Page:Journal of the Optical Society of America, volume 30, number 12.pdf/59

 each of the three grounds were computed in the usual manner. These means were multiplied by the appropriate constants to transform them from the investigator’s recording scales to the Munsell attributive scales. These constants were 1.0, 0.1, and 0.4, respectively. In this way, averaged estimates of the hue of each color were secured from the constant-value chart data, and averaged estimates of the value of each color were secured from the constant-hue chart data. Since the estimates from both sets of charts included chroma, the two sets of chroma data were weighted in proportion to the numbers of observations and averaged together to yield a single representative chroma determination.

Thus in the end, there became available one representative estimate for each attribute of each chromatic color on each ground. These 3500 determinations are presented in the body of.

The averaged estimates

The first column of shows the 1929 notation of hue, value, and chroma; the next three (double) columns to the right show the average hue estimates and uncertainties, corresponding to the observations with the three different viewing grounds; the next three columns present the corresponding value data; and the final three columns, the chroma data. All determinations are presented to the first decimal place of the respective Munsell attributive unit.

The measure of uncertainty or variability consists of the range within which the middle 80 percent of the individual estimates fall. This range could be found only approximately from our summary sheets; but it provides a consider ably more reliable and representative measure than would the full range. Where no measure is given, as is often true of the hue estimates, the fact is that the 80 percent fell within a single recording unit of estimate. Though expressed in tenths, the limits of the 80 percent attributive ranges are given only to the nearest unit of estimate. Thus, one may note, the hue ranges are expressed in full hue steps, chroma in 0.4 steps and value in 0.1 steps.

In certain rare instances the mean may be found to fall without the 80 percent range. This anomaly is possible because of the skewness of distributions and the fact that means are computed in smaller units than ranges.

Asterisks in the hue columns accent a few instances in which the hue means are absent because hue data could not be taken. These instances concern the /2 chroma intermediate colors which do not appear on the constant-value charts. Corresponding value and chroma data could be given in Table II, however, because they were secured from the constant-hue charts upon which the samples in question do appear.

Before pointing out some general results, one more technical detail concerning must be mentioned. This is the marked variation in the number, n, of cases upon which any given mean and range depend. In general, the chroma data are based on the largest numbers of observations (around 35) because results from both types of charts could be combined. Only in the case of the /2 chroma intermediate colors, mentioned above, are the chroma data scanty, for here only the few observers of the constant-hue charts could contribute. The hue data are next most plentiful (n≐25), being based on the relatively numerous observations with the constant value charts. The lightness data, on the other hand, could be secured only from the 10 subjects who observed the constant-hue charts, and the results from one of these could not be used because of a failure to follow instructions. More lightness data had been expected and, unquestionably, more are desirable. Fortunately, however, lightness has been the most investigated attribute, and there are visual data on Munsell value in the laboratory files of the Munsell company as well as in the literature. These sources will be consulted in conjunction with the final smoothing operation.

General indications

A detailed analysis of will constitute a part of the smoothing operation to be per formed in preparation for the final report, but