Interpreting Correlations (please use the attached document, bold the questions
ID: 3455807 • Letter: I
Question
Interpreting Correlations (please use the attached document, bold the questions and include your answers in non-bolded font)
A statistics instructor is interested in examining the relationship between students’ level of statistics anxiety and their academic self-efficacy and statistics performance. A class of N = 10 students was asked to respond to a self-efficacy scale and an anxiety scale. Each student’s average statistics exam score was also recorded.
The results are as follows:
EFFICACY
ANXIETY
STATS EXAM
EFFICACY
Pearson Correlation
Sig. (2-tailed)
N
1.00
.000
10
-.617
.057
10
.888**
.001
10
ANXIETY
Pearson Correlation
Sig. (2-tailed)
N
-.617
.057
10
1.00
.000
10
-.661*
.038
10
STATS EXAM
Pearson Correlation
Sig. (2-tailed)
N
.888**
.001
10
-.661*
.038
10
1.00
.000
10
a. Explain what is meant by a correlation coefficient using one of the correlations as an example.
b. Study the table and comment on the patterns of results in terms of which variables are relatively strongly correlated and which are not very strongly correlated.
c. Comment on the limitations of making conclusions about direction of causality based on these data. In other words, discuss the issue of making cause-effect statements using correlations.
EFFICACY
ANXIETY
STATS EXAM
EFFICACY
Pearson Correlation
Sig. (2-tailed)
N
1.00
.000
10
-.617
.057
10
.888**
.001
10
ANXIETY
Pearson Correlation
Sig. (2-tailed)
N
-.617
.057
10
1.00
.000
10
-.661*
.038
10
STATS EXAM
Pearson Correlation
Sig. (2-tailed)
N
.888**
.001
10
-.661*
.038
10
1.00
.000
10
Explanation / Answer
a. Correlation coefficient is a statistic used to find how strong a relationship is between data. The formulas return a value between -1 and 1, where a value 1 indicates a strong positive relationship, -1 indicates a strong negative relationship and a result of zero indicates no relationship at all. In the table above, the correlation between self efficacy and statistics exam performance is 0.88, indicating a string positive relationship between the variables. A positive relationship implies the the increase in one variable is accompanied by a corresponding increase in the other.
b. From the table, it appears that self efficacy and statistics exam performances are strongly positively correlated. Whereas, there is a moderate negative correlation between anxiety and statistics performance, and anxiety and self-efficacy.
c. The values derived from correlation coefficient simply indicate the degree and direction of relationship between two variables and whether the change in one variable is accompanied by the change in another variable. It makes no inferences about cause and effect relationships.
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