When looking at EQAO, don’t confuse ‘average’ with ‘standard’

Re: Students are edging closer to average — Sept. 20

Your story on the performance of local students on the provincewide EQAO tests appears to confuse the average mark with the provincial “standard.”

It states that “local elementary students ... were testing four percentage points behind the Ontario average, across all tests.” This statement is flawed.

The provincial “standard” is the fixed minimum threshold level of performance that is considered desirable, while the average mark on any test is simply the arithmetic mean mark of all test takers.

A tally of the number of Waterloo Region students vs. Ontario students who meet or exceed the arbitrary threshold “standard” provides, in fact, no insight whatsoever as to the degree to which these students may have exceeded (or fallen short of ) that threshold and no insight whatsoever as to the relative averages and standard deviations of these two groups.

Consider two groups, A and B, with five students each, undertaking a test in which the “standard” is set at 70 per cent and the students achieve the following test marks:

Group A: 55, 65, 75, 85, 95; Group B: 65, 65, 65, 95, 95.

For Group A, three students exceed the standard and the group average mark is 75. For Group B, only two students exceed the standard; however, the group average of 77 is actually higher than that of Group A.

Further, the two students who exceed the standard in Group B outperform the three students who exceed the standard for Group A.

Even our educational officials seem to be held in thrall of fallacious thinking.

Each school board is convinced that with some effort, they can match or exceed the average percentage of students meeting or exceeding the threshold, evidently failing to realize that by statistical definition, roughly 50 per cent of boards will be at or above the average and 50 per cent of the boards will be at or below the average, regardless of any improvements to student performance, locally or provincewide.

Even in a class of gifted students where everyone scores in the 90s, half the class will fall below the median, by definition.

Discerning readers are wary of the natural, but unfortunate, tendency to draw sweeping conclusions about large samples and populations from discrete statistical values (e.g. means, modes, averages, medians) and arbitrary thresholds.

John Stephenson

Cambridge