Table 3.
Example dataset structure for Equation 1 [erroneous results for β2 (level change)] versus Equation 2 [correct results for β′2 (level change)]
|
Equation 1
(erroneous)
|
Equation 2
(correct)
|
||||
|---|---|---|---|---|---|
| T | X t | TX t | T | X t | (T − Ti)Xt |
| 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 1 | 0 | 0 |
| 2 | 0 | 0 | 2 | 0 | 0 |
| … | … | ||||
| 99 | 0 | 0 | 99 | 0 | 0 |
| 100 | 1 | 100 | 100 | 1 | 0 |
|
101 |
1 |
101 |
101 |
1 |
1 |
|
102 |
1 |
102 |
102 |
1 |
2 |
| … | 1 | … | 1 | … | |
| 150 | 1 | 150 | 150 | 1 | 50 |
Where T is the time elapsed since the start of the study, Xt is a dummy variable indicating the pre-intervention period (coded 0) or the post-intervention period (coded 1). Ti represents the time point when the intervention starts (Xt = 1 for T ≥ Ti). In this example, Ti = 100.