Chi-square

Mass Communication Research
Chi-Square

Chi-square is a statistic used to compare categories or contrast among samples. It is appropriate only with nominal and ordinal data when sample values are independent, and it makes no assumption about normally distributed data. How do we get the statistic? Chi-square equals the observed frequencies of phenomena minus the expected or hypothesized frequencies, squared, then divided by the expected frequencies.

The chi-square statistic is a tool we can use while conducting "goodness-of-fit" tests or contingency table analysis.

Goodness of Fit

Let's say we have taken a random sample of the student population. How close is our sample to the actual population? We can call the registrar and find out the exact percentages of freshmen, sophomores, juniors and seniors attending UT this semester. Then we can compare our sample distribution to the actual sample distribution to find out if the proportions of freshmen, sophomores, juniors and seniors are significantly different. If they are not significantly different, we can say that the sample passes a "goodness of fit test."

The goodness-of-fit test can be used to test the null hypothesis that the population distribution from which a data sample is drawn is the same as the hypothesized distribution. In other words, researchers can compare observed frequencies of a phenomenon with the expected frequencies. Differences in observed frequencies are significant if the chi-square value exceeds the value on the chi-square value table.

The idea is to test the independence of the variables under study, to decide whether the variation of the mean scores are not random, and whether the random distribution is different than what would be observed by chance.

Assumptions:

* The sample values are independently distributed.

* The samples are grouped into exhaustive and mutually exclusive categories.

* The number of sample values in each category is recorded.

* The expected distribution is specified in advance so observations appearing in each category can be calculated without reference to the sample values.

Limitations

* Chi-square is a nonparametric statistical procedure, so the variables must be measured at the nominal or ordinal level.

* Because the chi-square distribution is sharply skewed for small samples, type II error may occur, i.e. small samples may not produce significant results in cases that could have yielded significant results if a larger sample had been used.

Chi-Square test for Independence

Say you conducted a survey of college students to test their attitudes on press freedom issues in the wake of Michael Jackson's death. You wanted to know whether students favor restraints on the press in pursuing stories about celebrities. You're also interested if there's a statistically significant difference between communication students and other students on campus, i.e. you want to find out if students' attitudes toward restraints on the press depends on their major. If the Chi-Square test for independence is significant, we would say that student's attitudes toward restraints on the press depend on their major. If the test is not significant, we would say that the two variables are independent.

Contingency table analysis, another nonparametric statistical procedure, will allow us to test for significant differences between groups by using a chi-square test in SPSS, and then generate a crosstab table to graphically show how the groups differ in their attitudes about press freedom. A cross-tabulation presents tabular data in frequencies and percentages. Tables organize data into an easy-to-read, convenient form for statistical analysis. It is used to test the difference between two or more variables simultaneously.

Interpretation

To interpret chi-square, it's important to set up the crosstabs correctly. You want the independent variable to be in columns and the dependent variable to be in rows. Then you will be able to correctly interpret chi-square by comparing column percentages across rows. This all sounds complicated, but as you'll see in the lab exercise, the SPSS statistical package makes it easy.

If you don't understand something in this Web note, please e-mail Dr. Sitton.

©M. Mark Miller & Ronald W. Sitton 2009
Revised 092811 — http://www.uamont.edu/FacultyWeb/sitton/crz/mrea/chi-square.html