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Journal of Applied Psychology 1983, Vol 68, No 3, 407^114
In the public domain
Individual Differences in Productivity: An Empirical Test of Estimates Derived From Studies of Selection Procedure Utihtv Frank L. Schmidt
John E. Hunter
U.S Office of Personnel Management and George Washington University
Michigan State University
Schmidt, Hunter, McKenzie, and Muldrow (1979) presented and applied a method for estimating the standard deviation of employee output in dollars This study cumulates empirical data from the research literature to estimate the standard deviation of employee output as a percentage of mean output For jobs with nonpiecework compensation systems, the standard deviation was found to average 20% of mean output Thisfigureis not greatly different from the 24% lower bound predicted on the basis of previous studies in which the standard deviation was in dollar form The figure for piecerate jobs was found to average about 15% of mean output For both piecerate and nonpiecerate jobs, the variability around the mean was small We conclude that the findings support the use of 40% of salary as an estimate of the standard deviation of productivity in dollars Use of 20% of mean output as the standard deviation value (or 15% for piecework jobs) in utility formulas allows evaluation of the impact of selection and nonselection programs in terms of percentage increase in output For organizations that want to hold output constant, this increase can be translated into payroll savings from reduced hiring
A critical parameter in studies of the economic utility of personnel selection and other personnel programs (such as training) is the standard deviation of employee contributions in dollars (SDy; Schmidt, Hunter, McKenzie, & Muldrow, 1979; Schmidt, Hunter, & Pearlman, 1982) Difficulties in estimating this value have long discouraged much needed utility analyses We have devised a practical method for estimating SZ>V (Schmidt et al., 1979) and have examined the resulting values as a percentage of salary for the jobs in question. The SDy as a percentage of salary has ranged from 42% (Mack, Schmidt, & Hunter, Note 1) to 60% (Hunter & Schmidt, 1982, p 258). As a rule of thumb, we have recommended (Hunter, Note 2; Schmidt, Note 3) that the round lower bound
The opinions expressed herein are those of the authors and do not necessarily reflect official policy of the institutions with which they are affiliated Requests for reprints should be sent to Frank L Schmidt, Office of Personnel Research and Development, Room 3G29, U S Office of Personnel Management, 1900 E Street, N W, Washington, DC 20415
figure of 40% of salary be used as a conservative estimate of SDV when time and/or resources do not permit the use of estimating SDt In addition to indices of employee variability in terms of dollars and in terms of a percentage of salary or wages, it would also be useful to express individual differences in output in percentage terms. That is, it would be useful to know the standard deviation of output as a percentage of mean output (SDP) for the job in question This figure would allow gains from improved selection to be expressed as percentage increases in output. Aside from this practical value, knowledge of the extent and magnitude of individual differences in productivity is of general informational and theoretical interest to the field of applied differential psychology. We would like to know how much employees in the same job typically differ in productivity, probably the most important dependant vanable in industrial/organizational psychology. Given the fact that in the United States economy, wages and salaries make up approximately 57% of the total value of goods
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FRANK L SCHMIDT AND JOHN E HUNTER
and services produced (Hunter & Schmidt, 1982, p 268), we can derive lower and upper bound predictions for the value of SDP: Lower bound prediction = 42% (57%) = 24% Upper bound prediction = 60% (57%) = 34% The purpose of this study is to compare these upper and lower bound predictions to empirical figures for SDP that can be extracted from the cumulative research literature. This literature consists of (a) studies that report the mean and standard deviation of actual employee production or output and (b) studies that report the ratio of actual output of highest producing employees to actual output of lowest producing employees. In the latter type of study, given the assumption of normality of the full output distribution, the standard deviation as a percentage of mean output can be computed for all studies that give the sample size In either case, only studies based on actual physical counts of employee output can be used The mean of these SDP values across studies can be compared with the predicted lower and upper bound values of 24% and 34% The standard deviation of the empirical SDP values provides information on the job to job variability in the magnitude of individual differences Finally, one can compute from each empirical SDP value the ratio of output at the 95th percentile of production to the output at the 5th percentile, again based on the assumption of normality of the full distribution of output ' The mean of these ratios can then be compared with the ratios predicted by our lower and upper bound estimates 2.30 and 3.54, respectively.
it was not always possible to determine with certainty whether an incentive system was present or not Such uncertain cases were analyzed separately However, our hypothesis was that in such cases compensation was not on a piecerate basis It appeared that authors have described a compensation system only when it was a piecerate system In the studies reviewed, employee output was selfpaced, in none of the studies did employee rate of production appear to be constrained by the production technology, as it would be in the case of an assembly line A number of studies presented findings separately for experienced employees and all employees, in such cases, only the results for the experienced employees were used Other studies specified that only data from experienced employees were analyzed For the incentive condition, there were 11 usable reports, for the nonmcentive condition, there were 14 For the uncertain condition, there were 24 reports, but because of missing data. SDP and the ratio of output of the 95th to 5th percentiles could be computed for only 15 of these reports For studies that reported the mean and standard deviation of actual output, the ratio of the standard deviation to the mean was computed directly For those studies that reported only the ratio of output of the highest producing to the lowest producing employee (R) and the sample size, the following procedure was used The z score in the normal distribution was determined for the highest and lowest producing employees, and the distance in standard deviation units (d) between these two points was computed For example, if the two : scores are +2 00 and - 2 00, d = 4 00 The ratio of the 95th to 5th percentile (Ra) is then _(R + l)/2+ 1645(i?- \)/d "~ (R +l)/2 - 1 645(/? - \)ld The ratio of the SD to mean output is then SD Re- 1 " X ' 1 645tRo +1)
Results and Discussion Results for SDP
Table 1 shows the results for the nonincentive condition. The last column shows the standard deviation as a percentage of mean output. The mean of this value across studies is 185. The standard deviation of these values is quite small ( 052), even though it has Method not been corrected for the effects of sampling A review of the literature revealed 18 sources reporting error and is therefore an overestimate of real either distributions of actual employee output or ratios variability across jobs (Hunter, Schmidt, & of output of highest to lowest producing employees These reports ranged in time from 1928 to 1978 Rothe Jackson, 1982, chap. 3). (The formula for the (1978) and Rothe and Nye (1959) have presented evi- sampling error variance of this statistic is not dence that variance of productivity distributions and magnitude of productivity ratios vary as a function of whether there is a piecerate incentive system We therefore analyzed the two kinds of data separately, however, because of descriptive deficiencies in some of the studies.
1 For example, if SDP = 20, this ratio is (1 + 1 645 ( 20))/1 - 1 645 ( 20)) or 1 98
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INDIVIDUAL DIFFERENCES IN PRODUCTIVITY
known.) The value of 18.5% of mean output is 1.1 standard deviation units smaller than our predicted lower bound value of 24%. Although this difference is statistically significant (p < .01), the observed mean value is still 77% as large as the predicted lower bound value The mean ratio of output at the 95th and 5th percentiles is 1 93, which is again somewhat smaller than the predicted lower bound value of 2.30. Although the difference is again statistically significant, the observed value is 84% as large as the predicted lower bound value. The difference in standard deviation units is 93. The results for piecerate systems are shown in Table 2. Consistent with Rothe's (1978) hypothesis, both means are smaller than the corresponding values in Table 1, although those differences are not statistically significant. Both Table 2 mean values are significantly smaller than our predicted lower bound values, which is not unexpected because our predictions were derived from, and intended to apply to, jobs without incentive based compensation systems. As in Table 1, the variation around the mean values is quite small For the mean SDn, the standard de-
viation is only .044; for the mean ratio of 95th to 5th percentiles, it is only .29. Both figures are again overestimates because there has been no correction for sampling error. Table 3 shows the results for studies in which the compensation system could not be determined with certainty. This table includes one extreme data point, the value of 17 35 for sales clerks from the study by Lawshe (1948) This value is 24.84 standard deviations above the mean of the distribution of the values and is clearly an outlier Table 3 presents means and standard deviations with and without this anomalous value included; however, our discussion and conclusions are based on the data with suspect value excluded The mean value for SDP is .215, which is not significantly different from our predicted lower bound value of .24 The mean output ratio of 2.20 is also not significantly different from the predicted lower bound value of 2.30 The observed values in Table 3 are 90% and 96% as large as their respective predicted lower bound values Both observed values are larger than the corresponding values for the nomncentive condition in Table 1 (although the differences are
Table 1 Productivity Ratios Under Nonpiecework Compensation Systems
Study Klemmer & Lockhead (1962)" Study 1 Study 2 Rothe(1946) Rothe (1947) Time 1 Time 2 Time 3 Rothe & Nye (1958) Rothe &Nye (1961)" 1958 1960 Rothe (1970) Stead &Shartle (1940) Lawshe (1948) Tiffin (1947) Barnes (1958)" M SD a b
Job
N
Ratio of 95th to 5th percentiles
Card punch operators Proof machine operators Dairy workers
Not reported Not reported 8
1 47 1 57 2 23
116 135 232
Machine operators Machine operators Machine operators Industrial workers
130 130 130 27
190 2 69 2 80 1 94
189 .278 288 194
Machine operators Machine operators Welders Typists Cashiers Electrical workers Assembly workers
37 61 25 616
1 77 1 41 1 91 1 89 1 95 1 83 160
169 103 190 .187 196 178 140
193 40
185 052
29 33 294
Means and standard deviations for experienced workers given, ratios are based on these Ns are averages across 11-12 weeks
Ratio ofSZ> to average
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FRANK L SCHMIDT AND JOHN E HUNTER
not statistically significant). Both values are significantly larger (p < .05) than the corresponding values for the incentive condition (Table 2). These findings support our hypothesis that studies in the uncertain category are based predominantly or wholly on data from jobs without piecerate compensation systems and should be combined with the studies in Table 1. When this is done, the combined figures for Tables 1 and 3 are both significantly larger (p < .05) than the corresponding values in Table 2 These results indicate that individual differences in productivity may be somewhat smaller under incentive conditions than under nomncentive compensation systems. It may be that the effect of piecerate systems is to reduce individual differences in work motivation, thereby reducing the contribution of motivational differences to output differences. Under incentive conditions, output differences may be determined primarily by job-related abilities, whereas under nomncentive conditions, both ability and motivation may make large contributions. The combined nomncentive condition and uncertain condition data yield a mean SDP value of 20.0% of mean output (SD = .062) The mean ratio of 95th to 5th percentiles is 2.06 (SD = .53). These values are 83% and 90% as large, respectively, as our predicted
lower bound estimates, although the difference between each figure and the lower bound estimate is statistically significant
0>
