Chapter 19 – Correlation
This chapter explores positive and negative correlations.
Exercises
Exercise 19.1
Scatter plots
Have a look at the scatter plots below and select a description in terms of strength (weak, moderate, strong) and direction (positive, negative or curvilinear).
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Figure 1: strong, positive
Figure 2: moderate, negative
Figure 3: strong, curvilinear
Exercise 19.2
Calculating Pearson’s and Spearman’s correlations
You’ll need one of these data sets for this exercise
The data set in the file correlation.sav (SPSS) or correlation.xls (Excel) is for you to use to calculate Pearson’s r and Spearman’s r (two-tailed) either by hand or using SPSS or a spreadsheet programme. Copy the table below and enter, using either p = or p ≤. Don’t worry if your answer is out by a small amount as this might be due to rounding errors.
| Pearson’s r = | p = | p ≤ | |
| Spearman’s r = | p = | p ≤ |
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| Pearson’s r = | -.48 | p = 0.005 | p ≤0.01 |
| Spearman’s r = | -.492 | p = 0.004 | p ≤0.01 |
Exercise 19.3
A few questions on correlation
1. Jarrod wants to correlate scores on a general health questionnaire with the subject that students have chosen for their first degree. Why can’t he?
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First degree choice is a categorical variable.
2. Amy wants to correlate people’s scores on an anxiety questionnaire with their status – married or not married. Can she?
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Yes, she can use the point biserial correlation coefficient (though better to conduct a difference test e.g., unrelated t).
3. As the number in a sample increases the critical value required for a significant correlation with p ≤ .05 increases or decreases?
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Decreases.
In the first set of exercises for this chapter, question 2 asks you to draw the scatterplot for the maths and music data in Table 19.5. Here is a possible answer:
The maths and music score scatterplot – answer to exercise in Chapter 19.
Exercise 19.4
Have a go at this short quiz to test your understanding of correlation and identify any gaps in your knowledge.
Weblinks
Correlation
This is the link to the correlation application that lets you plot points and watch how these affect the scatter plot and regression line.
http://www.shodor.org/interactivate/activities/Regression/
You can amuse yourself for ages by looking at very high correlations between quite unrelated variables (remember the cheese consumption and strangulation in bedsheets one?) but don’t forget these are chance associations out of millions of attempts to find them:
Spurious Correlations (tylervigen.com)
A website where you can click to enter points on a scattergram and try to make the coefficient any size or direction (+/–) you like. You can also see the regression line and the residuals for each data point– see next Chapter 20:
Correlation and Regression (bfwpub.com)
To convert a correlation coefficient to a t value:
Free t-Value Calculator for Correlation Coefficients – Free Statistics Calculators (danielsoper.com)
A specialist site just giving normal distribution and z tables with the value of the y ordinate. Only needed for the biserial correlation coefficient calculation.http://academic.udayton.edu/gregelvers/psy216/tables/area.htm