Introduction to the Chi-Square Goodness-of-Fit Test
The Chi-Square (x2) Goodness-of-Fit Test: What It Is and What It Does
The chi-square (x2) goodness-of-fit test is used for comparing categorical information against what we would expect based on previous knowledge. As such, it tests what are called observed frequencies (the frequency with which participants fall into a category) against expected frequencies (the frequency expected in a category if the sample data represent the population). It is a non-directional test, meaning that the alternative hypothesis is neither one-tailed nor two-tailed. The alternative hypothesis for an x2 goodness of- fit test is that the observed data do not fit the expected frequencies for the population, and the null hypothesis is that they do fit the expected frequencies for the population. There is no conventional way to write these hypotheses in symbols like statistical tests. To illustrate the x2 goodness-of-fit test, let’s look at a situation in which its use would be appropriate.
Suppose that a researcher is interested in determining whether the teenage pregnancy rate at a particular high school is different from the rate statewide. Assume that the rate statewide is 17%. A random sample of 80 female students is selected from the target high school. Seven of the students are either pregnant now or have been pregnant previously. The x2 goodness-of-fit test measures the observed frequencies against the expected frequencies. The frequencies observed represent the number of high school females in the sample of 80 who were pregnant versus not pregnant. The expected frequencies represent what we would expect based on chance, given what is known about the population. In this case, we would expect 17% of the females to be pregnant because this is the rate statewide. If we take 17% of 80 (.17 x 80 = 14), we would expect 14 of the students to be pregnant. By the same token, we would expect 83% of the students (.83 x 80 = 66) to be not pregnant. If the calculated expected frequencies
The chi-square (x2) goodness-of-fit test is used for comparing categorical information against what we would expect based on previous knowledge. As such, it tests what are called observed frequencies (the frequency with which participants fall into a category) against expected frequencies (the frequency expected in a category if the sample data represent the population). It is a non-directional test, meaning that the alternative hypothesis is neither one-tailed nor two-tailed. The alternative hypothesis for an x2 goodness of- fit test is that the observed data do not fit the expected frequencies for the population, and the null hypothesis is that they do fit the expected frequencies for the population. There is no conventional way to write these hypotheses in symbols like statistical tests. To illustrate the x2 goodness-of-fit test, let’s look at a situation in which its use would be appropriate.
Suppose that a researcher is interested in determining whether the teenage pregnancy rate at a particular high school is different from the rate statewide. Assume that the rate statewide is 17%. A random sample of 80 female students is selected from the target high school. Seven of the students are either pregnant now or have been pregnant previously. The x2 goodness-of-fit test measures the observed frequencies against the expected frequencies. The frequencies observed represent the number of high school females in the sample of 80 who were pregnant versus not pregnant. The expected frequencies represent what we would expect based on chance, given what is known about the population. In this case, we would expect 17% of the females to be pregnant because this is the rate statewide. If we take 17% of 80 (.17 x 80 = 14), we would expect 14 of the students to be pregnant. By the same token, we would expect 83% of the students (.83 x 80 = 66) to be not pregnant. If the calculated expected frequencies