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Chi-square is used when the data come in the form of counts or frequencies and each participant provides only one entry for the table of data (i.e., gets counted once only). The statistic is χ² (pronounced "ky" as in "sky" square). This statistic, χ² , must be greater than or equal to the critical value to be statistically significant. The information you need to provide to enable someone to check the significance of your obtained value of χ² is the degrees of freedom. You should also report the total number of observations.
Example
In an observational study to examine whether there is an association between gender of driver (male or female) and whether or not the driver is breaking the speed limit on a stretch of urban road (coded as speeding or not speeding), one hundred drivers were observed, with each driver being observed once only. These data have 1 degree of freedom, and the obtained value of χ² = 10.83 has an associated probability of p = .001.
These findings are reported succinctly in Section 4.6.1 of the book.
Has each participant been counted once only? Do you have enough participants? (If too many of your cells have expected frequencies of five or less, then the test will be invalid.) If you employ the correction for continuity, then mention this. In some statistical software packages chi-square is called Pearson's chi-square.
Rho is a nonparametric measure of the correlation between scores on two variables. The statistic is rS (pronounced "rho"). This statistic, rS , must be greater than or equal to the critical value to be statistically significant. The information you need to provide to enable someone to check rS is the number of participants.
In a study relating a measure of mood (higher ratings indicating more positive mood) to ratings of the mean attractiveness of a set of photographs of members of the opposite sex (higher ratings indicating greater attractiveness), using 40 participants, the obtained value of rS = .48 with associated probability = .002 (two-tailed test).
These findings are reported succinctly in Section 4.6.2 of the book.
Is the correlation in the direction that you predicted? If you have lots of participants, even relatively small correlations can be statistically significant, so it is important to focus on the size of the correlation and not just whether or not it is statistically significant. Are there lots of correlations to report? If so, consider putting them in a table (called a correlation matrix ). If two or more participants have the same score on the same variable they will have tied ranks. Under these circumstances report the version of rho corrected for ties.
Tau is a nonparametric measure of the correlation between scores on two variables. The statistic is (pronounced "tow" as in cow ). This statistic, must be greater than or equal to the critical value to be statistically significant. The information you need to provide to enable someone to check is the number of participants.
Kendall's tau can be reported in the same way as Spearman's rho (see Section 4.6.2 of the book).
Unless you are calculating the statistic by hand, Kendall's tau raises the same issues as Spearman's rho. See section B2.2 of this Web site for more details. If you are calculating tau by hand, then you use your sample size to look up the statistic in probability tables. (There can be some exceptions to this, so check your statistics textbook for details.)
This parametric measure of the correlation between scores on two variables is the one you will see most commonly used. The statistic is r and it must be greater than or equal to the critical value to be statistically significant. The information you need to provide to enable someone to check r is the degrees of freedom, given by the N of observations minus 2.
In a study relating age to ratings of the mean attractiveness of a set of photographs of members of the opposite sex (higher ratings indicating greater attractiveness), 40 participants were used. The degrees of freedom thus = 40-2 = 38. With degrees of freedom = 38, the obtained value of r = -.37 has an associated probability = .02 (two-tailed test).
These findings are reported succinctly in Section 4.6.3 of the book.
These are the same as for Spearman's rho. However, with Pearson's r a very useful statistic is the squared value of r (called r2 funnily enough). This value tells you the proportion of the variance that the two variables have in common. The more the variables are correlated, the more variance they will share. This tells you how strong the relationship is. For instance, with a correlation of r = .37,
r2 = .14 ( r2 = .37 x .37 = .14). In this example, therefore, the variables age and ratings of attractiveness have 14 percent of the variance in common. The relationship is thus perhaps rather weaker or smaller than you might have thought, given r = .37. It is always worth reporting r2 for statistically significant values of r as this will help to discourage you from overestimating the size of the relationship. In this example it would be useful, therefore, to add a statement pointing out that the variables had 14% of the variance in common and that despite being statistically significant the relationship was thus rather weak. (See Section 12.3.1 of the book for more on r2 .) In some tables of significance of r you may be asked for the number of pairs of observations rather than the degrees of freedom, so watch out for this if you are looking up r in tables. |
