Based on the responses to a questionnaire completed by 232 Taiwanese undergraduate students, Chiu, Hong & Chiu (2016) looked at the relationship between the students' psychological characteristics and the types of lies they told. The results table below gives the value of the Pearson correlation coefficient (r) calculated for each relationship. This is called a correlation matrix. Notice that the rows and columns have identical labels, which correspond to the variables included in the study. (The abbreviations for the variables are explained below the table.) To find the relationship between any two variables, find one variable listed in the rows, and the other listed in the columns and then find where that row and column intersect. The number you will find there is the correlation coefficient, the "Pearson r."
Notice the diagonal line of "1"s. This occurs where the row and column indicate the same variable. For example, row 5 is "anxiety" and so is column 5. Of course, the correlation between "anxiety" and "anxiety" is positive 1 -- a perfect positive correlation because they are the same variable! Above that diagonal, the cells are left blank because they would be an exact mirror image of the values below the diagonal. For example, the correlation between anxiety and self-esteem is the same as the correlation between self-esteem and anxiety!
Choose one of the correlations from the table (not "1") and answer the questions that follow based on that correlation.
Table 1. Correlations between psychological characteristics (1-6) and day-to-day lying behaviors(7-11). (Chiu, et al., 2014)
1 S 2 SE 3 IF 4 N 5 A 6 MC 7 EL 8 AL 9 CL 10 NL 11 SL
1 S 1
2 SE .315 1
3 IF -.592 -.376 1
4 N -.453 -.222 .639 1
5 A -.491 -.260 .672 .794 1
6 MC -.531 -.267 .688 .663 .765 1
7 EL -.095 .057 .038 .148 .107 .103 1
8 AL -.100 .088 -.001 .157 .070 .083 .655 1
9 CL -.187 .017 .163 .238 .209 .176 .557 .673 1
10 NL -.084 -.077 .072 .176 .215 .145 .414 .482 .483 1
11 SL -.067 .056 .035 .123 .125 .058 .533 .644 .571 .583 1
Psychological characteristics (See column and row labels):
S= self-esteem
SE =- social extraversion
IF = feeling of inferiority
N= nervousness
A= anxiety
MC = melancholy
Types of lies told (See column and row labels):
EL = excuse lie
AL = absenteeism lie
CL = cheating lie
NL = negative lie
SL = spending lie
1. What is the calculated value of the test statistic (Pearson 4)? Notice that you do not have to calculate it; the correlations between any two variables included in the study are provided in the table.
2. Using the statistical calculator at this link https://www.socscistatistics.com/pvalues/pearsondistribution.aspx, what is the p-value for this r? Note that this particular calculator asks for N, not df. But, you will use the df (N-2) to report the results in "APA" format.
3. Is the correlation statistically significant?
4. From the online calculator, click on the box that says "How to report Pearson's r (APA)". Then write the results here in "APA" format:
5. Based on Cohen's conventions for correlations, is the effect small, medium, or large?
6. In one or two sentences, summarize the finding related to this r. (Include in your summary the two variables involved.)
