February 28, 2023

This is the fourth in a series of short pieces stemming from our November 2022 Community and Belonging Survey of Students, involving 96 independent schools and 22,297 students.

If you had to name a list of topics that would most *polarize* dinner table conversation, *diversity* would likely be the ironic item on the list.

Diversity is not, at its best, a binary conversation. For the sake of argument, I’m going to take the position that neither total heterogeneity nor total homogeneity are desirable. Of course, this position will depend on what kind of diversity we’re talking about. If we’re a group of people looking to push a car out of deep mud, homogeneity in the direction we’re pushing would be a good thing. The discussion that leads to the decision on that direction, however, might benefit greatly from diverse inputs.

At the same time, there’s also a case for diminishing and negative returns from excessive levels of diversity. A diverse collection of contributors, for example, can make a wonderful meal. Having “too many cooks in the kitchen” is quite another matter. In the same vein, I’ve seen school mission statements that say so much and so many things that they could not ever be considered a unifying call to action. As my policy professor at business school 40 years ago would say, “if your mission statement has more than 15 words, it’s not a mission statement, it’s an essay.” My own mission proposition is: *How can we add value to conversations in education management? *Ten words… thank you Dr. Bart. Too many mission statements are hijacked by large committees who effectively water them down by trying to cover far too many bases.

But, I digress…

My aim today is to explore how we look at diversity in quantitative terms, to make a few observations related to our recent Community and Belonging Survey, and at the same time to draw attention to a small number of related pitfalls.

I’ve seen diversity presented on schools’ websites in numerous ways:

- ___% of our students come from minority groups.
- Our students represent ___ countries… counties, etc.
- Our students speak ___ languages.
- ___% of our students receive financial assistance from the school.

… and so on.

The context for today’s entry is racial diversity. In quantitative terms, I’d like to present the formula we used to assess racial diversity levels across schools and between the two countries involved in the Community and Belonging Survey.

Don’t get caught up in the math if it’s not your cup of tea. The next short section (highlighted in blue) is for those who drink this kind of tea. Others can just skip to the next section.

Call this a Diversity Index. In purely mathematical terms (and this is an important qualifier), the Diversity Index is: *the average of the absolute value of the differences between each of the proportions and all other proportions.*

To illustrate this, using both extremes, consider the following examples:

In example #1, there are 10 racial categories. One of the categories holds 100% of respondents. Nine of the categories, therefore, each hold 0% of respondents. In Excel, these figures were in column “B” and occupied rows 1 through 10.

100% |

0% |

0% |

0% |

0% |

0% |

0% |

0% |

0% |

0% |

The formula, for those who care, looks like this:

=((ABS(B1-B2) +ABS(B1-B3) +ABS(B1-B4)+ABS(B1-B5)+ABS(B1-B6)+ABS(B1-B7)+ABS(B1-B8)+ABS(B1-B9)+ABS(B1-B10))+(ABS(B2-B3)+ABS(B2-B4)+ABS(B2-B5)+ABS(B2-B6)+ABS(B2-B7)+ABS(B2-B8)+ABS(B2-B9)+ABS(B2-B10)) +(ABS(B3-B4)+ABS(B3-B5)+ABS(B3-B6)+ABS(B3-B7)+ABS(B3-B8)+ABS(B3-B9)+ABS(B3-B10))+(ABS(B4-B5)+ABS(B4-B6)+ABS(B4-B7)+ABS(B4-B8)+ABS(B4-B9)+ABS(B4-B10))+(ABS(B5-B6)+ABS(B5-B7)+ABS(B5-B8)+ABS(B5-B9)+ABS(B5-B10))+(ABS(B6-B7)+ABS(B6-B8)+ABS(B6-B9)+ABS(B6-B10))+(ABS(B7-B8)+ABS(B7-B9)+ABS(B7-B10))+(ABS(B8-B9)+ABS(B8-B10))+ABS(B9-B10))/45

The answer for this series of 45 pairs, then, works out to 20. This, I think you’ll agree, is the least possible diverse community, but yields the maximum possible score. The minimum score is always zero. The maximum score depends on the number of pairs, which in turn depends on the number of racial categories. Given that this number of categories may vary, we standardize the result by “normalizing” the Index on a scale from 0-100. For this particular score to be normalized to 100, we need to multiply it by 5 (20 x 5 = 100).

Now consider the distribution across categories as follows:

10% |

10% |

10% |

10% |

10% |

10% |

10% |

10% |

10% |

10% |

The answer for this series of 45 pairs or terms, then, works out to 0, perfect mathematical diversity. For this particular score to be normalized, we still need to multiply it by 5 to get to 100. Of course, zero times 5 equals zero, but it’s still part of the exercise.

For all points in between, the same procedure applies. Consider this third and final example:

20% |

15% |

10% |

33% |

12% |

2% |

4% |

1% |

3% |

0% |

In this one, the Diversity Index is calculated at 11.7. Normalized to 100 (with the multiple of 5), it becomes 58.7.

Remembering that greater diversity is reflected in an Index score closer to zero and lesser diversity in an Index score closer to 100, we applied this formula to each of the 96 participating schools.

Math lesson over! I hope I haven’t given you a headache.

Here’s some of what we found from our survey:

- the mathematical Diversity Index for the aggregated 96 participating schools was 79.7
- the aggregated Index for the 80 participating American schools was 81.6
- the aggregated Index for the 16 participating Canadian schools was 70.4
- the school with greatest Diversity (lowest Index) had a score of 60.4
- the school with least Diversity (highest Index) had a score of 100.0 (every single student identified as White)

As we consider the diversity of our student population, we want to understand, of course, how this diversity relates to other survey measures, and to explore how this diversity may relate to other student experiences. I’m sure there’s a doctoral dissertation in there somewhere, but that’s a very complex subject for another day. It gives me a headache just to consider it.

Here’s a small part of why:

- What is the Diversity Index for the American population at large? For the Canadian Population?
- How does my school’s Diversity Index compare to the population of our country or city or region? Everything is relative, isn’t it? “Compared to what?” are the three most important words in the review of any statistic.
- How do I look at these numbers if our school has a boarding program with students coming from all over the world? Again, everything is relative.
- Not to be overlooked, is our Diversity Index static, or evolving steadily over time, or in a period of dramatic change?

In case I haven’t yet presented enough confounding variables (e.g., intersectionality), consider the following. Remember still that this is purely a mathematical diversity index. Without context, it’s meaningless.

- Canada displays a more diverse population, meaningfully more so than the United States.
- Canadian independent schools in our pool are more diverse than the Canadian population at large (as measured in government statistics).
- American independent schools in our pool are less diverse than the American population at large (as measured in government statistics).
- (Of course, these comparisons with the general populations are immediately flawed because they’re restricted to a small section of the population, enrolled in Grades 9-12.)

I find myself asking why these distinctions between Canada and the United States may exist. Here’s where I leave the realm of what the data tells me and enter the realm of speculation. The only explanation I can find is in our very different immigration policies. Many times, I’ve heard Congressional members complaining that the American immigration practice should follow more closely the very selective practice in place here in Canada. To be blunt about it, in relative terms, to immigrate into Canada, those who have education and those who have money stand a much better chance of approval. The stringency in this filter, I’m told, is much greater than on the American side of the border. If this is true, it would explain, at least in part, why Canadian independent schools enjoy greater racial diversity than their American counterparts. Do varied tuition assistance programs make a difference? So many questions.

On average, schools with greater racial diversity have greater proportions of students reporting that they’ve been affected by incidents of racial discrimination. No surprise there. Schools without racial diversity see little report of racial discrimination. Here’s where one needs to be very careful in the interpretation of data into actionable response. I’m sure there are folks out there who would use this distinction to make a case for segregation. Let’s not go there.

I touched earlier on the dynamic of change in racial diversity. Schools may look at their own diversity figures, relative to the aggregate findings, and draw conclusions related to how they’re doing on the discrimination front. My response to them would be to take great caution in doing so. If you are experiencing higher levels of racial discrimination at your school, but have also witnessed a dramatic shift in racial diversity in recent years, your observations, while real, may need to be placed in the context of rapid change. Change of any kind is stressful. Rapid change, even more stressful. Students… and their parents… need to learn to be adaptable and accepting of the new “other”. For all of human history, we’ve immediately raised red flags with the introduction of new “others”. It’s a tribal thing. Evolutionary experience aside, we live in a world that will be better served if we can succeed in shaking off this knee-jerk tribal reaction. Get over it! From my seat, adaptability may be the 21^{st} century skill that most separates success from failure.

If your community has not changed in racial demographics in several decades, higher reported rates of discrimination might well be viewed through a somewhat different lens, involving history more than dynamic change.

Of course, education and learning… and adaptability… is the answer in both instances.

This is just one more thin sliver of findings – along with my own ruminations – stemming from a massive survey database. So much data… so little time.

With respect,

Kevin Graham

I welcome your feedback. Feel free to contact me by e-mail.