A researcher studying the relationship between maternal age and length of breastfeeding in a sample of 75 primiparas found a correlation of .19, which was not statistically significant at the .05 level.

Given the following circumstances, determine whether the calculated values of r are statistically significant:

a) r = .29, N = 35, ?= .01, two-tailed

b) r = .50, N = 15, ?= .05, two-tailed

c) r = .12, N = 500, ?= .05, two-tailed

d) r = .55, N = 12, ?= .05, one-tailed

e) r = .44, N = 26, ?= .01, one-tailed

For each correlation coefficient below, calculate what proportion of variance is shared by the two correlated variables:

a) r = .76

b) r = .33

c) r = .91

d) r = .14

In a random sample of 100 people, the correlation between amount of daily exercise and weight was found to be –.21. What would be the likely effect on the absolute value of the correlation coefficient under the following circumstances? (Hint: would r be greater or smaller? Why?)

The sample is restricted to people who weighed less than 180 pounds

The sample is restricted to people who get virtually no daily exercise versus those who exercise at least 30 minutes a day.

The mean sample weight is 150 pounds, and one person is added to the sample who weighs 275 pounds.

A researcher studying the relationship between maternal age and length of breastfeeding in a sample of 75 primiparas found a correlation of .19, which was not statistically significant at the .05 level. What was the estimated power of the statistical test? Conversely, what was the risk that a Type II error was committed?

Assuming in question 4 that .19 is a good estimation of the population correlation, what sample size would be needed in a replication study to achieve power = .80 at ?= .05?


 

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