Comparing treatment groups at baseline
Is anything more aggravating than a statement that treatment group differences were 'not statistically significant' at baseline? This can mask two fundamental misunderstandings - the meaning of statistical differences or the purpose of comparing groups.
What is desired is an indication that the treatment groups are exchangeable - on all relevant characteristics. This means identical centers (e.g. means) or proportions, and/or p values approaching 1.
Trait Interv Cntrl n p-value Interpretation Mean age 49.1 49.2 10,000 <.01 NO difference Mean age 23.5 46.2 10 0.46 Different!
Of course you could have identical means and very different distributions, e.g. young and old in one group, middle-aged in the other. Some day I'll ask a statistician about another idea that someone must have proposed already - an overlap statistical for describing similarity. To lay out the idea...
Histograms of continuous variables would be smoothed according to sample size. The overlap statistic would be the proportion of the area under both curves to the total area.
For categorical variables the overlap statistic would be the sum of the minimum percentage in each category. It's easy to illustrate in a table:
Category %F %M min sum Female 45 50 45 45 Male 52 45 +45 90 Other 3 5 +3 93
Conclusion: The overlap statistic would be 0.93 (i.e. 93%), because for every 100 people in the two groups 7 would not have a matching 'partner' in the other group.