Analyze/Stats - Paired t-test

Paired t-Test

The paired t-test is a fundamental statistical method designed to compare the means of two related groups. Whether you’re analyzing pre-test vs. post-test results, repeated measurements, or matched pairs, this test helps determine if the observed differences are statistically significant. Unlike independent t-tests, it accounts for natural variability within pairs, making it more precise for dependent data.

Why Use This Test?
When Should You Use the BWS Test?
Common Alternatives (When Paired t-test Isn’t the Best Fit)
How to Interpret the Results
How the Function is Called
Conclusion

Why Use This Test?

The paired t-test is particularly useful when working with dependent samples, where measurements are naturally linked. Common applications include:

Before-and-after studies (e.g., evaluating the effect of a training program).
Repeated measurements (e.g., blood pressure readings before and after treatment).
Matched experiments (e.g., comparing two treatments on the same subjects).

This test assumes that the differences between pairs follow a normal distribution, though it remains fairly robust with slight deviations. Since it focuses on within-pair changes rather than overall group differences, it often provides greater statistical power than independent-sample tests.

The figure above shows examples of two groups in a row with data suitable for analysis with a paired t-test. Note that the two groups, before and after treatment, are related to the same source, which is the same patient. If you believe your data is not following this pattern, check the Unpaired t test.

When to Use the Paired t-Test

You should consider this test when:

Your data consists of two related samples (e.g., the same individuals measured twice).
Your measurements are continuous (interval or ratio scale).
You need to assess whether the mean difference is statistically significant.

Common Alternatives (When Paired t-test Isn’t the Best Fit)

Wilcoxon signed-rank test (non-parametric alternative)
Independent t-test (for unrelated groups)

How to Interpret the Results

The paired t-test returns two key numbers:

t-statistic – Indicates the magnitude and direction of the difference
p-value – Determines whether the difference is statistically significant

This is how you see the Paired t-test results with SimpliStats.

Decision Rule:

If p-value < 0.05 (or your chosen significance level): Reject the null hypothesis (the two groups likely have different distributions).
If p-value ≥ 0.05: No strong evidence of a difference (but doesn’t prove they’re the same).

Obs: Note that SimpliStats will always return the raw p-value (column “p-value”) and to make your life easier, the p-value stratified by rounding (column “p-value rounded”) and by ns/*asterisk encoding (column “p-value *”)

Real-World Example

Suppose a study measures patient pain levels before and after a new therapy:

t-statistic = 3.42
p-value = 0.004

Since 0.004 < 0.05, we conclude: “The therapy leads to a statistically significant reduction in pain.”

How the Function is Called

				
					from scipy.stats import ttest_rel  

# Example: Test scores before and after a course  
before = [65, 70, 80, 75, 90]
after = [72, 75, 85, 80, 95]

t_stat, p_value = ttest_rel(before, after, alternative="two-sided")

Input

a, b: Paired datasets (must be equal in length).
Important: SimpliStats will automatically attempt to pair your samples (rows) from each group (columns), ignoring those that are not paired.
alternative: Specifies the hypothesis (“two-sided”, “less”, “greater”)

Output

t-statistic: Measures effect size (higher absolute values = stronger evidence)
p-value: Probability that observed differences occurred by chance
Degrees of freedom (df): Sample size minus one (n-1)

Conclusion

The paired t-test is an essential tool for analyzing dependent data, offering higher sensitivity than independent tests by reducing extraneous variability. It’s widely used in medical research, psychology, and business analytics to assess changes over time or between matched conditions.

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