14.10: Correlation Exercises

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Exercise \(\PageIndex{1}\)

What does a correlation assess?

Answer: Correlations assess the strength and direction of a linear relationship between two quantitative variables.

Exercise \(\PageIndex{2}\)

What sort of relation is displayed in the scatterplot in Figure \(\PageIndex{1}\) below?

Scatterplot with weak relation generally going up and to the right. — Figure \(\PageIndex{1}\): Sample Scatterplot. (CC-BY-NC-SA Foster et al. from An Introduction to Psychological Statistics)

Answer: Strong, positive, linear relation

Exercise \(\PageIndex{3}\)

Create a scatterplot from the data from Table \(\PageIndex{1}\).

Table \(\PageIndex{1}\)- Raw Data
Hours Studying	Overall Class Performance
0.62	2.02
1.50	4.62
0.34	2.60
0.97	1.59
3.54	4.67
0.69	2.52
1.53	2.28
0.32	1.68
1.94	2.50
1.25	4.04
1.42	2.63
3.07	3.53
3.99	3.90
1.73	2.75
1.9	2.95

Answer: Figure \(\PageIndex{2}\): Scatterplot of data from Table \(\PageIndex{1}\). (CC-BY-NC-SA Foster et al. from An Introduction to Psychological Statistics)

Exercise \(\PageIndex{4}\)

Using the data from Table \(\PageIndex{1}\), test for a statistically significant relation between the variables.

Answer

Step 1:

Research Hypothesis: “There is a positive linear relation between time spent studying and overall performance in class.”

Null Hypothesis “There is no liner relation between time spent studying and overall performance in class.”

Step 2: \(df = 15 – 2 = 13, \alpha = 0.05, r_{Crit}= 0.514\).

Step 3: Using the Sum of Products table, you should find: \(\overline{X_{HS}} = 1.65, \overline{X_{OCP}}= 2.95, r = 0.65\). [Your means might differ due to rounding differences.

Step 4: Obtained statistic is greater than critical value, reject \(H_0\). There is a statistically significant, strong, positive relation between time spent studying (\(\overline{X_{HS}} = 1.65) and performance in class (\overline{X_{OCP}}= 2.95), \(r(13) = 0.65, p < .05\). This supports the research hypothesis.