Hypothesis Testing Service: t-Test, ANOVA, Chi-Square and Non-Parametric Tests

Tests we run

• Independent, paired and one-sample t-tests
• One-way, factorial and repeated-measures ANOVA with post-hoc comparisons (Tukey, Bonferroni, Games-Howell)
• ANCOVA and MANOVA when you need to adjust for covariates or compare several outcomes
• Chi-square tests of independence and goodness of fit, and Fisher’s exact test for small counts
• Non-parametric alternatives: Mann-Whitney U, Wilcoxon signed-rank, Kruskal-Wallis and Friedman
• Effect sizes: Cohen’s d, eta squared and Cramer’s V
• Corrections for multiple comparisons

Choosing between a t-test, ANOVA and chi-square

The choice depends on the type of outcome and the number of groups. A numeric outcome compared across two groups points to a t-test; across three or more groups it points to ANOVA. When both variables are categories, such as gender and a yes/no answer, a chi-square test is the usual choice. When the data are skewed, ordinal or very small, a non-parametric test is safer. Our free test selector walks through these questions, and the t-test calculator lets you try a quick comparison yourself.

Assumptions we check before every test

A test is only as reliable as its assumptions. We check normality of the outcome or residuals, equal variances (Levene’s test), independence of observations and, for chi-square, whether expected counts are large enough. When an assumption fails we do not simply push on: we apply a Welch correction, transform the variable, use bootstrapping or switch to a non-parametric test, and we say so in the methods text.

Reporting the result correctly

Journals and examiners expect the full picture, for example: t(48) = 2.31, p = .025, d = 0.65. We report the test statistic, degrees of freedom, exact p-value and an effect size, with means and standard deviations for each group, and we explain in plain words what the result means for your question. You can convert a test statistic to an exact probability with the p-value calculator.

For relationships rather than group differences, see regression analysis. For overall data summaries, see descriptive and inferential statistics.

How the work runs

1. You send the data and the hypotheses you want to test.
2. We confirm the variables, scales and groups, and agree the tests.
3. We check assumptions, run the tests and calculate effect sizes.
4. You get formatted tables, a written interpretation and the syntax used.