| CT | S | E | L | W |
|---|---|---|---|---|
| 4. | 58 | 1 | 1 | 1.5 |
| 4.5 | 45 | 11 | 4 | 9.5 |
| 5. | 32 | 13 | 15 | 21.5 |
| 5.5 | 19 | 16 | 25 | 27 |
| 6. | 5 | 4 | 51 | 7 |
| 6.5 | 1 | 2 | 57 | 2 |
We can calculate the value of the average ET if we assume that the distribution of wrong judgments is in general in accordance with the law of error curve. We see by inspection of the first three columns that this value lies between 5.0 and 5.5, and hence the 32 cases of S for CT 5.0 must be considered correct, or the principle of the error curve will not apply.
The method of computation may be derived in the following way: If we take the origin so that the maximum of the error curve falls on the Y axis, the equation of the curve becomes
y = ke-γ2x2
and, assuming two points (x1 y1) and (x2 y2) on the curve, we deduce the formula
| ±D √ log k/y1 | |
| x1 = | ———————— |
| √log k/y1 ± √log k/y2 |
where D = x1 ± x2, and k = value of y when x = 0.
x1 and x2 must, however, not be great, since the condition that the curve with which we are dealing shall approximate the form denoted by the equation is more nearly fulfilled by those portions of the curve lying nearest to the Y axis.
Now since for any ordinates, y1 and y2 which we may select from the table, we know the value of x1 ± x2, we can compute the value of x1, which conversely gives us the amount to be added to or subtracted from a given term in the series of CT's to produce the value of the average ET. This latter value, we find, by computing by the formula given above, using the four terms whose values lie nearest to the Y axis, is 5.25 secs.
In Table II are given similar computations for each of the nine subjects employed, and from this it will be seen that in every case the standard is overestimated.