Overview of Reporting Statistics

In Chapter 11, How It Works 11.1, we described a study about gender differences in humor (Azim, Mobbs, Jo, Menon, & Reiss, 2005). Let’s recap the results of the analyses and then use this information to report statistics in the Methods and Results sections of a paper written in the style of the American Psychological Association (APA). In the analyses of the humor data, we used fictional data that had the same means as the actual study by Azim and colleagues. We used the following raw data:

• Percentage of cartoons labeled as “funny”
• Women: 84, 97, 58, 90
• Men: 88, 90, 52, 97, 86

We conducted an independent-samples t test on these data and found a test statistic, t, of −0.03. This test statistic was not beyond the cutoff, so we failed to reject the null hypothesis. We cannot conclude that men and women, on average, find different percentages of the cartoons to be funny; we can only conclude that this study did not provide evidence that women and men are different on this variable.

The statistics for this test, as reported in a journal article, would include the symbol for the statistic, the degrees of freedom, the value of the test statistic, and, for statistics calculated by hand, whether the p value associated with the test statistic was less than or greater than the cutoff p level of 0.05. In the humor example, the statistics would read:

(Note that when we conducted this hypothesis test using SPSS, we got an exact p value of 0.977, so we would say p = 0.98 instead of p > 0.05 if we had used software.) In addition to the statistics, we also would report the means and standard deviations for the two samples:

We can also calculate that the percentage difference between women and men is 82.25 − 82.60 = −0.35. There is just a 0.35% difference between women and men.

In How It Works 11.2, we calculated a confidence interval for these data. The 95% confidence interval, centered around the difference between means of 82.25 − 82.60 = −0.35, is [−27.88, 27.18].

In How It Works 11.3, we calculated the effect size for this study, a Cohen’s d of −0.02. We now have sufficient information to write up these findings.

There are three topics to consider when reporting statistics, all covered in various sections of the Publication Manual of the American Psychological Association (APA, 2010):

1. In the Methods section, we justify the study by including information about the statistical power, reliability, and validity of any measures we used.
2. In the Results section, we report the traditional statistics, which include any relevant descriptive statistics and often the results of hypothesis testing.
3. In the Results section, we also report the newer statistics that are now required by the APA, including effect sizes and confidence intervals (APA, 2010).