Critical Value

The critical value is the value needed for rejection of the null hypothesis when it is true. For example, if the critical value for a particular type of statistic's distribution and the sample size at a particular level[Page 203] of Type I error is 3.45, then the observed or computed value must exceed 3.455 for the outcome to be significant.

The following points about critical values should be remembered:

1.
There is a different critical value depending on the size of the sample being evaluated (reflected in the degrees of freedom) and the Type I error set by the experimenter.
2.
Critical values are usually shown in tables that accompany many statistical texts. A typical table, such as the one used for testing the difference between two independent means, would appear like Table 1. Note that the research hypothesis can be tested at both the .01 and .05 levels of significance.
3.
Each test statistic (such as the t test or the F test) has its own distribution of critical values.
4.
With the advent of computerized statistical analysis programs, critical values are no longer needed for comparison's sake. Rather, the exact probability of an outcome (the Type I error level) is printed out. For example, instead of the statement “The results were significant beyond the .05 level,” a more accurate statement might be, “The probability of a Type I error was .043.”