Inferential Statistics in SPSS: Writing About Your Outputs

One of the goals of this book is to help you write a research report or thesis using the outputs. Thus, we have provided an example later that could be two paragraphs from a research paper based on the expanded HSB data used in the assignments in this book.

Before demonstrating how you might write about the results of research questions 1 and 2, we would like to make several important points. There are several books listed in the bibliography that will help you write a research paper and make appropriate tables. Note especially the APA manual (2010), Nicol and Pexman (2010), and Morgan, Reichert, and Harrison (2002). The example that follows and the samples provided in each output interpretation section give only one way to write about outputs. There are other good ways.

Based on your outputs, you should first describe descriptive statistics about the demographics (e.g., gender, age, ethnicity) of the participants in your sample in your Method section. You should add to any literature-based evidence about the reliability and validity of your measures or instruments. You also should include in your report whether statistical assumptions of the inferential statistics were met or how adjustments were made.

The Results section includes a description (but not a discussion) of the findings in words and tables. Your Results section should include the following numbers about each statistically significant finding (in a table or the text):

1. The value of the statistic (e.g., t = 2.05 or r = .30) to two decimals.
2. The degrees of freedom (often in parenthesis) and for chi-square the N(e.g., X = 5.26, df = 2, N = 49).
3. The p or Sig. value (e.g., p = .048), preferably the exact p value to 2 or 3 decimal places.
4. If the statistic is significant, the direction of the finding (e.g., by showing which mean is larger or the sign of the correlation.)
5. An index of effect size from either the d family or the r family, and, if the statistic is significant, a statement about the relative size of the “effect.” (See Table 6.5 and accompanying text.)

When not shown in a table, the prior information should be provided in the text, as shown later. In addition to the numerical information, describe your significant results in words, including the variables related, the direction of the finding, and an interpretive statement about the size/strength of the effect based on Table 6.5 or, better still, based on the effect sizes found in the literature on your topic. Realize that our effect size terms are only rough estimates of the magnitude of the “effect” based on what is typical in the behavioral sciences; they are not necessarily applicable to your topic.

If your paper includes a table, it is usually not necessary or advisable to include all the details about the value of the statistic, degrees of freedom, and p in the text because they are in the table. If you have a table, you must refer to it by number (e.g., Table 1) in the text and describe the main points, but don’t repeat all of it or the table is not necessary. You can mention relationships that are not significant, but do not discuss, in the text, the direction of the finding or interpret the meaning of nonsignificant findings because the results could well be due to chance. Do provide effect sizes or at least the information (e.g., ns, means, and standard deviations) necessary for other researchers to compute the effect size, in case your study is included in a future meta­analysis.

The Discussion chapter puts the findings in context in regard to the research literature, theory, and the purposes of the study. You should also discuss limitations of the study and attempt to explain why the results turned out the way they did.

An Example of How to Write Results

Based on what we reported earlier about the results of research questions 1 and 2, we might make the following statements in our Results section:

Results

For research question 1, there was a statistically significant difference between male and female students on math achievement, t(48) = 2.05. p = .04, d = .33. Males (M = 14.70) scored higher than females (M = 12.70), and the effect size was small to medium according to Cohen’s (1988) guidelines. The confidence interval for the difference between the means was .50 to 6.50, indicating that the difference could be as little as half a point, which is probably not a practically important difference, but also could be as large as six and one half points.

For research question 2, there was a statistically significant positive correlation between math courses taken and math achievement, r (48) = .30, p = .03. The positive correlation means that, in general, students who took more math courses tended to score high on the math achievement test and students who did not take many math courses scored low on math achievement. The effect size of r = .30 is considered medium or typical.

We present examples of how to write about the results of each statistic that you compute in the appropriate chapter.

Source: Morgan George A, Leech Nancy L., Gloeckner Gene W., Barrett Karen C.

(2012), IBM SPSS for Introductory Statistics: Use and Interpretation, Routledge; 5th edition; download Datasets and Materials.