Making Data Make Sense- Extreme Scores

What are extreme scores? They are scores far outside the norm for a variable or population, leading to the conclusion that they are not part of your true population and probably do not belong in your analyses. A common operational definition for extreme scores is +/-3 standard deviations (SDs) from the mean.  

Recall that standard normal distribution of a population has 68.26% of the population between +1 and -1 SD of the mean (see attached diagram: 34.13% between 0 to +1 SD +  34.13% between 0 and -1 SD = 68.26%). 

 

So 95.44% of the population should fall between 2 SD from the mean (34.13% + 34.13% + 13.59% +13.59% = 95.44%), and 99.74% of the population should fall 3 SD of the mean. In other words, the probability of randomly sampling an individual more than 3 SD from the mean in a normally distributed is 0.26%, which gives good justification for considering scores outside 3 SD as suspect. Our concern is that these scores are not part of the population of interest in your study. 

Next time we will consider how extreme scores affect statistical analyses. Do you have an issue or a question that you would like me to discuss in a future post? Would you like to be a guest writer? Send me your ideas! leann.stadtlander@waldenu.edu