Report Card on Ontario's Secondary Schools : 2001 Edition
Appendix 1 Calculating the Overall rating out of 10 and Trends
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?" The following is a simplified description of the procedure used to convert the raw indicator data into the Overall rating out of 10.
For each year, an Overall rating out of 10 was only calculated for those schools that had values for Percentage of advanced courses taken, Percentage of courses passed, and Core courses taken per student.
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Year by year, all the academic indicator results were 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. - Year by year, the five standardized results were then combined to produce a weighted average overall standardized score for the school. Where a school had values for all five indicators, we used an equal weighting of 25% for all but the Gender gap indicators, which were each given a weighting of 12.5%. If one or both of the gender gap indicators had not been calculated (whether due to lack of data or enrollment of just one sex at the school), then the overall standardized score was calculated without reference to the gender gap indicators.
- This summary standardized score was then "re-standardized."
The resulting "re-standardized" score was converted into an overall rating between zero and 10 as follows:
- The maximum and minimum standardized scores were set at 2.0 and -3.29 respectively. Scores equal to, or greater than, 2.0 received the maximum overall rating of 10. This cut-off was chosen because the occasional, although infrequent, occurrence of scores above 2.0 (two standard deviations above the mean) allows the possibility that more than one school in a given year can be awarded a "10 out of 10." Scores equal to, or less than, -3.29 will receive the minimum overall rating of 0 (zero). Schools with scores below -3.29 are likely 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, therefore, chose 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
and StanScore is the standardized score calculated in (3) above and adjusted as required for minimum and maximum values as noted in (4) above. As noted in (4) above, ORmin equals zero, Zmin equals -3.29; and Zmax equals 2.0. - Finally, the derived Overall rating is rounded to one decimal place to reflect the significant number of decimal places found 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.
Trends
For each indicator, the "least squares" method was used to determine change, if any, in the standardized values over time. The result indicated whether or not any statistically significant change--in this context, at the 90% level--had taken place in the school's performance. Where the co-efficient of the indicator was less than (at the maximum) 1/200th of the possible range of the values of the indicator, any statistically significant change was ignored and no trend was indicated.
Significant improvement is indicated in the tables by an up arrow (
); significant deterioration is indicated by a down arrow (
). No change is indicated by a dash (—). Where fewer than six years of data were available, no trend was calculated and "n/a" appears in the tables.
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