Statistical Tables &amp; Critical Values

Z-Table (Standard Normal)

The complete standard normal distribution table (Z-table). Look up cumulative probabilities for any Z-score from -3.99 to +3.99. Includes left-tail and right-tail variants.

t-Distribution Table (Student’s t-Table)

Find critical t-values using degrees of freedom, significance level and one- or two-tailed tests. Includes guidance for confidence intervals.

Chi-Square Table

Chi-square critical values for goodness-of-fit tests, independence tests, and confidence intervals for variance. Covers degrees of freedom 1–100.

F Table

F distribution critical values for ANOVA and variance ratio tests. Includes alpha levels 0.10, 0.05, and 0.01, PDF downloads, and an interactive calculator.

Standard Normal Table: Right Tail

The Standard Normal Table for the right tail provides probabilities and critical values for the area to the right of a given z-score in the standard normal distribution.

Binomial Distribution Table

Complete binomial table showing exact P(X = k) and cumulative P(X ≤ k) for n = 1–20 and p = 0.05–0.95. Includes calculator, PDF download, and step-by-step guide.

Poisson Distribution Table

Poisson Distribution Table provides probability values for discrete rare events using λ (lambda) and x values for probability and cumulative calculations.

Geometric Distribution Table

The Geometric Distribution Table provides probabilities for the number of trials needed to achieve the first success in a sequence of independent Bernoulli trials.

Exponential Distribution Table

The Exponential Distribution Table provides cumulative probabilities and related values for modeling waiting times and the time between events in a Poisson process.

Negative Binomial Distribution Table

The Negative Binomial Distribution Table provides probabilities for the number of trials or failures required to achieve a specified number of successes in repeated independent trials.

Hypergeometric Distribution Table

The Hypergeometric Distribution Table provides probabilities for sampling successes from a finite population without replacement.

Noncentral t Distribution Table

The Noncentral t Distribution Table provides probabilities and critical values based on degrees of freedom (ν) and the noncentrality parameter (λ).

Nonparametric & rank-based tests

Distribution-free tests for rankings, paired data and group comparisons

13 tables

Mann-Whitney U Table

Mann-Whitney U Table provides critical values for comparing two independent samples using the non-parametric Mann-Whitney U test across different sample sizes and significance levels.

Wilcoxon Signed-Rank Table provides critical W values for determining the statistical significance of paired-sample differences in the Wilcoxon signed-rank test across different sample sizes and significance levels.

Sign Test Table

The Sign Test Table provides critical values for the Sign Test, helping determine whether paired observations differ significantly without assuming a normal distribution.

Runs Test Table

The Runs Test Table provides critical values for the Runs Test, helping evaluate whether the order of observations in a sequence is random.

Kolmogorov-Smirnov (K-S) Table

The Kolmogorov-Smirnov (K-S) Table provides critical values for the K-S test, helping assess whether a sample follows a specified probability distribution.

Kruskal-Wallis Table

Kruskal-Wallis critical values for H statistics, degrees of freedom, and significance levels. Includes α = 0.10, 0.05, and 0.01 with guidance for making rejection decisions.

Kruskal-Wallis Critical Value Table

The Kruskal-Wallis Critical Value Table provides cutoff values for the Kruskal-Wallis test, helping determine whether differences among three or more independent groups are statistically significant.

Friedman Test Table

The Friedman Test Table provides critical values for the Friedman test, helping compare three or more related groups when the assumptions of repeated-measures ANOVA are not met.

Cochran's Q Table

Cochran's Q Table provides critical values for Cochran's Q test, helping researchers analyze differences between three or more related proportions across various significance levels.

McNemar Test Table

McNemar Test Table provides critical values for McNemar's test, allowing researchers to evaluate changes in paired categorical data and determine statistical significance.

Fisher's Exact Test Table

Understand 2×2 contingency tables, observed cell counts, and exact p-values calculated from the hypergeometric distribution. Explains why Fisher's exact test does not use a universal critical-value table.

Kendall's Tau Critical Value Table

The Kendall's Tau Critical Value Table provides critical values for testing the significance of the association between ranked variables using Kendall's tau.

Spearman Footrule Table

The Spearman Footrule Table provides critical values for evaluating rank differences using the Spearman footrule statistic.

ANOVA, variance & post-hoc comparisons

Critical values for group differences and multiple comparisons

7 tables

Tukey's Q Table

Tukey's Q Table provides critical q values for performing Tukey’s Honestly Significant Difference (HSD) test, helping determine whether differences between group means are statistically significant across various significance levels and degrees of freedom.

Advanced

Dunnett’s Table

Dunnett’s Table provides critical values to compare multiple treatments with a control after ANOVA using k, df, and α levels (0.10, 0.05, 0.01).

Scheffé Test Table

Scheffé Test Table provides critical values for Scheffé's multiple comparison procedure, allowing researchers to identify significant differences among group means after an ANOVA while controlling the family-wise error rate.

Duncan's Multiple Range Table

Duncan's Multiple Range Table provides critical values for Duncan's Multiple Range Test, helping identify which group means differ significantly after ANOVA.

Newman-Keuls Table

The Newman-Keuls Table provides critical values for the Student-Newman-Keuls (SNK) test, helping identify significant differences between group means following ANOVA.

Hartley's Fmax Table

The Hartley Fmax Table provides critical values for testing homogeneity of variance across groups using the maximum-to-minimum variance ratio.

Levene's Test Table

Levene's Test Table provides critical values for Levene's test, helping researchers assess the equality of variances across multiple groups before performing statistical analyses.

Correlation, regression & agreement

Interpret correlation, residual patterns and inter-rater agreement

5 tables

Pearson Correlation Table

Pearson Correlation Table provides critical r values for determining the statistical significance of Pearson correlation coefficients across different degrees of freedom and significance levels.

Spearman Correlation Table

Spearman Correlation Table provides critical values for Spearman’s rank correlation coefficient (ρ), helping determine the statistical significance of relationships between ranked variables across different sample sizes and significance levels.

Fisher's Z Transformation Table

The Fisher's Z Transformation Table provides values for converting correlation coefficients into Fisher's z scores for statistical analysis and inference.

Advanced

Durbin-Watson Table

The Durbin-Watson Table provides critical values used to test for autocorrelation in the residuals of regression models.

Cohen's Kappa Table

The Cohen's Kappa Table provides interpretation guidelines, critical values, formulas, and examples for measuring agreement between two raters beyond chance.

Normality, goodness-of-fit & outliers

Reference values for distribution checks and potential outliers

5 tables

Shapiro-Wilk Critical Value Table

Shapiro-Wilk W critical values by sample size and significance level. Learn how to compare your calculated W with the critical value and interpret evidence against normality.

Lilliefors Test Table

The Lilliefors Test Table provides critical D values for normality testing when the population mean and standard deviation are estimated from the sample.

Anderson-Darling Table

Anderson-Darling Table provides critical values for the Anderson-Darling goodness-of-fit test, helping researchers determine whether a dataset follows a specified probability distribution.

Grubbs Test Table

Grubbs Test Table provides critical values for Grubbs' outlier test, helping researchers identify a single outlier in normally distributed datasets at various significance levels.

Dixon's Q Table

Dixon's Q Table provides critical values for Dixon's Q test, helping researchers identify potential outliers in small datasets while maintaining a specified significance level.

Applied statistics & research methods

Quality control, reliability, survival analysis and research adjustments

7 tables

Bonferroni Adjusted Critical Value Table

Bonferroni Adjusted Critical Value Table provides adjusted significance levels for multiple hypothesis testing, helping control the family-wise error rate by applying the Bonferroni correction across different numbers of comparisons.

Random Digit Table

Random Digit Table provides randomly generated digits for use in probability, sampling, simulations, experimental design, and statistical research where unbiased random selection is required.

Advanced

Log-Rank Test Table

Log-Rank Test Table provides critical values used to compare survival distributions between two or more groups, supporting hypothesis testing in survival and reliability analysis.

Weibull Reliability Table

Weibull Reliability Table provides reliability and cumulative failure probabilities for Weibull distributions, supporting life testing, reliability engineering, and failure time analysis.

Control Chart Constants Table

The Control Chart Constants Table provides A2, D3, D4, d2, and related constants used to calculate control limits for X-bar, R, and other statistical process control charts.

Acceptance Sampling Table

The Acceptance Sampling Table provides sample sizes, acceptance numbers, and related values used to determine whether a batch or lot meets specified quality requirements.

Effect Size Table

Cohen's d effect size thresholds and interpretation, including small, medium, and large effects. Includes the pooled standard deviation formula and six worked examples.