Results

Q-Q Plots

For each Q-Q plot we want to compare the distance of the points to the diagonal line to the same distances for the raw scores. For the raw scores, the observed values deviate from normal (the diagonal) at the extremes, but mainly for large observed values (because the distributioon is positively skewed).

- The log transformation improves the distribution a bit. The positive skew is mitigated by the log transformation (large scores are made less extreme) resulting in dots on the Q-Q plot that are much closer to the line for large observed values.

- Similarly, the square root transformation mitigates the positive skew too by having a greater effect on large scores. The result is again a Q-Q plot with dots that are much closer to the line for large observed values that for the raw data.

- Conversely, the reciprocal transformation makes things worse! The result is a Q-Q plot with dots that are much further from the line than for the raw data.