1 The t statistic in a two sample test does not depend
1. The t-statistic in a two-sample test does not depend on the units of the comparison. (We could, for example, measure the data in dollars or cents.)
2. If the boxplots of the data for the two groups overlap, then the two means are not significantly different.
3. If the confidence interval for m1 does not overlap the confidence interval for m2, then the two means are statistically significantly different.
4. If the two sample standard deviations are essentially the same (s12 ≈ s22), then the pooled two-sample t-test agrees with the regular two-sample t-test for the difference in the means.
5. Pooling two samples to estimate a common variance σ2 avoids complications due to confounding.
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