What is Chi-Squared Analysis?
Chi-squared (or X2) analysis is used to compare two or more frequencies to investigate the probability that their values depart from what would be expected by chance alone. Chi-squared is most often used in one-way or two-way X2 analyses. One-way X2 is used to compare the frequencies of different levels of a single variable. So in a study of 100 randomly selected high school students from each of five prefectures in Japan, the frequency of students who went on to university could be studied using chi-squared analysis to see if the frequencies are significantly different from what would be expected by chance alone (for more on chi-squared analysis, see Brown 1988, 2001, or Hatch & Lazaraton, 1991). I will focus here on two-way X2 analyses, like that in the Shimura example you refer to in your question. Shimura (2003) shows three contingency tables in grey shading (see Example 2), one each for 1st Advice, 2nd Advice, and 3rd Advice. In each contingency table, she compares frequencies in
