spacing-estimates did not total eight, they were proportionally adjusted before application to the preliminary data.
Table I. Average value determinations derived from the estimates of general value spacing, exclusive of the preliminary estimates. The observations were made for samples of each value on white, gray, and black grounds.
| MUNSELL HUE |
MUNSELL VALUE | ||||||||||||||||||||
| 2/ | 3/ | 4/ | 5/ | 6/ | 7/ | 8/ | |||||||||||||||
| Wh | Gr | Bl | Wh | Gr | Bl | Wh | Gr | Bl | Wh | Gr | Bl | Wh | Gr | Bl | Wh | Gr | Bl | Wh | Gr | Bl | |
| R | 1.8 | 1.8 | 2.3 | 2.8 | 2.8 | 3.7 | 3.8 | 3.8 | 4.8 | 4.8 | 4.7 | 5.6 | 5.9 | 6.2 | 6.6 | 6.9 | 7.2 | 7.4 | 8.0 | 8.1 | 8.2 |
| 10R | 1.7 | 1.7 | 2.1 | 2.6 | 2.7 | 3.4 | 3.6 | 3.7 | 4.6 | 4.5 | 4.7 | 5.5 | 5.6 | 6.1 | 6.5 | 6.7 | 7.3 | 7.4 | 7.8 | 8.1 | 8.2 |
| YR | 1.7 | 1.7 | 2.2 | 2.6 | 2.7 | 3.6 | 3.6 | 3.6 | 4.7 | 4.5 | 4.6 | 5.6 | 5.6 | 6.0 | 6.6 | 6.7 | 7.2 | 7.5 | 7.8 | 8.1 | 8.3 |
| 10YR | 1.8 | 1.8 | 2.2 | 2.8 | 2.8 | 3.6 | 3.8 | 3.6 | 4.7 | 4.7 | 4.7 | 5.6 | 5.7 | 6.2 | 6.5 | 6.7 | 7.3 | 7.4 | 7.9 | 8.1 | 8.2 |
| Y | 1.7 | 1.8 | 2.3 | 2.6 | 2.6 | 3.6 | 3.7 | 3.6 | 4.8 | 4.6 | 4.7 | 5.7 | 5.7 | 6.1 | 6.6 | 6.8 | 7.2 | 7.4 | 7.9 | 8.1 | 8.2 |
| 10Y | 1.7 | 1.7 | 2.2 | 2.7 | 2.7 | 3.5 | 3.6 | 3.6 | 4.8 | 4.6 | 4.6 | 5.7 | 5.6 | 6.1 | 6.6 | 6.7 | 7.2 | 7.4 | 7.9 | 8.1 | 8.2 |
| GY | 1.7 | 1.7 | 2.2 | 2.7 | 2.7 | 3.7 | 3.7 | 3.5 | 4.8 | 4.6 | 4.5 | 5.7 | 5.7 | 6.0 | 6.7 | 6.8 | 7.2 | 7.5 | 7.9 | 8.1 | 8.2 |
| 10GY | 1.7 | 1.8 | 2.2 | 2.6 | 2.7 | 3.7 | 3.6 | 3.7 | 4.8 | 4.6 | 4.7 | 5.7 | 5.6 | 6.1 | 6.6 | 6.7 | 7.3 | 7.4 | 7.8 | 8.2 | 8.2 |
| G | 1.8 | 1.8 | 2.2 | 2.7 | 2.7 | 3.7 | 3.6 | 3.7 | 4.9 | 4.6 | 4.6 | 5.7 | 5.6 | 6.1 | 6.7 | 6.7 | 7.3 | 7.6 | 7.8 | 8.1 | 8.3 |
| 10G | 1.7 | 1.7 | 2.2 | 2.7 | 2.6 | 3.5 | 3.7 | 3.6 | 4.7 | 4.6 | 4.6 | 5.6 | 5.7 | 6.1 | 6.6 | 6.7 | 7.2 | 7.5 | 7.8 | 8.1 | 8.2 |
| BG | 1.8 | 1.8 | 2.3 | 2.8 | 2.8 | 3.8 | 3.7 | 4.8 | 4.8 | 4.8 | 4.8 | 5.6 | 5.8 | 6.2 | 6.6 | 6.9 | 7.3 | 7.4 | 8.0 | 8.1 | 8.2 |
| 10BG | 1.7 | 1.7 | 2.2 | 2.6 | 2.7 | 3.4 | 3.6 | 3.7 | 4.5 | 4.6 | 4.7 | 5.5 | 5.6 | 6.1 | 6.5 | 6.7 | 7.2 | 7.3 | 7.8 | 8.1 | 8.2 |
| B | 1.7 | 1.7 | 2.2 | 2.6 | 2.7 | 3.6 | 3.6 | 3.7 | 4.7 | 4.6 | 4.6 | 5.7 | 5.6 | 6.0 | 6.6 | 6.7 | 7.2 | 7.5 | 7.8 | 8.1 | 8.2 |
| 10B | 1.8 | 1.8 | 2.2 | 2.8 | 2.8 | 3.6 | 3.8 | 3.6 | 4.7 | 4.7 | 4.6 | 5.6 | 5.7 | 6.1 | 6.5 | 6.8 | 7.2 | 7.4 | 7.9 | 8.1 | 8.2 |
| PB | 1.8 | 1.8 | 2.3 | 2.6 | 2.7 | 3.6 | 3.6 | 3.7 | 4.7 | 4.6 | 4.7 | 5.6 | 5.7 | 6.1 | 6.6 | 6.8 | 7.3 | 7.4 | 7.9 | 8.1 | 8.2 |
| 10PB | 1.7 | 1.7 | 2.2 | 2.7 | 2.7 | 3.7 | 3.7 | 3.6 | 4.9 | 4.7 | 4.6 | 5.8 | 5.7 | 6.0 | 6.7 | 6.8 | 7.2 | 7.5 | 7.9 | 8.1 | 8.2 |
| P | 1.7 | 1.7 | 2.2 | 2.7 | 2.7 | 3.7 | 3.6 | 3.5 | 4.8 | 4.6 | 4.5 | 5.7 | 5.7 | 6.0 | 6.7 | 6.8 | 7.2 | 7.5 | 7.9 | 8.1 | 8.2 |
| 10P | 1.7 | 1.8 | 2.2 | 2.6 | 2.7 | 3.8 | 3.6 | 3.7 | 4.8 | 4.6 | 4.7 | 5.7 | 5.6 | 6.2 | 6.6 | 6.6 | 7.4 | 7.5 | 7.8 | 8.2 | 8.2 |
| RP | 1.8 | 1.8 | 2.2 | 2.7 | 2.7 | 3.7 | 3.6 | 3.7 | 4.9 | 4.6 | 4.6 | 5.8 | 5.6 | 6.1 | 6.7 | 6.7 | 7.3 | 7.6 | 7.8 | 8.1 | 8.2 |
| 10RP | 1.7 | 1.8 | 2.2 | 2.7 | 2.6 | 3.5 | 3.7 | 3.6 | 4.8 | 4.6 | 4.6 | 5.7 | 5.7 | 6.1 | 6.6 | 6.7 | 7.2 | 7.5 | 7.8 | 8.1 | 8.2 |
| Average | 1.7 | 1.7 | 2.2 | 2.7 | 2.7 | 3.6 | 3.7 | 3.6 | 4.8 | 4.6 | 4.6 | 5.7 | 5.7 | 6.1 | 6.6 | 6.7 | 7.2 | 7.5 | 7.9 | 8.1 | 8.2 |
All of the observers of the constant-hue charts made the general spacing-estimates just referred to, and these modified the preliminary value estimates so substantially that it seemed well to provide some means of recovering the preliminary adjustments in case they should ever be wanted separately. This can be accomplished easily by subtracting out the grosser effects of the final step. The necessary constants for this purpose are supplied in Table I. Munsell value is indicated in the top row across the table while in the several columns below are presented mean spacing estimates corresponding to sample hue and background. To determine the magnitude of a preliminary adjustment, given the total estimate, all that is necessary is to find the difference between the total estimate recorded in Table II and the corresponding partial estimate in Table I. Thus, for instance, in the case of G 5/6 on the white ground, the total estimate is found in Table II to be 4.7; the corresponding figure for the final step in Table I is 4.6; and the difference, 0.1, represents the amount of the preliminary adjustment required. The averages for all hues given in the bottom row of Table I may be taken as approximate lightness estimates of the Munsell neutral samples.
Unlike hue and value, there was in the case of chroma no special problem in arriving at the summarized estimates, but only a simple averaging operation which will be mentioned presently.
(b) The other principal step in the averaging procedure was to enter the summarized final estimates (unencircled initials) as numerical frequencies in averaging sheets of the form shown at the bottom of Fig. 6. The arithmetical means[1] of the estimates of the given color on- ↑ Often the distributions proved to be violently skewed, so the question arose as to the most appropriate central representation to employ. Were the median chosen there would be less weighting of the extreme cases. On the other hand, there is some reason to believe that the extreme cases should be weighted. The reason is that there is a tendency to make “O.K.” judgments (estimates of zero displacement) unless there is somewhat clear evidence that displacement should be indicated. As a result one may reasonably suppose that the mode and median fall in the “O.K.” division more frequently than they should. Displacement
