There are generally two different methods for calculating Rate of Improvement from an academic sense.
- The simple model.
y=(x2 - x1) / w
- Where y = ROI, x2 = last data point, x1 = first data point, w = number of weeks between x2 and x1
- The problem with this method is it ignores fluctuations within the period between x2 and x1
- In the example below, the ROI calculated using this method would be 1.52. However this does not represent the actual growth of the student - as they didn't see a surge in test scores until the last three data points.
- The Linear Regression model.
y = mx + b
- y = mx + b is not the formula of a linear regression - but we use the linear regression to get the components of the slope of a line formula - which gives us our ROI.
- Where y = ROI, m = slope, x = Date, b = intercept
- Using a linear regression for calculating ROI is much more reliable as it takes into account the fluctuations in scores - and levels outliers.
- In the example above, the intervention ROI is 1.36 - which is much more telling of the progress the student made.