Outcome = continuous, non-normal (skewed) distribution

In the Descriptive statistics module it was pointed out that the the Mean and Standard Deviation are not good statistics to use for skewed distributions (i.e., distributions of scores that are not normally distributed). The preferred measure of central tendency is the Median (Mdn).

When you have a distribution with a few very extreme scores, a safe way to analyze the results is to change the outcome from a continuous variable to a categorical one (this gets around the problem of a non-normal distribution). Changing a continuous outcome to a categorical one is done by splitting the scores at the Median. The result is a count -- # of high scorers versus # of low scorers. That goes on a contingency table. Then use Chi-square to see if there is a difference.

For example, in comparing history majors versus math majors on their liking of drama, instead of using their liking ratings, you would

1. calculate the median liking score for the entire group (the grand median)
2. count the number of history majors above and below the grand median
3. count the number of math majors above and below the grand median
4. create a 2x2 contingency table

More ....

5. Calculate Chi-square (see next module).

Self-test #4: Selecting statistics

Next module: Inferential statistics for categorical outcomes