Power and Correlation Worksheet



Correlation Worksheet

1. Download the Optimal Balance data from the course website. Conduct an item analysis on the 18 items. Remove items until you have maximized your Cronbach’s alpha.

Imagine if you were using this 18-item scale in your research. A reviewer expresses concern over the low reliability of the 18 items. You proceed to delete items to maximize alpha. What are your thoughts on this process? What do you think the author of the 18-item scale would say about what you have done? (summarize some of our discussion from class, even though I could not give definite advice on this issue)

2. Go to Philip B. Stark’s statistics “Correlation and Regression” online demo (). A correlation program should run after a few moments. In this program, set the sample size to some adequate number (e.g., 100 or 200) and then toggle on the “Regression Line.” Next, increase the correlation from -1 to +1. As the correlation increases from -1 to +1, what do you notice about the slope of the regression line? At the same time, what do you notice about the spread of the data about the regression line? Which is more important for determining the magnitude of the correlation coefficient: the slope of the regression line, or the spread of the data about the line (or are both important factors)?

3. Suppose a researcher hypothesizes a positive linear relationship between extraversion and intelligence; specifically, extraverts will be more likely to score higher on an IQ test than introverts. The data follow:

IQ (WAIS) I-E (int/ext; high score = more introversion)

100 75

104 56

100 68

108 53

96 41

98 48

115 35

111 50

101 65

90 34

108 50

a. Enter the data into SPSS and obtain the correlation.

b. Do the results support the researcher’s hypothesis?

c. Create a scatterplot of the data. How would you interpret the findings?

4. Consider the two variables below:

Sex Handedness

(0 = F, 1 = M) (0 = R, 1 = Left)

1 0

1 1

1 1

0 0

1 0

1 0

0 1

1 1

0 1

1 0

0 1

1 1

1 0

a. Compute Pearson’s correlation in SPSS.

b. Conduct an independent samples t-test on the data above in SPSS. Set up Sex as the grouping variable and Handedness as the dependent variable. Compute eta-squared for the observed t-value and then take the square root of eta-squared. What do you notice about this computed value? How does the p-value for your t-test compare to the p-value from the correlation?

c. What have you learned about these two statistical tests in this problem?

5. Consider the following correlation matrix:

| |Extraversion |Neuroticism |Agreeableness |

|Extraversion |1 |0.15 |.17 |

|Neuroticism | |1 |-.61 |

|Agreeableness | | |1 |

All correlations based on n=50.

a. Suppose a researcher wishes to use the correlation between Extraversion and Agreeableness as an estimate of the true population correlation around which to compute power for her upcoming study. How many participants will she need in her study to achieve an estimated power of .90 (alpha = .05)? Use GPower to find the answer.

b. Suppose another researcher wishes to compare the correlation between Extraversion and Neuroticism in his study to the correlation between these same two variables above. He tested 105 participants in his study and obtained a correlation of .33. Did his correlation differ significantly from the correlation reported above (alpha = .05)?

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