Don't Be Misled By "p-Statements" (B)

In this chapter, the focus has been on the data-based p-level. If the p is very small, you may be tempted to think that there is a large effect in the data or, stated differently, that Ho is false by a mile. Similarly, you may be tempted to think that ps that are not small turned out that way because there was a small effect in the data or, stated differently, because the null hypothesis (if false at all) was false by a small amount. Resist these temptations! For any given degree of discrepancy between the sample evidence and Ho, there is an inverse relationship between the sample size and the data-based p-level. For example, consider a study in which a researcher is concerned with Pearson's product-moment correlation, conducts a two-tailed test of Ho: r = 0.00, and finds that r = .40 for the sample. Now, if the size of that sample is 10, then p is .24. If n = 30, then p = .03. And if n = 500, then p = .00006. Now consider the same study but this time with a very small difference between Ho and the sample evidence. For the case where Ho: r = 0.00 and r = .03, the p-value will turn out to be very small if the sample size is very large. If n = 25,000, p < .00002.

(From Chapter 9, p. 249)

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