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Example Test of Pearson’s

27 November, 2015 - 17:13

Imagine that the health psychologist is interested in the correlation between people’s calorie estimates and their weight. He has no expectation about the direction of the relationship, so he decides to conduct a two-tailed test. He computes the correlation for a sample of 22 college students and finds that Pearson’s is −.21. The statistical software he uses tells him that the value is .348. It is greater than .05, so he retains the null hypothesis and concludes that there is no relationship between people’s calorie estimates and their weight. If he were to compute Pearson’s rby hand, he could look at Table 13.5 and see that the critical value for 22 − 2 = 20 degrees of freedom is .444. The fact that Pearson’s for the sample is less extreme than this critical value tells him that the value is greater than .05 and that he should retain the null hypothesis.

KEY TAKEAWAYS

  • To compare two means, the most common null hypothesis test is the t test. The one-sample t test is used for comparing one sample mean with a hypothetical population mean of interest, the dependent- samples ttest is used to compare two means in a within-subjects design, and the independent- samples ttest is used to compare two means in a between-subjects design.
  • To compare more than two means, the most common null hypothesis test is the analysis of variance (ANOVA). The one-way ANOVA is used for between-subjects designs with one independent variable, the repeated-measures ANOVA is used for within-subjects designs, and the factorial ANOVA is used for factorial designs.
  • A null hypothesis test of Pearson’s ris used to compare a sample value of Pearson’s rwith a hypothetical population value of 0.

EXERCISES

  1. Practice: Use one of the online tools, Excel, or SPSS to reproduce the one-sample t test, dependent- samples t test, independent-samples t test, and one-way ANOVA for the four sets of calorie estimation data presented in this section.
  2. Practice: A sample of 25 college students rated their friendliness on a scale of 1 (MucLoweThan Average) to 7 (MucHigheThaAverage). Their mean rating was 5.30 with a standard deviation of 1.50. Conduct a one-sample ttest comparing their mean rating with a hypothetical mean rating of 4 (Average). The question is whether college students have a tendency to rate themselves as friendlier than average.
  3. Practice: Decide whether each of the following Pearson’s rvalues is statistically significant for both a one-tailed and a two-tailed test. (a) The correlation between height and IQ is +.13 in a sample of 35. (b) For a sample of 88 college students, the correlation between how disgusted they felt and the harshness of their moral judgments was +.23. (c) The correlation between the number of daily hassles and positive mood is −.43 for a sample of 30 middle-aged adults.