One common way to understand test scores is to compare them to the scores from a sample of people representing the larger target population. For instance, if you administered a test of math skills to a random sample of adults in the United States, you could find the average, or mean, score. This would make your test more useful because anyone who completed it could see whether his or her score was above the population average, about average compared to the population, or below the population average with respect to math ability. You could also compute the standard deviation of scores in your sample. This would tell you how far, on average, the scores are (or deviate) from the mean (i.e., how spread out they are). Standard deviation scores are used to create standardized scores, which can be used to show exactly how far above or below the mean any person’s score is in standard deviation units (i.e., a score that is 1 standard deviation above the mean has a standard score, or z-score, of 1). For example, it can be used to provide a precise location of any one individual’s math score compared to the overall population. Closely related to standard deviation is variance, which is the squared standard deviation; or more accurately, the mean of the squared deviation scores. Though not an intuitively useful number on its own, variance is used in many statistical procedures.

Correlation is another statistical concept that is crucial in psychometrics. Correlation tells you the strength and direction of the relationship between two variables, such as IQ and job performance. This strength, or degree, can range from -1.00 to +1.00, with 0 indicating no relationship.

For this Knowledge Assessment, you use SPSS to calculate the mean, standard deviation, and variance of two variables and also to compute the correlation coefficient between the two variables in this week’s dataset in the Learning Resources. To begin, open SPSS, click on File>Open>Data and open the dataset.

The data file was collected over the Internet and shows the responses of 1,146 U.S. residents who answered questions about themselves and their spouses or romantic partners. You will complete calculations using the variables INC1, the participant’s annual income, and INC2, the partner or spouse’s annual income.

Question 1

Find the mean income for partner or spouse. Click ANALYZE>DESCRIPTIVE STATISTICS>DESCRIPTIVES. Move INC2 into the variable box and click on “OK.” The mean partner or spouse income is:

Question 2

Find the standard deviation of income for partner or spouse. You will see it as part of the output for Question 1. The standard deviation of partner or spouse income is:

Question 3

The variance of participant income is:

Question 4

Find the correlation between participant income and spouse income. Click on ANALYZE>CORRELATE>BIVARIATE. Move INC1 and INC2 into the variable box and click on “OK.” The correlation is: