Residuals and RPIs
A residual is an unexplained variation between the actual result and the value provided by the regression model.
For example, the chart above shows the year-on-year performance in art and design compared with that expected. The first year shows the department significantly underperforming.
The chart below shows the variation of each subject.
Relative Performance Indicators in RAISEonline
The Relative Performance Indicators (RPIs) presented in RAISEonline are a type of residual. Their purpose is to help schools to evaluate the variation in the level of performance across subjects taken by pupils in a school at GCSE.
Task
Using music as an example the following steps are taken to calculate RPI figures:
- Calculate the average points score for pupils in the school taking music.
- Calculate the average points score in all other subjects for those pupils who took music.
- Subtract 2 from 1 to give the 'school difference'.
- Perform the same calculation with all pupils nationally to provide 'national difference'.
National figures are used to adjust the observed school differences by the national differences. This ensures that the school difference is not influenced by the fact that grade distributions differ nationally across different subjects. - RPI is equal to 3 minus 4.
- Calculate, with 95% confidence, whether or not the difference between attainment in music and attainment in other subjects taken by music pupils in the school is significantly different from the national picture.
The RPI is a within school measure. This means that a school might have a subject with a significantly positive RPI but be performing well below the national average in that subject. This occurs if a school is performing 'less badly' in this particular subject than others. Similarly a school might be achieving well above the national average for a subject but have a negative RPI if performing 'less well' in this particular subject compared with other subjects.