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14.10: Correlation Exercises

  • Page ID
    22157
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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
    Scatterplot showing weak relationship but that generally goes up and to the right.
    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.


    14.10: Correlation Exercises is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Michelle Oja.

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