2: Explaining Variability

Overview Section

 Case-Study: Risk of Heart Attack

As a health care professional, Susie is amazed at the large discussion about the value of taking low dose aspirin to decrease the risk of a heart attack. Recently, she read an article about taking low dose aspirin to prevent heart attacks. The article discussed stated that the variability between the two groups (taking low dose aspirin and not taking low dose aspirin) was significant, however, the calculation of an effect size actually demonstrated that this “significant difference” did not mean that the effect of taking the aspirin was meaningful. Thus, the effect of taking aspirin was so small that, given the possibility of negative side effects, it was better removed for most patients. Susie decided to read more about variability and effect sizes to help her understand that simply stating the statistical results may be misleading, and unethical, given the actual effect size may lead to a different conclusion.

Taking a step back from the low dose aspirin, let’s think about the incidence of heart attacks. There are some people who have a heart attack despite leading healthy lives, then there are other people we might think would have a heart attack and do not. The heart (pun intended) of statistics is to understand real-world phenomena, in this example, why some people get heart attacks and some do not. To put this more technically, we seek to understand the variability in terms of heart attacks. If everyone suffered a heart attack there would not be anything to explain! We would already know that everyone will get a heart attack, end of story and there is no need for any statistics! In statistical terms, we could say there is no variability in the incidence of a heart attack, or it is a constant. But our world is full of variability and curious researchers and people in the field are constantly trying to explain it. So this unit will take a look at variability and what it means. The importance of this unit cannot be understated. This is literally the pillar of everything else we will do in this course. So let’s get started!


Upon completion of this lesson, you should be able to:

  • Identify variability in data
  • Differentiate within group variability (error) and between group variability
  • Identify small, medium, and large effect sizes
  • Be able to correctly interpret a mean, median, and standard deviation from statistical output
  • Identify the correct percentiles and standard deviations for the Empirical Rule
  • Correctly calculate and interpret a z score