Don't Be Misled By "pStatements"
(B)
In this chapter, the focus has been on the databased
plevel. 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 databased plevel. For example,
consider a study in which a researcher is concerned with Pearson's productmoment
correlation, conducts a twotailed 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 pvalue 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)
