Writing Statistical Results

Throughout the entire course, emphasis will be placed not on numbers and answers but on ways to communicate both descriptive and inferential statistics through writing. This is an especially beneficial exercise for students who have to create reports or even write results sections for scientific journals.   An example of this is shown below for the following research example:
      Is there a mean difference in self-confidence in mathematics at the end of the semester compared to the beginning
      of the semester for freshmen mathematics students taking PreCalculus?

Descriptive Statistics (Numerical and Graphical):

The means for scores on a test measuring self-confidence in mathematics were measuring at both the beginning and end of the semester for 139 freshmen students taking PreCalculus as shown in Table 1. The mean self-confidence score at the beginning of the semester, 33.20, does not seem much different from the mean self-confidence score taken at the end of the semester, 33.45. The standard deviation of the self-confidence scores taken at the end of the semester, 8.21, is slightly larger than the self-confidence scores taken at the beginning of the semester, 6.21. Figure 1 shows that the sample differences in self-confidence look approximately normally distributed.

Table 1
Descriptive Statistics Comparing Scores on Self-confidence in Mathematics Taken at the Beginning and End of the Semester

Figure 1. Histograms of sample difference scores for self-confidence in mathematics.

Inferential Statistics:

A dependent two-sample t-test was conducted to evaluate the hypothesis that there is a difference in the self confidence in mathematics between the end of the semester and the beginning of the semester (see Table 2). The test was not significant, t(138 df) = -.929-, p=.354. The mean for self confidence at the end of the semester (M = 33.45, SD = 8.21) was not different from them mean for self confidence at the beginning of the semester (M = 33.02, SD = 6.25).

Table 2
Results of the Two-sample Dependent t-test for Self-Confidence Measured at the Beginning and End of the Semester