Sample statistics are used to estimate population parameters. Mode, median, and mean are measures of central tendency. Range, variance, and standard deviation are measures of variability. Measures of central tendency and variability are used as descriptive statistics to characterize a sample.
Inferential statistics are used to make inferences about the true difference in the population on the basis of sample data. The chi-square (χ2) test for independence is used to assess the statistical significance of frequency data for two variables measured at the nominal level. The t test can be used to test the difference in means between two groups or the difference in means for one group measured at two points in time. The F test can be used to test the differences in means for more than two groups or for two or more independent variables.
Inferential statistics provide a direct test of the null hypothesis of no difference in population means. To select a critical value for a statistic, such as a t or F test, the researcher must specify the degrees of freedom, significance level, and directionality of the test (i.e., one-tailed or two-tailed). The significance level indicates the probability of a Type I error of mistakenly rejecting the null hypothesis of no difference in population means.