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Chapter 9 Questions
Complete the following questions. The questions may include pictures or graphics to illustrate or aid in solving the problem. You can check your answer by clicking View Answer. If the question is unclear, confusing, or if you need further clarification, send me an email.
1. Imagine that we wanted to know whether height and weight were more closely related to one another than age and IQ. Below are the measures of height (in inches), weight (in pounds), age (in years), and IQ for ten subjects. Calculate the covariance for height and weight and compare this with the covariance for age and IQ.
Answer
2. Define covariance. Why should we be cautious in comparing covariances across samples with different measurement scales?
Answer
Covariance: Measure of the degree to which two scores vary together about their respective means. Covariance is dependent upon the scales of measurement used in its calculation. Scales with larger standard deviations will result in larger covariances.
3. For the data above, calculate the correlation coefficient for height and weight and compare this with the correlation coefficient for age and IQ.
Answer
4. Define the correlation coefficient. What is it about the correlation coefficient which allows us to use it for comparisons of samples with different measurement scales?
Answer
Correlation coefficient: Standardized covariance. It allows us to compare correlations across samples because the covariance of the samples is standardized (divided by the products of the two samples' standard deviations). Or, in other words, the covariance is transformed from the original scales of measurement to standard units.