Table 6.
Three possible methods of averaging ratios between successive score values
| equal baseline scores: | |||||
|---|---|---|---|---|---|
| |
S
1,i
|
ratio (R
i
) |
S
2,i
|
log(R
i
) |
C
i
= (R
i
-1)/(R
i
+ 1) |
| 50 |
2 |
100 |
0.301 |
0.333 |
|
| 50 |
1 |
50 |
0.000 |
0.000 |
|
| 50 |
0.5 |
25 |
0.301 |
-0.333 |
|
|
Method (1): |
mean S
1,i
= 50.0 |
Method (2): mean of R
i
values: 1.17 |
|||
| mean S
2,i
= 58.3 | |||||
| (mean S
2,i
)/(mean S
1,i
) = 1.17 | |||||
|
Method (3): |
mean of log(R
i
) values: 0.000 ; mean R: 1.00 |
||||
| |
(re-transformed mean log-value:10(mean log(Ri)) |
||||
| mean of C
i
values: 0.000 ; mean R: 1.00 | |||||
| |
|
(re-transformed mean C-value: (1 + C)/(1-C)) |
|||
|
non-equal baseline scores, largest baseline with smallest R
i
value:
| |||||
| |
S
1,i
|
ratio (R
i
) |
S
2,i
|
log(R
i
) |
C
i
= (R
i
-1)/(R
i
+ 1) |
| |
20 |
2 |
40 |
0.301 |
0.333 |
| 40 |
1 |
40 |
0.000 |
0.000 |
|
| 60 |
0.5 |
30 |
-0.301 |
-0.333 |
|
|
Method (1): |
mean S
1,i
= 40.0 |
Method (2): mean of R
i
values: 1.17 |
|||
| mean S
2,i
= 36.7 | |||||
| (mean S
2,i
)/(mean S
1,i
) = 0.917 | |||||
|
Method (3): |
mean of log(R
i
) values: 0.000 ; mean R: 1.00 |
||||
| |
(re-transformed mean log-value:10(mean log(Ri)) |
||||
| mean of C
i
values: 0.000 ; mean R: 1.00 | |||||
| |
|
(re-transformed mean C-value: (1 + C)/(1-C)) |
|||
|
non-equal baseline scores, largest baseline with largest R
i
value:
| |||||
| |
S
1,i
|
ratio (R
i
) |
S
2,i
|
log(R
i
) |
C
i
= (R
i
-1)/(R
i
+ 1) |
| |
20 |
0.5 |
10 |
0.301 |
0.333 |
| 40 |
1 |
40 |
0.000 |
0.000 |
|
| 60 |
2 |
120 |
-0.301 |
-0.333 |
|
|
Method (1): |
mean S
1,i
= 40.0 |
Method (2): mean of R
i
values: 1.17 |
|||
| mean S
2,i
= 56.7 | |||||
| (mean S
2,i
)/(mean S
1,i
) = 1.42 | |||||
|
Method (3): |
mean of log(R
i
) values: 0.000 ; mean R: 1.00 |
||||
| |
(re-transformed mean log-value:10(mean log(Ri)) |
||||
| mean of C
i
values: 0.000 ; mean R: 1.00 | |||||
| (re-transformed mean C-value: (1 + C)/(1-C)) | |||||
S 1,i and S 2,i , subsequent score values of three items ( i = 1..3) at times ‘1’ and ‘2’ respectively. R i , ratio between S 2,i and S 1,i (multiplication factor of S 1,i ). log(R i ), logarithmically transformed R i -values. C i , R i -values transformed as Contrast-values. Three methods of averaging ratio values are illlustrated; Methods (3) includes two variants of data transformation, logarithmically and as Contrast. For further explanation, see text.