Composite Score

The goal of using several items to measure a construct is to produce a single composite score that is more reliable than any single item in your measure. In the current example, we want a single composite score for the 11 BSS items. Typically, researchers do this by computing the mean of the items. To do this in SPSS, select Transform → Compute Variable.... In the dialog that opens, type "BSS" into the "Target Variable" box. In the "Numeric Expression" box, type the word "mean" and then type an open parenthesis. Inside that parenthesis, put a comma-separated list of the variables that you want to average together:

Note that you are using the reverse-scored variables (bss02r, bss03r, and bss07r) and not their original values. Press "OK" to compute the mean. When you’re done, look in the Data Window and scroll all the way to the right. You should see a new variable called "BSS":

That new variable is the composite score. It is a single variable that will take the place of the 11 individual BSS items and is more reliable (has less error) than any of the original items. It’s a good idea to take a look at this new mean score to see if it has any extremely high or low values and whether it is approximately normally distributed, with most scores in the middle and fewer scores at the high and low ends. An easy to way check this is with a stem-and-leaf plot. To make a stem-and-leaf plot in SPSS, select Analyze → Descriptive Statistics → Explore:

Put "BSS" into the "Dependent List" and press "OK". You should get this:

This plot shows you every value for BSS. At the top, the "3.00 Extremes (=<2.4)" indicates that there were 3 people with extremely low scores (less than 2.4). In the second row, one person got a 2.4. In the third row, one person got a 2.6 and one person got a 2.8. You can see that the most frequently-occurring scores were between 4.0 and 4.4, and the highest score was a 5.8. To provide a more global evaluation, take a step back and look at the shape of the stem-and-leaf plot. The scores are roughly centered around 4, and they have a longer tail at the low end of scores than at the high end. Also, there don't appear to be any ridiculously extreme scores and they appear to be on the 1-7 scale that we would expect. Now make a stem-and-leaf plot for item bss07.

You should get:

All those zeroes indicate that there aren't any decimals, just whole numbers. That is the stem-and-leaf plot for item #7 of the BSS. The shape of that plot indicates that the scores are piling up at the low end, which means that most people are disagreeing with this item. The most popular response is a 2.

You would typically not report a stem-and-leaf plot in a research report, but it is a very good thing to look at before you begin data analysis to make sure that your variables do not have any strange values. A more common element to include in a report would be the mean and standard deviation of your new variable. To get those, we’ll use descriptive statistics.

Descriptive Statistics

If you go to the Output Window, where the stem-and-leaf plots were, and scroll up to just above the stem-and-leaf plot fot the BSS compositve variable, you will see the descriptive statistics for that variable:

As we suspected from the stem-and-leaf plot, the mean is slightly above 4, and the minimum and maximum scores are still within the expected 1 to 7 range. Your report of a new score should include:

  1. How many items went into the new score (11 in this case).
  2. How the item values were combined (mean, sum, etc.).
  3. The Cronbach’s alpha reliability.
  4. The minimum, maximum, mean, and standard deviation of the scores.
  5. An interpretation of high scores. Look back at the items from the BSS to see what high and low scores indicate. Think about how you could describe the beliefs of a person who agrees with items 1, 4, 5, 6, 8, 9, 10, 11, and who disagrees with 2, 3, and 7.

For example:

A Benevolent Sexism Scale (BSS) score was computed for each participant by taking the mean of the 11 items of the Benevolent Sexism Scale after reverse-scoring the appropriate items. The Cronbach's alpha reliability of the BSS was 0.74. BSS scores ranged from 2.00 to 5.82, with a mean of 4.30 and standard deviation of 0.85. High scores on the BSS indicate that a person believes that men should protect women, that men need women, or that women have positive qualities that men lack.

There is a 5-question stats homework assignment on reliability analysis that accompanies this tutorial. To begin the assignment, you can log in to your moodle account for this course and select the "Stats 2: Reliability Analysis" quiz.