## 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.