Crosstabulation and x2 Analyses
The chi-square statistic is computed by summing the squared deviations [observed value ( fo) minus expected value (fe)] divided by the expected value for each cell:
χ2 = Σ[(fo − fe) 2/fe]
For every inferential statistic (this is the first of many in this book!), there are three questions that you need to ask as a researcher. The first question is, “Are you fairly certain that the difference tested by this statistic is real instead of random?” In this case, if there is a large discrepancy between the observed values and the expected values, the χ2 statistic would be large, suggesting a significant difference between observed and expected values. (“Significant difference” is statistics-speak for “fairly certain that this difference is real.”) Along with this statistic, a probability value is computed. The value of p is the probability that the difference between observed and expected values tested by the χ2 statistic is due to chance. With p < .05, it is commonly accepted that the observed values differ significantly from the expected values and that the two variables are NOT independent of each other. More complete descriptions and definitions are included in the Output section of this chapter.