Reporting Traditional Statistics

The Results section should include any relevant summary statistics. For analyses with a scale dependent variable, include means, standard deviations, and sample sizes for each cell in the research design. For analyses with a nominal dependent variable (chi-square analyses), include the frequencies (counts) for each cell; there won’t be means or standard deviations because there are no scores on a scale measure.

Summary statistics are sometimes presented first in a Results section but are more typically presented after a description of each hypothesis test. If there are only two or three cells, then the summary statistics are typically presented in the text; if there are more cells, then these statistics should be displayed in a table or figure.

Reports of hypothesis tests typically begin by reiterating the hypothesis to be tested and then describing the test that was conducted, including the independent and dependent variables. The results of the hypothesis test are then presented, usually including the symbol for the statistic, the degrees of freedom, the actual value of the statistic, and, if using software, the actual p value associated with that statistic. The format for reporting this information is included after each hypothesis test in this text and is presented again in Table F-1.

Table : TABLE F.1. The Format for the Results of a Hypothesis Test There is a general format for reporting the results of hypothesis tests. The symbol for the statistic is followed by the degrees of freedom in parentheses, then the value of the test statistic, and finally the exact p value associated with that test statistic. This table presents the way that format would be implemented for several of the test statistics discussed in this text. (Note that you will only have the exact p value if you use software. If you conduct a test by hand, you may report whether the p value is greater than or less than 0.05.)
Symbol Degrees of Freedom Value of the Test Statistic Information About the Cutoff Effective Size Example
z (df) = XX, p = 0.XX d = XX z(54) = 0.60, p = 0.45, d = 0.08
t (df) = XX, p = 0.XX d = XX t(146) = 2.29, p = 0.024, d = 0.50
F (dfbetween, dfwithin) = XX, p = 0.XX R2 = XX F(2, 142) = 6.63, p = 0.002, R2 = 0.09
χ2 (df, N = XX) = XX, p = 0.XX V = XX χ2(1, N = 147) = 0.58, p = 0.447, V = 0.06
T None = XX, p = 0.XX None T = 7, p = 0.04
U None = XX, p = 0.XX None U = 19, p = 0.14

After the statistics are presented, a brief statement summarizes the results, indicating the direction of any effects. This brief statement does not draw conclusions beyond the actual finding. In the Results section, researchers do not discuss the finding in terms of the general theories in the field or in terms of its potential implications or applications (which go, appropriately enough, in the Discussion section). Researchers should present the results of all hypothesis tests that they conducted, even those in which they failed to reject the null hypothesis.

F-2

To summarize this aspect of Results sections:

The statistics for the study from How It Works in Chapter 11 that compared the mean percentages of cartoons that women and men found funny might be reported as follows:

To examine the hypothesis that women and men, on average, find different percentages of cartoons funny, we conducted an independent-samples t test. The independent variable was gender, with two levels: female and male. The dependent variable was the percentage of cartoons deemed funny. There was not a statistically significant effect of gender, t(7) = −0.03, p = 0.98; this study does not provide evidence that women (M = 82.25, SD = 17.02) and men (M = 82.60, SD = 18.13) deem, on average, different percentages of cartoons to be funny. The difference between the mean percentages for women and men is just 0.35%.