## 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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