## The logic behind the error term

Understanding the error term is important concept because future tests (e.g., ANOVA) also use error terms. Without an understanding of what the error term means, students cannot really understand what statistical significance means.

To set up the need for an error term, ask students if looking at looking at the differences between the control and experimental group means is sufficient to determine whether the treatment had an effect. If they don't say "no" with conviction, prompt them by re-asking the question, giving them an example of two group means that are very similar (e.g., 51.8 vs. 51.9). In addition, ask them if the two groups could have slightly different scores even if the treatment had no effect whatsoever.).

Once students appreciate the need for the error term, you can explain how it is derived. Emphasize that differences within a treatment group must be due to nontreatment effects (such as individual differences). That is, these differences must be due to random error. Then, explain how the same random factors that could cause scores within a group to differ from each other could also cause the two groups to differ from one another. That is, individual differences between participants could cause scores within a group to differ from each other as well as cause the two groups' (average scores) to differ from each other. Once students understand the principle of the error term, you can go into detail about how it is calculated. Realize that students will tend to confuse the following

1. Standard deviation, standard error of the mean, and standard error of the difference.

2. p <.05 and p >.05,

3. whether p<.05 suggests that we should or should not be confident that the results are due to the treatment, and

4. the difference between a low p value and a low t value (we have even been at undergraduate research conferences where the presenter said that the results were significant because the value of the statistic [not the p value] was near zero and was "less than .05.").

A good reference to help you explain the general idea behind inferential statistics is

Zerbolio, D. J. (1989). A "bag of tricks" for teaching about sampling distributions.

Teaching of Psychology, 16, 207- 209.

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