• # Statistics 301 for Reward Professionals

By Nicol Mullins

“One of the first things taught in introductory statistics textbooks is that correlation is not causation. It is also one of the first things forgotten.” ― Thomas Sowell

The first paragraph in our last edition noted that ‘the capacity to collect, process, draw relevant conclusions and make a valid recommendation from different sources of data is an essential activity for reward professionals.’ The quantified relationships between variables and the strength of such a relationship lends statistical credibility to analysis. This article will explore the relationship that exist between actual and exponential regressions. The specific application will focus on the drawing up of pay ranges from actual data to smoothed data applying regression. In this year there will be a focus on working through various regression models, explaining the concepts and the practical application of such regression models.

Excel provides the functionality to work with various regression models, predominantly exponential and polynomial regression is applied, other models are logarithmic, linear, power and moving average. Figure 1 provides an overview of market midpoints (market anchor) plotted by company grade with a range width of +/- 20% (80% – 120%) and a spread of 50% [(Maximum minus Minimum)/Minimum]. The blue dots on the market anchor points reflect the ideal positioning for the organisation for which we will be drawing up the pay ranges. It can be observed that that the differential between grade D and E are greater when compared to E and F. An organisation might want to smooth out these differences by applying exponential regression to get an equal incremental change from one grade to another for ease of progression.

Figure 1: Actual market data If one wants to determine what the line of best fit and what the correlation to the actual data would be, we will insert a trendline by right clicking on the graph and choosing trendline. A new menu will pop-up where one will choose “Exponential” and tick “Display R-squared value on chart” as can be seen in Figure 3. Figure 3: Adding exponential trendline with R-squared R-squared (R2) is a statistical indicator of the strength of the relationship between actual and the fitted regression. In this example the value is 0.9728, which means there is a 97.28% fit between the actual and exponentially regressed data. Typically, in compensation a r-squared greater than 0.7 is deemed acceptable, but the closer the value tends to 1.00 the better the fit is.

Figure 4: Exponential trendline overlayed on actual market data It is possible applying this exponential regression formula to smooth out the market data to have an exact fit to draw up pay ranges. Once again Excel provides the functionality to smooth out the data by applying a few clicks.

Figure 5: Series Fill Functionality Figure 6: Growth trend R-squared is now equal to 1.00 which indicates a perfect fit. Remuneration managment is both an art and a science, applying regression provides the science balancing the appropriate fit the art. 