5.4 – Comparing Scores Between Individuals

Now that we have compared two scores from the same individual, you will see that the strategy is basically the same when comparing scores from two different individuals with scores from different scales. For example, let’s say two roommates, Ernie and Bert, just received some test scores from their college classes and they made a bet on who did better on their test compared with the other students in the class, with the winner getting dinner. Ernie earned a 78 on his Math test, while Bert earned an 81 on his Biology test.

On the surface, it appears that Bert did better, but remember that to really know how each of them performed relative to the other students, we need to consider the mean and the standard deviation for each class on the test. Let’s say that these were the results:

As we did when comparing scores from different scales from one individual in the previous section, we will need to standardize Ernie’s and Bert’s scores by calculating their z-scores:

[latex]\text{Ernie:  } z=\frac{X-\mu}{\sigma}=\frac{78-70}{4}=\frac{+8}{4}=+2.00[/latex]

[latex]\text{Bert:  } z=\frac{X-\mu}{\sigma}=\frac{81-76}{3}=\frac{+5}{3}=+1.67[/latex]

Now that we have standardized the two scores and put them on the same scale, we can now directly compare these two numbers. It is now apparent that Ernie had the higher z-score, and thus scored better compared to his class than Bert scored compared to his class. Thus, Ernie wins the bet.