When the difference of the means is larger, or smaller, what are the implications for tests of statistical significance?
What will be an ideal response?
You can calculate the difference between two means by subtracting the mean of one variable (say a pre-test) from another (say a post-test). This difference is the effect size. The question is, is the difference between the means large enough for you to conclude that exposure to some treatment is causing a meaningful difference in the means? We can interpret the difference of the means as: The larger the difference of the means the more likely that the difference is not due to chance and is instead due to a relationship between the independent and dependent variables. In other words, if the difference between the means is quite small, it is likely that the intervening treatment did not really have an effect. It is essential, then, to establish a way to determine when the difference of the means is large enough to conclude that there was a meaningful effect.
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