How do I compute slopes of linear trend for single cases?
It is often useful to produce a summary measure of a variable measured over time (e.g. to assess learning). This can be later used, for example to correlate with IQ, to assess if rate of learning is related to IQ. SPSS and other packages only produce these for groups, rather than individuals.
The table below gives formulae (derived from regressions) for obtaining estimates of slopes corresponding to individual linear trends for three or more points. these may be computed from the data assuming each time point is entered in a separate column.
The formula is obtainied by multiplying the k observed responses, y1 to yk, (in chronological order) by orthogonal polynomial coefficients and dividing by the sum of their squared coefficients (Theee may be found on page 678 of Howell DC (1997). It should, in fact, be found in the appendices of any of the five editions of this book.
No. Points |
Slope |
|
3 |
(y3 - y1)/2 |
|
4 |
(-3y1 -3y2 + y3 + 3y4) / 20 |
|
5 |
(-2y1 -y2 + y4 + 2y5) / 10 |
|
6 |
(-5y1 -3y2 - y3 + y4 + 3y5 +5y6) / 70 |
|
Howell DC (1997) Statistical methods for psychologists. Fourth Edition. Duxbury Press:Belmont,CA