28.5 About finding $P$-values

As demonstrated in Sect. 27.5.1, often $P$-values can be approximated by using the the 68–95–99.7 rule and using a diagram of a normal distribution. The $P$-value is the area more extreme than the calculated $t$-score; the 68–95–99.7 rule can be used to approximate this tail area.

For two-tailed tests, the $P$-value is the combined area in the left and right tails. For one-tailed tests, the $P$-value is the area in just the left or right tail.

When software reports two-tailed $P$-values, a one-tailed $P$ is found by halving the two-tailed $P$-value.

More accurate estimates of the $P$-value can be found using $z$-tables, though we do not demonstrate this in this book. Even more precise estimates of $P$-values can be found using specially-prepared $t$-tables. Again, we do not do so in this book.

For more precise $P$-values, we will take the $P$-values from software output.

When using software to obtain $P$-values, be sure to check if the software reports one- or two-tailed $P$-values.

For example, some software (such as SPSS) always reports two-tailed $P$-values.