Independent-Samples t-Test

Starter example

Runnable scripts and synthetic inputs are provided. Expand this chapter with output, figures, authoritative references, and review before publication.

Your question

What is the mean difference in scores between independent groups B and A?

When to use this method

The outcome is numerical and the groups contain different participants. Welch’s t-test allows unequal population variances. It does not correct dependence, selection bias, or confounding.

What it estimates or tests

The effect is the population mean of B minus the population mean of A. The two-sided null hypothesis is a zero mean difference.

Check before running

Check the study design, group counts, missing data, and distributions. Inspect extreme observations. With small samples, strong skew or outliers can undermine the t approximation.

The example file has one row per synthetic participant. Its independence is part of how the example was generated.

Run the analysis

From the project root, choose either implementation:

python3 scripts/python/05-independent-t-test.py

Rscript scripts/R/05-independent-t-test.R

Both use data/example/independent-groups.csv, calculate B minus A, and export separate TSV results under results/tables/.

Understand the output

Read the mean difference and its 95% confidence interval together. The interval expresses uncertainty under the model and sampling assumptions. The p-value measures incompatibility with the zero-difference null under those assumptions; it does not measure practical importance.

Report the finding

Report sample sizes, group means, the B-minus-A difference, its confidence interval, Welch’s t statistic, degrees of freedom, and p-value. These synthetic scores illustrate a method and support no claim about a real intervention.

Common mistakes and alternatives

Do not use an independent-groups test for paired measurements. Do not select tests solely from a normality-test p-value. Rank tests answer a different question and are not automatic tests of medians.

References

Add checked statistical and software references during chapter development.