Not all scores can be directly compared. Getting a score of 10 on your math test and 50 on your English test does not necessarily mean, for example, that you did better in English than in math. These numbers cannot be directly compared because each test is probably scored differently, the total points available on each test may be different and the subject matter being tested is unique for each test. Transforming each of these numbers into a z-score puts both scores on the same normal distribution so they can be easily compared.

Enter two columns of data into the Minitab worksheet and leave two columns blank for Minitab to insert calculated Z-scores. For example, use column C1 for math scores, and column C4 for English scores. Label column C2 "Math Z" and Column C4 as "English Z" but leave both these columns blank.

Select the "Calc" option from the menu choices and then select the "Standardize" option.

Select your inputs. In the example, select both the math and English data by double-clicking on these choices in the column list.

Next, select the columns for the "Store Results in" box. In the example, you will select Math Z and English Z.

Select the "Subtract mean and divide by standard deviation" option and click "OK". Note that a z-score has been calculated for the scores.

Compare the z-scores. In the example, the average math score for your group was 4.08 and the standard deviation was 3.92. Minitab would calculate a z-score of 2.27 for your math score. For your English score, the average score for your group was 83.87 and the standard deviation was 20.74. Minitab would calculate a z-score of -1.6.

Interpret your results. Always interpret z-scores as the number of standard deviations above or below the mean your particular score falls, relative to the group. In the example, your math score was about two standard deviations higher than the average group score, however your English score was about two standard deviations lower than the average score for all the English students who took the test.

#### Warning

These steps have been written for Minitab 16. Earlier versions may have slightly different steps.

#### Tips and warnings

- These steps have been written for Minitab 16. Earlier versions may have slightly different steps.

### Things you need

- Minitab 16
- Paper
- Pencil

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