Difference Score

The difference score indicates the amount of change between two testings. It is computed by subtracting the score on the first testing from the score on the second

where

d is the difference score (sometimes called change score or gain score), X is the first test score (sometimes called the baseline or pretest score), and

Y is the second test score (sometimes called the posttest score).

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In SPSS, difference scores are created by computing a new variable. This is done using the Compute function found under the Transform window. The syntax for computing a new variable called “change” to indicate the change from anxiety1 to anxiety2 would be as follows:

COMPUTE change = anxiety2 − anxiety1.

EXECUTE.

See the example in Table 1.

Table 1 Example of Difference Scores
ANXIETY1	ANXIETY2	CHANGE
23	20	−3.00
45	40	−5.00
26	23	−3.00
34	35	1.00
52	44	−8.00

In Table 1, four of the five participants showed a decrease in anxiety as indicated by the negative difference scores.

Difference scores can be treated like any other variable. The mean of difference scores equals the difference between the means from the two testings. In the above example, the mean of anxiety1 is 36.0, the mean of anxiety2 is 32.4, and the mean of the difference scores is –3.6. This shows that the average change from the first to the second testing was a decrease in anxiety of 3.6.

Advantages

Difference scores generally have much less variation than the scores from which they were created. This is because the subtraction operation removes any variation due to individual characteristics that is constant between the two testings. Thus, analyses using difference scores offer more statistical power than analyses conducted on posttest scores.

Difference scores allow a simpler design to be used. A one-way ANOVA comparing the means of difference scores yields a main effect that is identical in both value and meaning to the interaction term in a two-way ANOVA that used the pretest and posttest scores as a second, repeated measures variable. Post hoc comparisons of the mean changes are easier to conduct and interpret in the one-way design.

Disadvantages

Difference scores contain measurement error from both the pretest and posttest scores, and are also negatively correlated with baseline because of measurement error. However, neither of these factors prohibits their use as valid measures of change.

On the other hand, when data are skewed—for example, by a floor or ceiling effect—difference scores may not reflect the true amount of change.

Appropriateness for Comparing Changes in Means

In a randomized experiment, where the goal is to compare the mean changes of groups that receive different treatments, analysis of covariance (ANCOVA), with pretest as the covariate and posttest as the dependent variable, should be used instead of difference scores. ANCOVA provides a better adjustment for minor differences in the pretest means because these differences are entirely due to chance and will regress on the second testing.

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