The purpose of this activity is to give you guided practice in testing whether the data provide evidence of a significant linear relationship, and in verifying that the basic conditions under which the results of such a test are reliable are met.
Recall the example from the previous activity:
A method for predicting IQ as soon as possible after birth could be important for early intervention in cases such as brain abnormalities or learning disabilities. It has been thought that greater infant vocalization (for instance, more crying) is associated with higher IQ. In 1964, a study was undertaken to see if IQ at 3 years of age is associated with amount of crying at newborn age. In the study, 38 newborns were made to cry after being tapped on the foot and the number of distinct cry vocalizations within 20 seconds was counted. The subjects were followed up at 3 years of age and their IQs were measured.
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We would now like to test whether the observed (weak-to-moderate) linear relationship between cry count and IQ is significant (in other words, we would like to carry out the "t-test for the slope" for this example)
- State the appropriate hypotheses, and explain (to someone who has never studied statistics) in plain words (without using the words "significant") what is being tested.
- Verify that the general conditions that allow you to reliably use the test in 1 are met.
Comment: Note that not all the information you need is given in the problem description. In particular, no information is given about how the babies were selected for the study, which is important for assessing whether we can assume that the observations are independent. To get this information, click here and read the first couple of pages of the paper that describes the study.
- Now carry out the test.
Give the p-value of the test and state your conclusions in context.
- Choose: Stat → Regression → Simple Linear
- Select explanatory and response variables
- Press: Calculate