Independent Samples t-Test

The independent samples t-test compares the means of one continuous variable measured in two separate groups. The groups are made up of different people: a participant belongs to only one of them. The test divides the difference between the two means by the variability within the groups to produce a t value, which says how often a difference this large would appear if the null hypothesis (equal population means) were true. YouReply Analyze first runs Levene's test to see whether the variances are homogeneous; if they are not, it switches on its own to the Welch version, which adjusts the degrees of freedom, and states in the result which version was used.

• Do women and men differ in their average life satisfaction score?
• Do participants who attended a training programme score differently on the test than those who did not?
• Does brand satisfaction differ between participants living in the city centre and in rural areas?
• Do two independent groups evaluating two different packaging designs give different ratings?

• When exactly two groups are being compared.
• When each participant appears in only one group, so you are not comparing two measurements of the same person.
• When the dependent variable is measured on a continuous scale (a score, a duration, an amount, a scale total).
• When the size and direction of the difference between group means is the question, rather than a difference in ranks.

• Dependent variable: continuous (interval or ratio). In the panel this is a numeric column whose measurement level is set to 'scale' on the Variable tab.
• Independent variable: a grouping column with exactly two categories (gender, treatment/control, attended/did not attend).
• One row per participant; designs in which the same participant appears in both groups call for a different test.

Independence of observations

One participant's measurement does not influence another's, and each participant belongs to a single group. This comes from the study design, not from the test itself.

Continuous dependent variable

A mean is only meaningful if the dependent variable is measured at interval or ratio level. On an ordinal variable the mean may not be interpretable.

Normality within groups

Each group's distribution should be approximately normal. As group sizes grow (roughly 30 and above) the central limit theorem makes the test more tolerant of departures from normality.

Homogeneity of variances

The two population variances are assumed equal. When they are not, the Welch correction replaces the classical (Student) t-test.

• Independence of observations: The panel does not check this assumption automatically; the researcher evaluates it.
• Continuous dependent variable: The method picker requires a numeric column for this field; where a column does not fit, the method is dimmed and the reason is spelled out. You can correct the measurement level on the Variable tab.
• Normality within groups: The panel does not check this automatically while running the t-test. Normality tests are offered as a separate method, so you can inspect the distributions first.
• Homogeneity of variances: Levene's test runs automatically on every run. If p > 0.05 the Student version is used, otherwise the Welch version; the version applied and the Levene p value appear in a separate block of the result.

1. 1Upload your data file (CSV or Excel) to the panel, with participants in rows and variables in columns.
2. 2On the Variable tab, confirm that the dependent variable is numeric with the right measurement level and that the grouping column has two categories.
3. 3On the Analysis tab, open the method picker and search for the method by name or pick it from the group comparison category; the 'Only ones that fit my data' switch filters the list.
4. 4In the parameter form choose the grouping column and the dependent variable; you can leave the variance assumption on automatic or set it yourself.
5. 5Run the analysis. The results panel opens the test statistics, the group descriptives, the Levene block and the effect size as separate sections.
6. 6Download the results as Excel and the chart as PNG; the computation credits card shows which library call produced the numbers.

t statistic and degrees of freedom

For the Student version the degrees of freedom are n1 + n2 - 2; for the Welch version they are the fractional value from the Welch-Satterthwaite approximation.

Significance (p) value

Reported as two-tailed or one-tailed according to the direction chosen; the heading in the result states which was used.

Group descriptives

Mean, median, mode, standard deviation and sample size for each group, in a separate table.

Homogeneity of variance block

Levene's p value, whether the variances are treated as homogeneous, and which version of the t-test was applied as a result.

Group means chart

The results panel draws a bar chart comparing the group means, which can be downloaded as a PNG.

Cohen's d

The size of the difference between the two means expressed in pooled standard deviations. The conventional benchmarks are 0.20 for a small, 0.50 for a medium and 0.80 for a large effect; they are conventions, not thresholds, and should be read against what is typical in your field.

This method does not return a confidence interval for the mean difference; in the panel a confidence interval is computed only for the one-sample t-test (95% for the mean difference). The effect size is reported as a point estimate as well, without an interval. If your journal requires an interval, you need to compute it separately.

The numbers below are a representative example, not data from a real study or a real user.

Research question

In a customer satisfaction study, does the overall satisfaction score (0-100) differ between people who use the mobile app and those who do not?

Variables

Dependent variable: overall satisfaction score (continuous) · Independent variable: app usage (uses / does not use)

Example result

App users (n = 148) averaged 72.4 (SD = 12.1); non-users (n = 132) averaged 67.9 (SD = 13.4). Levene's p = 0.214, so the Student version was applied: t(278) = 2.94, p = 0.004, Cohen's d = 0.35.

Interpretation

Levene's test supported homogeneity of variance, so the classical t-test was used. The 4.5-point difference is statistically significant and the effect size sits between small and medium. Significance describes how unlikely the result is under the null hypothesis, not how large the difference is; whether 4.5 points matters in practice depends on the context of the study.

Research question: Does satisfaction differ between remote and office employees?

Grouping variable

work_mode

Measured variable

satisfaction

Variance assumption

auto

Computation credits: scipy 1.18.0 · statsmodels 0.14.6 · scikit-learn 1.9.0 · numpy 2.5.1 · pandas 3.0.5 · semopy 2.3.11 · 89fc29a · Data seed: 20260912

App users reported higher satisfaction (M = 72.4, SD = 12.1) than non-users (M = 67.9, SD = 13.4), t(278) = 2.94, p = .004, d = 0.35.

An example sentence close to APA style; the numbers are representative.

• Not for three or more groups; running several t-tests instead inflates the Type I error rate.
• Not for before-and-after measurements on the same people; that design needs the paired t-test.
• If the dependent variable is ordinal (a single Likert item, for example), interpreting a mean is contentious and a rank-based test fits better.
• In small samples with clearly skewed distributions the normality violation matters; do not interpret the result without looking at the distribution.
• Outliers move the mean and the standard deviation together, so they can make the t value misleadingly small or large.

• Mann-Whitney U TestWhy: When normality does not hold or the dependent variable is ordinal; it compares ranks rather than means.
• One-Way ANOVAWhy: When three or more groups are compared; it keeps the Type I error rate under control in a single test.
• Paired Samples t-TestWhy: When the measurements come from the same people or from matched pairs, so independence does not hold.

• Mann-Whitney U Test
• One-Way ANOVA
• Paired Samples t-Test
• One-Sample t-Test

What happens if the variances are not equal?

The panel runs Levene's test on every run. If its p value is below 0.05 the variances are not treated as homogeneous and the Welch version, which adjusts the degrees of freedom, is used automatically. The result states which version was applied; you do not need to do anything.

Do the groups need to be the same size?

No. Unequal group sizes do not invalidate the test; they only make the result more sensitive when the variances are unequal as well, and in that case the Welch version is already used.

Should I run a normality test first?

The panel does not check normality while running the t-test. With small groups (roughly under 30) it is worth running the Normality tests method first and looking at the distributions; in larger samples the central limit theorem gives some tolerance.

The p value is significant, so is the difference important?

Significance and importance are different things. The p value gives the probability of a result at least as extreme, assuming the null hypothesis and the model assumptions hold. Judge the practical value of the difference from the effect size (Cohen's d) and from the units of your scale.

• Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics
• Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences
• Delacre, M., Lakens, D., & Leys, C. (2017). Why Psychologists Should by Default Use Welch's t-test Instead of Student's t-test
• scipy.stats.ttest_ind documentation