| A Biometrical Study
of the Influence of Size of Brood Cell Upon the Size and Variability
of the Honeybee (Apis mellifera L.) by Roy A. Grout, 1931 |
| EXPERIMENTAL Throughout the following presentation of data, the measurements on the parts of the bee will be designated as follows: (A) dry weight, (B) length of right foe wing, (C) width of right fore wing, (D) sum of the widths of the third and the fourth tergites and (X) the measurement upon which the regression is made. In Table 7 are presented further data concerning the measurements of bees from colony 25 in which there is a regression of (A) dry weight, (B) length of right fore wing, (C) width of right fore wing and (D) sum of the widths of the third and the fourth tergites on (X) length of proboscis. The data consist of the standard deviations of the above-mentioned measurements, the standard regression coefficients, the multiple correlation coefficient, the standard error of estimate, the significance of regression and the regression equations for the bees from each size of cell. An analysis of variance of the length of proboscis between and within all three groups, namely, the groups of bees from size of cell "A", the group of bees from size of cell "B" and the group of bees from size of cell "C", is also presented. An examination of the standard deviations of the measurements of the bees from the three sizes of cells shows that the variation is greatest in the case of length of right fore wing and length of proboscis with the bees from size of cell "A" and least in the case of the bees from size of cell "B". The standard deviation of the width of the right fore wing is greatest in the case of the bees from size of cell "A" and the least in the case of bees from size of cell "C". The standard deviation of dry weight increases as the size of the cell is increased. The standard deviation of the sum of the widths of the third and the fourth tergites is greatest in the case of the bees from the size of cell "B" and least in the case of bees from the size of cell "A". The significance of the standard regression coefficients was tested by dividing the standard regression coefficient by its standard deviation and comparing the resulting value with the significant values for "t" as given in Table 16 by Wallace and Snedecor (69). The significance of the multiple correlation coefficients was determined by comparing the values obtained with significant values of "R" given by Wallace and Snedecor (69) in Table 16. The significance of the regression for the bees from each size of cell and the analysis of variance of length of proboscis of all three groups was tested by calculating one-half the difference of the natural logarithms of the mean squares and comparing the values obtained with the significant values of "Z" as given in Table 6 by Fisher*. An examination of the standard regression coefficients shows that only the standard regression coefficint of length of proboscis and length of right fore wing is significant for the bees from each of the three sizes of cells. The multiple correlation coefficient for the bees from size of cell "A" and size of cell "C" are highly significant, while the corresponding value for the bees from size of cell "B" is not significant. The "Z" test of the significance of the regressions further substantiates the significance of the multiple correlation coefficients by showing that the regressions of the measurements on the bees from size of cell "A" and size of cell "C" has been significantly accounted for. A study of the standard errors of estimate shows that the standard deviation of the length of proboscis of bees from size of cell "A" has been reduced 29.61% due to the extension of statistical control over factors relating to length of proboscis. In the case of the bees from size of cell "B" the standard deviation of length of proboscis has only been reduced 2.11%, while in the case of bees from size of cell "C" the reduction is 19.86%. In the latter case, the standard deviation of length of proboscis has been notably reduced by the inclusion of dry weight, length of right fore wing, width of right fore wing and the sum of the widths of the third and the fourth tergites in the regression. A study of the regression equations for the bees from the three sizes of cells shows, in general, that length of the right fore wing is the dominating factor in these estimation equations of length of proboscis. An analysis of the variance between and within the groups of bees from all three sizes of cells shows that the variation between the groups is significantly greater that that within groups. This further substantiates the proof presented under section 1 of the presentation of data of a significant difference between the means of the length of proboscis of the three groups. In Table 8 are presented statistical constants of measurements on bees from colony 25 concerning a regression of (A) dry weight, (B) length of right fore wing, (C) width of right fore wing and (D) sum of the widths of the third and the fourth tergites on (X) length of mentum. In Table 9 are presented data concerning the statistical constants of measurements on bees from colony 25. In this table the regression is dry weight, length of right fore wing, width of right fore wing and sum of the widths of the third and the fourth tergites on length of glossa. Statistical constants of measurements on bees from colony 25 concerning a regression of dry weight, length of right fore wing, width of right fore wing and sum of the widths of the third and the fourth tergites on the sum of the lengths of the mentum and the glossa are presented in Table 10. A comparison of Tables 7, 8, 9 and 10 shows that the data presented in Tables 9 and 10 proffer the same conclusions as were drawn from the data of Table 7. From the data presented in Table 8, there is an agreement with the data of the other three tables in the variation of the length of mentum as indicated by the standard deviation of length of mentum of the bees of all three sizes of cells, the multiple correlation coefficient and the significance of the regression of the bees from size of cell "A", and the analysis of variance of length of mentum between and within the groups from all three sizes of cells. In no cases are the standard regression coefficients significant. In contrast to the data presented in the other three tables, the multiple correlation coefficients and significance of regression for the bees from the size of cell "C" are not significant. An examination of the regression equations shows that length of right fore wing has ceased to be a dominating factor in the estimation of length of proboscis. *Fisher, R. A., "Statistical Methods for Reasearch Workers", second edition revised and enlarged. Oliver and Boyd, Edinburgh. 1928. |