What should one take into consideration when testing the null hypothesis of the equality of two means using small samples?
When we are testing the null hypothesis of the equality of two means using small samples, we take into consideration that the two samples have been randomly drawn from two separate distributions which are normally distributed. This is the most important consideration. Now, we can take into consideration the equality (homogeneity) of variances, if the sample variances are approximately equal or close to each other. Based on this, we conduct the pooled variance t-test for equal variances or Welch's t-test for unequal variances. We also assume that the observations in the two samples are continuous.
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