These study tips are designed to clarify key points and help you to avoid errors that students commonly make. Review the Tips for Success as you study each chapter and review them again after you have studied each chapter.
- This chapter assumes you have a solid command of hypothesis testing. We recommend that you review Chapter 1 material before reading this chapter.
- Notice that in the chi squared formula that, for each category, you first divide the squared difference between observed and expected frequencies by the expected frequency, and then you sum the resulting values for all the categories. This is a slightly different procedure than you are used to from previous chapters (in which you often first summed a series of squared values in the numerator and then divided by a denominator value), so be sure to follow the formula carefully.
- It is important not to be confused by terminology here. The comparison distribution is the distribution to which we compare the number that summarizes the whole pattern of the result. With a t test, this number is the t score and we use a t distribution. With an analysis of variance, it is the F ratio and we use an F distribution. Accordingly, with a chi-squared test, our comparison distribution is a distribution of the chi-squared statistic. This can be confusing because when preparing to use the chi-square distribution, you compare a distribution of observed frequencies to a distribution of expected frequencies. Yet the distribution of expected frequencies is not a comparison distribution in the sense that we use this term in Step {2} of hypothesis testing.
- Note that in the example on p. 552, that the expected frequencies are figured based on what would be expected in the U. S. population. This is quite different from the situations we have considered before where the expected frequencies were based on an even division.
- Always ensure that you have the same number of expected frequencies as observed frequencies.
- For example, with a 2 x 3 contingency table, there will be 6 observed frequencies and 6 corresponding expected frequencies.
- As a check on your arithmetic, it is a good idea to make sure that the expected and observed frequencies add up to the same row and column totals.
