Executive Summary
Whether the two group means differ and how large the effect is
The difference in means between control (71.61) and treatment (77.48) is statistically significant (p = 0.0088 < alpha = 0.05). The raw mean difference is -5.862 (95% CI: [-10.221, -1.503]). Cohen's d = -0.486, indicating a small effect size. The evidence supports a real difference between the group means.
Descriptive Statistics by Group
Sample sizes, means, standard deviations, and 95% confidence intervals per group
| Group | N | Mean | SD | SE | CI Lower | CI Upper |
|---|---|---|---|---|---|---|
| control | 60 | 71.61 | 12.52 | 1.616 | 68.38 | 74.85 |
| treatment | 60 | 77.48 | 11.58 | 1.495 | 74.48 | 80.47 |
control has n = 60 observations with mean = 71.61 (SD = 12.52); treatment has n = 60 with mean = 77.48 (SD = 11.58). Standard errors are 1.616 and 1.495 respectively. 95% confidence intervals for the group means are [68.38, 74.85] and [74.48, 80.47].
Group Means with Confidence Intervals
95% CI for each group mean — non-overlapping CIs suggest a significant difference
Group means with 95% confidence intervals: control = 71.61 [68.38, 74.85], treatment = 77.48 [74.48, 80.47]. The confidence intervals overlap, which is consistent with a non-significant difference. The t-test p-value = 0.0088 provides the formal significance test.
Value Distribution by Group
Box plots comparing spread, median, and outliers between the two groups
Box plots show the spread and central tendency of each group's outcome values. control has median = 70.16 (IQR = 19); treatment has median = 77.12 (IQR = 15.32). The relative position of the boxes indicates whether one group consistently scores higher, while box width and whisker length reflect within-group variability and potential outliers.
T-Test Results and Effect Size
Key statistics from Welch's t-test including t-statistic, p-value, mean difference, and Cohen's d
Welch's t-test: t(117.3) = -2.663, p = 0.0088. The mean difference (control minus treatment) is -5.862. Cohen's d = -0.486, which is a small effect. The result is statistically significant (p = 0.0088 < alpha = 0.05).
Distribution Shape by Group
Within-group value histograms for visual normality assessment
Histograms show the value distribution within each group, allowing visual assessment of the normality assumption required by the t-test. control appears approximately normal (Shapiro-Wilk p = 0.6778); treatment appears approximately normal (Shapiro-Wilk p = 0.8126). The t-test is robust to mild non-normality, especially when both groups have n ≥ 30.
Assumption Test Results
Shapiro-Wilk normality tests per group and Levene's test for variance equality
| Test | Statistic | P Value | Conclusion |
|---|---|---|---|
| Shapiro-Wilk: control | 0.9851 | 0.6778 | Normality supported |
| Shapiro-Wilk: treatment | 0.9878 | 0.8126 | Normality supported |
| Levene's Test (Equal Variances) | 0.9734 | 0.3258 | Equal variances supported |
Shapiro-Wilk tests for control (p = 0.6778) and treatment (p = 0.8126) assess normality. Levene's test for equal variances gives p = 0.3258 — Equal variances supported. Both groups are consistent with normality, supporting parametric t-test validity.