Statistical Power

OK, so John Lennon didn’t really write this , but statistical power is a very abstract concept and the ability to "imagine" really helps.

Overview

Power is the probability to detect a difference if it is there.

Of course, your next question should be " How big a difference can the study detect?" More on that later.

The main factors that affect power are:

• The number of subjects that were studied
• the aforementioned treatment effect size (how big is the difference we expect or hope for)
• the variabliity of the data (standard deviation).

That last one is not a factor if you are studying non-parametric data (such as the percent of people who grew a second nose). For nominal and ordinal data there is are complicated equations and the calculations become just a black box for non-math-heads such as myself.

Before the Study Power Calculations

1. You need to decide what the smallest effect size you consider to be important and also what effect size you hope to find.
2. You need to decide what level of confidence you want to have that you will be able to detect that small of a difference.(this is power or 1-beta)
3. You need to estimate the variablility of the outcome, preferably from previous studies if available.

Here is a conceptual equation (don’t use this at home)

     (Variability of the Outcome ) (Power)
    ————————————————– = Number Needed (n)
      Expected effect size

As you can see:

• Increase in variability or power will increase the number needed in the study.
• Increase in expected effect size will decrease the number needed in the study.
• And Vice Versa

   

  After the Study Power Calculations

  If you found a difference, You had enough power! and you don’t need to calculate power.
  If you found "no difference":
  

  1. You need to decide what the smallest effect size you consider to be important (this will be smaller than you actually found in the study)
  2. You can now calculate the variablility of the outcome (rather than estimate)
  3. You have the number that you studied (unless you forgot to count

      (Expected effect size ) (N)
      ————————————————– = Power

        Variability of the Outcome

  • Increase in variability of the date will decrease the power.
  • Increase in expected effect size will increase the power.
  • Increase in the number studied will increase the power.
  • And Vice Versa