METHODOLOGY

    The methodology used for this analysis is such that it can be replicated.  Although just the 1997 budgets are used here, budgets or financial reports of counties can be used for past and future years to track any changes in amounts expended for particular services or objectives.  As such, this report might be updated periodically.

    The method used for comparing the counties is a statistical tool called "ordinary least squares" or "applied regression." Regressions are commonly used in the initial stages of statistical analyses for the purpose of discovering the relationship between two variables - one independent and one dependent. In the case of this analysis, the independent variable is population. The dependent variables (y-axes) are the various budgetary characteristics that were identified in the Saginaw report. These include the funding and staffing levels for 34 departments and special functions.

    The applied regression offers two features that are appealing to policy makers. First, it combines the information from all counties to give an estimate of the expected value for each county. This can be done by examining the departments individually or in groups - both of which are addressed in this report. The expected value should not be thought of as an ideal to which the county should strive to reach. The expected value takes into consideration the budgeted amounts for all counties and then uses the population as the only basis for determining a point estimate. The expected value does not take into consideration the stated objectives of a county. Specifically for this reason, it can be used to examine a county’s stated priorities and measure the degree of commitment in terms of funding to other counties.

    A second feature is that it identifies whether the budgetary characteristic is indeed related to county population. This is measured by the R-Squared number that also appears in the summary tables. An R-Squared value helps frame the significance of the expected value. Although the R-Squared value informs the analyst on the strength of the relationship, the nature of the research determines the value which the R-Squared must attain before the relationship is considered significant. For the purposes of this analysis, an R-Squared value of .7000 is treated as statistically significant. However, the significance level of the R-Squared is somewhat arbitrary. For other types of research, this value could vary from .6000 to .9000 before significance would be assumed.

    The expected value is a point estimate of the funding level if the particular variable were entirely dependent on population. The R-Squared then serves as a way of gauging the accuracy of the point estimate. A high R-Squared indicates that the expected value is fairly accurate while a low R-Squared indicates that the range of values around the point estimate could be quite large. Appropriate interpretation of these values appears in the analysis.

    Although the applied regression conveys a great amount of information, there are several difficulties with this type of analysis. First, budgeted dollars are used as a basis. Since budgeted dollars are only estimates of actual expenditures, there will be variance between what is budgeted and what is spent. Another problem with using the budgets as a basis for comparison among counties is that variance is bound to exist in the ways in which programs are funded. For example, special millages for programs such as transportation, emergency telephone services, parks, and law enforcement will result in inconsistent reporting among the counties. A county with a special millage is bound to have a higher budget for the particular cost category.

    Second, counties are also not completely uniform in the ways in which programs receive funds and the responsibilities of those programs. Not all counties have the same number of departments and similar functions may be carried out by several departments in one county but just one department in another county. Also, the structure of departments may vary from county to county. For example, the Clerk’s Office may or may not include costs of Register of Deeds or elections. This difference in reporting can yield significant variances in the results and low R-Squared values. When examined in groups of similar departments, the variances tend to decrease while the R-Squared values tend to increase, thereby revealing a stronger relationship.

    Third, outcomes are assumed to be reflected in the amounts budgeted for programs. A dollar budgeted for the sheriff in one county is assumed to yield the same output as a dollar budgeted for the sheriff in another county. However, the two departments might have a different set of responsibilities and objectives. One might include programs for drug awareness resistance education, community policing training, telemarketing fraud prevention, or a special weapons and tactics team. Yet if one incorrectly assumed the two departments had the same set of responsibilities, it would appear that one spends more resources for the same outcomes although the additional funding is due to additional responsibilities. Put another way, this sort of analysis can not differentiate between whether priorities or efficiency determines spending patterns. Where applicable, the differences in responsibilities between Ingham departments and those of other counties are stated so that a more informed conclusion may be made.

    A fourth concern is that fifteen (the number of counties) is a relatively small number of subjects for this sort of analysis. This number is even less in some instances because not all counties have the same departments as others. The applied regression is normally used for data sets of twenty or more subjects because the number of subjects is directly linked to the variance of the expected values - larger data sets tend to yield lower variances. Although more counties could have been included, this would have limited the conclusions that could be drawn. Larger counties as well as smaller counties are likely to have substantially different needs as well as different tools available to address those needs. For example, each of the fifteen counties studied in this report has a health department. Some rural counties which are not included in this report partake in regional health departments and rural health needs are substantially different than urban needs. Also, comparing counties of similar populations reduces the effect that economies of scale have in skewing results. It is therefore appropriate to compare only counties of similar size.

    Finally, an applied regression tends to over-emphasize larger subjects. The median county in terms of population is Muskegon. Ideally, the median would also be the average. Yet in this case, the difference in population between Muskegon and Kent (the largest) is 371,190 while the difference between Muskegon and Bay (the smallest) is just 54,089. The effect that this has on the outcomes is that the influence of Kent and Genesee counties tends to be somewhat overstated. Put another way, if both Kent and Genesee counties are over the trend line for a given variable, the majority of the remaining counties will be under the trend line.

    Although the above constraints limit the conclusions that can be drawn, several results can be found from an applied regression. First, the applied regression acts as a way of determining the level of funding that is expected of counties within the range of population. This is particularly true when departments are examined in groups of similar services, such as all departments relating to law and courts. In such groups, budgetary priorities can be accurately measured and compared to the stated priorities of the county. Second, the applied regression can identify potential inefficiencies and inequities. Some departments receive more funds than their counterparts in other counties. Such a department might require more funds to perform the same tasks or it might have additional responsibilities. In either case, a more thorough examination might be warranted. Examples of this will become apparent in the analysis.