Inferential Statistics

Sample Comparisons: t-Tests, ANOVAs, Non-parametric Comparisons... [return to Table of Contents]

• Student t-test (for comparing two samples)...
  • a very general Student t-test web page -- paired or unpaired, equal- or unequal-variance, from individual observations (which can be key-entered or copy/pasted) or summary data (N, Mean, SD or SEM). Includes explanations and advice on carrying out this type of test.
  • t-test, paired or unpaired
  • t-test, paired or unpaired
  • t-test, paired or unpaired
  • t-test, paired
  • Paired Student t Test -- on up to 42 pairs of values, along with a postulated population mean difference.
  • Testing Two Populations -- Unpaired Student t test for up to 80 observations in each sample. Also accepts a postulated difference between the two population means, which can be different from 0.
  • A general 2-sample comparison calculator, for paired, unpaired, equal-variance, obtaining its p-values from table lookup or from resampling
  • Unpaired t-test from summary data (N, mean, SD)
  • Very general t-test program for comparing measured quantities, observed counts, and proportions between two unpaired samples; also produces risk ratio, odds ratio, number needed to treat, and population analysis.
• ANOVA (Analysis of Variance) -- comparison of two or more samples ...
  • One-Way and Factorial ANOVA for uncorrelated samples (extension of unpaired Student t-test to more than 2 groups)...
    • One-way ANOVA, with graphical output
    • One-way ANOVA for 3 Independent Samples
    • ANOVA: Testing the Means -- One-way ANOVA for three groups, each containing up to 40 subjects.
    • One-way ANOVA for 4 Independent Samples
    • One-way ANOVA from summary data (N, mean, and SD or SEM)
    • Another 1-way ANOVA from summary data
    • Two-way factorial ANOVA for 2 rows by 2 columns
    • Two-way factorial ANOVA for 2 rows by 3 columns.
    • Two-Way ANOVA Test -- for blocked designs of up to 4 groups by 6 treatments.
    • Two-Way ANOVA with Replications -- for blocked designs of up to 4 groups by 6 treatments, with up to 4 replications.
    • Two-way factorial ANOVA for 2 rows by 2 columns, from summary data (N, mean, SD)
    • ANOVA for Condensed Data Sets -- Enter up to 10 sets of (N, mean, SD); page calculates a one-way ANOVA.
    • Very general n-way factorial ANOVA, with interactions, means table, interaction plots, Bonferroni post-hoc multiple comparisons, and confidence intervals. (When you get to the Rweb page, scroll down to the Analysis Menu and select ANOVA.)
  • Repeated-Measures ANOVA for correlated samples (extension of paired Student t-test to more than 2 matched measurements)...
    • One-way repeated-measures ANOVA for 3 correlated samples
    • One-way repeated-measures ANOVA for 4 correlated samples
    • ANOVA for repeated-measures or matched measurements -- Enter three sets of matched measurements (up to 40 points each); page calculates a repeated-measures ANOVA.
  • Bartlett's Test for Equality of Multi-variances -- for up to 14 sets of [N, variance].
  • Post-hoc Tests -- After doing a two-way (or other) ANOVA, post -hoc tests (also called post tests) compare individual pairs of groups. This calculator does not perform the ANOVA calculations, but takes the output from an ANOVA (residual means square error, degrees of freedom) performs a post-hoc test between any pairs of cells that you select (using cell means and N's), at whatever alpha you specify.
  • Tukey LSD (Least Significant Difference), using the standard table produced by an ANOVA
  • Scheffe Least Significant Difference, using data from a standard ANOVA table and the N's for the two groups being compared
• Non-parametric tests (use these when the data is not normally distributed)...
  • Sign test for matched pairs
  • Median test for unmatched pairs
  • Wilcoxon Signed-Ranks test for matched pairs -- This page takes case-by-case pairs of matched data
  • Another Wilcoxon Signed-Ranks test for matched pairs -- This page takes summarized, tabulated data: how many cases had differences of +1, +2, +3, etc., and -1, -2, -3, etc.
  • Comparing Two Random Variables -- by the Mann-Whitney U test, with up to 80 observations per sample.
  • K-S Test for Equality of Two Populations -- Given two sets of frequencies (using the same grouping intervals), this page calculates the Kolmogorov-Smirnov test.
  • Wilcoxon Sum-of-Ranks (Mann-Whitney) test for comparing two unmatched samples
  • Kruskal-Wallis test (non-parametric ANOVA) for 2 or more groups of unpaired data -- This page requires that you first cross-tabulate your data into a matrix, with a row for every group and a column for every different numeric value that any subject had; the cell of the matrix tell how many subjects (if any) in that group had exactly that numeric value.
  • Least Significant Difference between mean ranks (post-hoc test after a significant Kruskal-Wallis test)
  • Friedman test for comparing rankings (non-parametric)
  • Two-group ordinal comparisons to assess how probable it is that the two groups come from a single ordering, using Wald-Wolfowitz, Randomness Test, Mann-Whitney, and Kolmogorov-Smirnov
  • Two-group paired comparisons, using T-test, Wilcoxon, Signs test, and McNemar test
  • McNemar's test for the paired comparison of proportions (or for matched pairs of labels)
• Comparison of proportions between two groups...
  • Comparison of Binomial proportions
  • Paired Preferences Test -- Enter the sample size, and the two percentages (preferring A and preferring B), and this program will calculate the T score and significance level. This page is based on a normal approximation to the binomial distribution, and should not be used if the sample size is less than 30.
• Sequential Analysis -- each subject's data (usually paired comparisons) is tested as it becomes available, and a decision is made to accept or to reject the null hypothesis or to keep testing.
  • by Paired Preferences -- Each pair of observations is compared and rated qualitatively as "preferring A" or "preferring B"
  • by Paired Differences -- Each pair of numbers is subtracted to obtain a difference
• WebStat (an integrated (Java) applet) can perform Z-tests and T-tests (one- and two-sample) for population means, and Chi-square and Fisher-F tests for population variances