Often when you check the distribution of scores on a scale or measure (e.g. selfesteem, anxiety) you will find that the scores do not fall in a nice, normally distributed curve. Sometimes scores will be positively skewed, where most of the respondents record low scores on the scale (e.g.depression).
Sometimes you will find a negatively skewed distribution, where most scores are at the high end (e.g.
self-esteem). Given that many of the parametric statistical tests assume normally distributed scores, what do you do about these skewed distributions?
One of the choices you have is to abandon the use of parametric statistics (e.g. Pearson correlation, analysis of variance) and instead choose to use non-parametric alternatives (e.g. Spearman’s rho, Kruskal-Wallis). SPSS includes a number of useful non-parametric techniques in its package.
Another alternative, when you have a non-normal distribution, is to ‘transform’ your variables. This involves mathematically modifying the scores using various formulas until the distribution looks more normal. There are a number of different types of transformation, depending on the shape of your distribution. There is considerable controversy concerning this approach in the literature, with some authors strongly supporting, and others arguing against, transforming variables to better meet the assumptions of the various parametric techniques.
Procedure for transforming variables
(You need the following data file:
)
1. From the menu at the top of the screen, click on Transform, then click on Compute Variable.
2. Target Variable. In this box, type in a new name for the variable. Try to include an indication of the type of transformation and the original name of the variable. For example, for a variable called tnegaff I would make this new variable sqtnegaff, if I had performed a square root. Be consistent in the abbreviations that you use for each of your transformations.
3. Functions. Listed are a wide range of possible actions you can use. You need to choose the most appropriate transformation for your variable. Look at the shape of your distribution; compare it with those in the above Figure. Take note of the formula listed next to the picture that matches your distribution. This is the one that you will use.
4. Transformations involving square root or logarithm. In the Function group box, click on Arithmetic, and scan down the list that shows up in the bottom box until you fi nd the formula you need (e.g. Sqrt or Lg10). Highlight the one you want and click on the up arrow. This moves the formula into the Numeric Expression box. You will need to tell it which variable you want to recalculate. Find it in the list of variables and click on the arrow to move it into the Numeric Expression box. If you prefer,
you can just type the formula in yourself without using the Functions or Variables list. Just make sure you spell everything correctly.
5. Transformations involving Refl ect. You need to fi nd the value K for your variable. This is the largest value that your variable can have (see your codebook) + 1. Type this number in the Numeric Expression box. Complete the remainder of the formula using the Functions box, or alternatively type it in yourself.
6. Transformations involving Inverse. To calculate the inverse, you need to divide your scores into 1. So, in the Numeric Expression box type in 1, then type / and then your variable or the rest of your formula (e.g. 1/tslfest).
7. Check the fi nal formula in the Numeric Expression box. Write this down in your codebook next to the name of the new variable you created.
8. Click on the button Type and Label. Under Label, type in a brief description of the new variable (or you may choose to use the actual formula you used).
9. Check in the Target Variable box that you have given your new variable a new name, not the original one. If you accidentally put the old variable name, you will lose all your original scores. So, always double-check.
10. Click on OK (or on Paste if you wish to paste this command to the Syntax Editor window). To execute it after pasting to the Syntax Editor, highlight the command and select Run from the menu. A new variable will be created and will appear at the end of your data file.
11. Run Analyze, Frequencies to check the skewness and kurtosis values for your old and new variables. Have they improved?
12. Under Frequencies, click on the Charts button and select Histogram to inspect the distribution of scores on your new variable. Has the distribution improved? If not, you may need to consider a different type of transformation.
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