Report Card on British Columbia's Secondary Schools: 2001 Edition
Appendix 1: Calculating the Overall rating out of 10
The Overall rating out of 10 is intended to answer the question, "In general, how is the school doing, academically?" This year, we have adopted a different method for its calculation and, in order that all the historical data is consistent, we have re-calculated the Overall rating for all years using this new method. The following is a simplified description of the procedure used to convert the raw indicator data into the Overall rating out of 10.
- The School vs exam mark difference for each course and the English 12 and Mathematics 12 Gender gap indicators were calculated using the raw data.
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Course by course, all the results were then standardized by solving the equation
where X is the individual school's mean result,
is the mean
of the all-schools distribution of results,
and 
is the standard deviation of the same all-schools distribution.
- With the exception of the Gender gap indicators (these use the results from a single course), the course-by-course standardized data were then aggregated to produce weighted average indicator values. The weighting used was the number of examinations written in each course at the school relative to the total number of examinations written at the school.
- These weighted average results were then re-standardized.
- The seven standardized indicator results were then combined to produce a weighted average summary standardized score for the school. The weightings used in these calculations were Average exam mark—20%, Percentage of exams failed—20%, School vs exam mark difference—10%, English 12 gender gap—5%, Math 12 gender gap—5%, Exams taken per student—20%, and Graduation rate—20%. For schools that produced no results for the gender-gap indicators because they enrolled only boys or girls, the School vs exam mark difference was weighted at 20%.
- This summary standardized score was standardized.
This standardized score was converted into an Overall rating between 0 and 10 as follows:
- The maximum and minimum standardized scores were set at 2.2 and -3.29 respectively. Scores equal to, or greater than, 2.2 receive the highest Overall rating of 10. This cut-off was chosen because it allows more than one school in a given year to be awarded 10 out of 10. Scores of equal to, or less than, 3.29 will receive the lowest Overall rating of 0. Schools with scores below -3.29 are likely to be outliers—a statistical term used to denote members of a population that appear to have characteristics substantially different from the rest of the population. We chose, therefore, to set the minimum score so as to disregard such extreme differences.
-
The resulting standardized scores were converted into Overall ratings according to the formula:
where OR is the resulting Overall rating,
is the average calculated according to the formula:
where
is the standard deviation calculated according to the formula:
and StanScore is the standardized score calculated in (6) above and adjusted as required for minimum and maximum values as noted in (7) above. As noted in (7) above, ORmin equals zero, Zmin equals -3.29; and Zmax equals 2.2. - Finally, the derived Overall rating is rounded to one place of the decimal to reflect the significant number of places of the decimal in the original raw data.
Note that the Overall rating out of 10, based as it is on standardized scores, is a relative rating. That is, in order for a school to show improvement in its overall rating, it must improve more than the average. If it improves but at a rate less than the average, it will show a decline in its rating.
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