A Productivity Analysis for Generic Government Agency
Executive Summary
The Generic Government Agency is operating through 82 employees working in 19 regional offices located throughout the state. It is now time for a review of the current arrangement to determine if consolidating the offices into larger offices would increase productivity. An index method has been applied to the available data on each office's production, and this allowed for ranking of the 19 offices by their overall productivity per assigned worker. If the offices with the most workers accomplish more, or larger offices have higher productivity, the study will support consolidation of the offices. However, no clear evidence from the study supports a consistent correlation between office size and the level of productivity.
Two other techniques, the rank and the standard deviation methods, are applied to the same raw data to test the index method's findings. Although the three methods rank the 19 offices differently based on their converted overall productivity figures, all three methods reach a same conclusion: the data from the current operation does not support consolidation of the offices into fewer larger offices.
The Situation
A productivity analysis has been done on the Generic Government Agency's 19 regional offices scattered throughout the state. The outcome of the study does not support consolidating the offices into a few large offices. If larger offices are more productive than small of fices, charting the of fice size against productivity would show a positive relationship (upward sloping to the right). An index method was applied to compare the productivity at the 19 regional offices that range in size from 1 to 7 employees, with an overall average of 4.3 workers per office. This paper is interested in determining whether applying other statistical techniques to the same raw data will support the same conclusion drawn by the index method. The two other techniques applied are rank and standard deviation.
The raw data are summarized in Table One on the following page. The output figures are pulled from each of fice's records on number of personal and phone inquiries answered, number of applications received, informal complaints dealt with, formal legal complaints completed, and the number of truckers licensed. Inputs include the number of workers in each office and the cost of running each office. Using workers per office as input will give a very similar result to using office costs as input, because about 80 percent of the costs are payroll. The general formula for productivity is output divided by input. The resulting productivity figures per worker for each of the six output categories are summarized in Table Two, also on the following page. These figures are not yet comparable because they are not on a same scale. They need to be comparing to a same bench-mark figure. The index method is one way of comparing the 19 offices' productivity.
The Index Method
"An index number is a relative value, expressed as a percentage or ratio, measuring a given period against a designated base period."" Indexing the productivity figures in Table Two will put them on a same basis, each data will be compared to the base amount. Using the average (mean) outputs per assigned worker as the base amount, we can construct the simple indexes by dividing each productivity figure by the mean output for each output category. For example, the index number for Stockton's personal inquires answered is calculated as follows: 2,742/818*100=335. It means the Stockton's office answered 235 percent more of the personal inquiries than the average of all other offices. Table Three calculates and lists all the indexes. The 19 regional offices are ranked based on their overall indexed productivity. The table is shown in the next page.
The Rank Method
Compared to the other two methods, this statistical technique is the simplest and the easiest to apply. The six columns of output figures are ranked by column, then the overall rank for each office is computed by averaging these six ranks. Using Excel, the rank function can be inserted and copied/filled to all the other cells in the table. Ranking the output figures eliminates the amounts' magnitude and allows for a fair comparison among the data. The results are shown in Table Four on next page. The 19 regional of fices are ordered by their overall productivity ranks from the highest productivity ( 1 ) to the lowest (19).
The Standard-Deviation Method
Similar to the index method, this technique transforms the productivity figures to allow for meaningful comparison. Whereas the index method measures each productivity amount against the mean, this method measures each productivity figure's variance from the mean against the data set's standard deviation. Variance from the mean is obtained by subtracting the mean from the individual data point, then divide the variance by the standard deviation of the data set to get the distance measurement. Using Stockton's personal inquiry data, the calculation is (2,742-818)/598=3.220. This means that the data point is 3.220 standard deviation away from the mean. The results of replicating this calculation throughout the table are shown in Table Five on the next page. The 19 regional offices are ranked based on their overall productivity.
The Results
The three methods discussed above rank the 19 regional offices' productivity slightly different. As Table Six (next page) indicates, the productivity ranks produced by the standard deviation method differ from the list provided by the index method in only two places: it switches the ranks for San Bernadino and Eureka, also, for Santa Anna and Van Nuys. All the other offices have the same ranking by the two methods. Even though the Rank method produces a list that deviates from that by the other two methods, it follows the same direction as the other lists. A visual representation of the productivityranks by the three methods is provided after the tables.
Despite the differences in ranking the offices, both techniques support the same conclusion drawn by the index method. Since there is no evidence of a positive relationship between productivity and office size, the study does not support the consolidation of offices. In fact, the scatter diagram (on next page) of the office size and the productivity-ranks from all three methods hints at a trend of downward slope, a negative relationship. Charts of office size versus overall productivity-ranks by each of the three methods are available in the appendix.
Running simple regression analysis on office size and productivity ranks by the index, rank and standard deviation methods come out with adjusted r squares of 0.067, 0.065, and 0.090 respectively (the regression outputs are included in the appendix). These unacceptably low adjusted r squares indicate that the office size explained less than seven to nine percent of the productivity-ranks. These are the p-values for the office size coefficient: index method--0.149, rank method--0.153, and standard-deviation method-0. 113. These amounts are not below five percent, therefore, they are not sign)ficantly different than zero. Thus the data available for this research does not support consolidating the offices into fewer larger offices.
Appendix
