Question

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.

Answer 1

Solution:

From the given data we get the,

a. Explain what is meant by a correlation coefficient using one of the correlations as an example.
Correlation coefficient helps us to understand the strength and direction of relationship of between two variables.

The correlation coefficient takes a value between 0 and 1 and it can have a positive or negative sign depending on the relationship.

Higher the value, stronger is the relationship.
A positive sign indicates that as one variables increase or decreases, the other variable also increase or decreases in the same proportion.

A negative sign indicates that as one variables increases the other decreases and vice versa.

The correlation between efficacy and anxiety is -0.617. Hence they are moderately correlated with each other. The negative sign indicates an inverse relationship, that is as efficacy increases, anxiety decreases.

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.

efficacy and stats exam, as strong positively correlated

anxiety is moderately negatively correlated with efficacy and stats exam.

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.

correlation cannot be equated to causation. Since two variable are strongly correlated , we cannot conclude that one causes the other. There could be many factor that may bring about the effect understudy.

correlation only measured the behavior of one variable with respect to another variable.
Causation is one event cause the other event to happen.

Hence we cannot make cause effect statements from correlation.

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