An important concept when comparing groups from a population is that often the variation within the group will be greater than the variation between the groups. What is meant by this?

An example of this concept concerns the height of males vs. females. The average height for American men is 69 inches and for women it is 64 inches – a difference of 5 inches. However, the variation of height for men and for women is much greater than 5 inches! Most men vary between 5’1″ and 6’7″ – or 18″. The chart below shows this concept – there is much bigger range of heights within the groups than between the groups.

Knowledge of this concept is important when interpreting studies. Suppose there are two groups undergoing medical treatment. Group A receives the treatment and Group B receives a placebo. The results of the study find that the treatment Group on average had a better outcome than those in placebo group. The concept of within vs. between group statistics tells you that there is much greater variation within Group A and Group B than between them. So, there are some members of Group A who do not get better even though they received the treatment and members of Group B who get better even though they receive a placebo.

This concept of within vs. between differences also applies to human genetics. From an article by an anthropologist discussing this topic: “Research in human genetics has highlighted that there is more genetic variation within than between human groups, where those groups are defined in terms of linguistic, geographic, and cultural boundaries.” A great example I found on a psychology chat exchange is a hypothetical example of alien IQ. Martians have a higher average IQ than those from Pluto. Here’s what their intelligence samples look like:

As you can see from above. the variation within each group is very large, ranging from about 60 to 140 for both groups (with some outliers). However, the ranges average out so that Martians, on average, are slightly smarter than Plutons.

What this concept of within vs. between group variation is that it is often quite often hard to apply group stereotypes (which may be quite accurate as applied to the group) to individuals. An example of this might be thinking about the characteristics of Millennials vs Generation Xers. As a group Millennials may share some characteristics (connected, desire instant gratification, value work-life balance), and Gen Xers may share some characteristics (independent, disdain for authority, skeptical), but the variation of individuals are huge and it’s tough to categorize any given individual merely by their generation. If you meet an individual Millennial, it is really unfair to ascribe group characteristics to them given the great within group range of characteristics.

Note that there is an area of statistics that concerns measuring within vs. between group characteristics, the most common of which is called ANOVA . Click here for more on ANOVA.

Knowledge of within group vs. between group variation has had a meaningful impact on my worldview as I think about groups and also about whether to ascribe a group characteristic to an individual member of a group.