://www.statskingdom.com/doc_outliers.html) - [P-value](https://www.statskingdom.com/doc_pvalue.html) - [Skewness and kurtosis](https://www.statskingdom.com/doc_skewness_kurtosis.html) - [Standard deviation](https://www.statskingdom.com/doc_standard_deviation.html) - [Test power](https://www.statskingdom.com/doc_test_power.html) ### Exams [Free statistics exams with solution.](https://www.statskingdom.com/statistics-exam.html) ### Statistical Tests - [Chi-squared test](https://www.statskingdom.com/doc_chi_squared.html) - [Levene's test](https://www.statskingdom.com/doc_anova.html#levenes) - [Mann-Whitney U Rank test](https://www.statskingdom.com/test_mann_whitney.html) - [One Way ANOVA test](https://www.statskingdom.com/doc_anova.html) - [Proportion test](https://www.statskingdom.com/doc_proportion_test.html) - [Shapiro Wilk test](https://www.statskingdom.com/doc_shapiro_wilk.html) - [T-test](https://www.statskingdom.com/t_test.html) - [T-test vs Z-Test](https://www.statskingdom.com/doc_t_test_z_test.html) - [Tukey HSD test](https://www.statskingdom.com/doc_anova.html#tukey) - [Wilcoxon Sign Rank test](https://www.statskingdom.com/test_wilcoxon_signed_ranks.html) ### Goal The goal of this website is to make statistics accessible to anyone, converting complex statistical jargon into common everyday language. We help everybody to calculate statistics. The calculators also provide R codes for your convenience. We started adding a step-by-step work-through for education purposes, an easy guide on how to calculate test statistics. ### [Terms](https://www.statskingdom.com/terms.html) We put in a lot of effort to provide accurate results and we automatically test every new page, The older pages were tested manually, but we slowly also automate the old pages. We usually compare the results to the R results. The information and tools on this website are given AS IS WITHOUT ANY WARRANTY OF ANY KIND. ### Calculate statistics The best online calculator to calculate statistics.
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