Example of Dynamic Effect Size Graphics Routine

Graphical Interpretation of Post-transplant Effect Sizes

The X and Y axes maybe changed, currently the Y-axis is the effect size for symptom distress change post-transplant, and the X-axis is the effect size for symptom frequency change. As the graphic stands, the size of the effect size circles are represented by the average pre-transplant measure of symptom distress (this maybe changed). The color of the effect size circles are represented by the pre-transplant average frequence measure (this maybe changed). The lower slide bar represents the post-transplant time, which in this case is represented by the numbers 1901-1905 (1, 3, 6, 9 and 12 months post-transplant. These numbers are used due to program limitations.

This graphic provides access to the following variables:

• Base_mean_d = Average pre-transplant symptom distress measure
• Base_mean_f = Average pre-transplant symptom frequency measure
• dist = effect size measure for change in symptom distress pre to post-transplant
• freq = effect size measure for change in symptom frequency pre to post-transplant
• sig_d = binary variable indicating statistically significant change in distress effect, FDR adjusted
• sig_f = binary variable indicating statistically significant change in frequence effect, FDR adjusted

NOTE: Negative effect sizes indicate improvement in symptoms post-transplant, and positive effect sizes indicate increased symptom problems.

Basic Ridits

Ordered categorical data, such as subjective scaled symptom measures (Likert scales), may be handled using ridit analysis (Bross, 1958). Ridits are measures relative to an empirical distribution. Using initial assessments of symptoms on a reference population with the same response categories one may determine a ridit score for each category. This score for each category is simply the percentile rank of an item in the reference population and is equal to the number of items in all of the lower categories plus one-half the number of items in the subject category, divided by the population size.

The interpretation of the mean Ridit for a comparison group is as follows. If an item, X is selected at random from the reference population (e.g., pre-transplant symptom measure) and an item Y is selected at random from the comparison group (e.g., post-transplant symptom measure), then the assessment of the mean Ridit is an estimate of the probability that X is less symptomatic than Y. The initial group mean Ridit is always considered .5 under this definition.

A computer program that calculates the mean Ridit, significance tests, and effect sizes is available from the Roger Brown.