Consistency and Sales Volume Comparision

Performance assessments require many relevant statistical tests in a given scenario. Some of the statistical indicators that are useful to quantify these output types include the mean, variance, standard difference, mode, median and graphical display of results. In these cases, the best performer will be the vendor with the highest average sales volume and the lowest standard deviation.
We equate the means with the average revenue for each salesperson. The appropriate statistical tool to use in this case is the One-Way ANOVA test. The test entails the formulation of the null and alternative hypothesis to determine whether the salespersons have different volumes of sales. So, our initial assumption is that the performances of all the salespersons are the same and they, therefore, have same means of their sales volume. The claim here is that the average sales of the salespersons are the same.
We, therefore, have the following hypothesis statement:
Null hypothesis, H0: The mean sales volume of all the salespersons are equal
Alternative hypothesis, H1: The mean sales volume of all the salespersons are unequal
From the hypothesis testing, the conclusion would determine the best performing salesperson. Having defined the problem and formulated the null and alternative hypothesis, we choose significance level. In this case, we are going to use alpha (α) =0.05 as the significance level. Next is the determination of the p-value and the rule for making a decision. The decision rule is that we are going to reject the null hypothesis if the p-value < 0.05 (α)
Using Minitab, the calculation of the p-value from the one-way ANOVA is in the following output
One-way ANOVA: A, B, C, D Source DF SS MS F P
Factor 3 1420023 473341 11.88 0.000
Error 20 796875 39844
Total 23 2216899S = 199.6 R-Sq = 64.05% R-Sq(adj) = 58.66% Individual 95% CIs For Mean Based on
Pooled StDev
Level N Mean StDev ----+---------+---------+---------+-----
A 6 1830.8 76.2 (------*------)
B 6 1947.5 327.3 (------*------)
C 6 1310.2 149.5 (-----*------)
D 6 1604.0 155.1 (------*------)
----+---------+---------+---------+-----
1250 1500 1750 2000Pooled StDev = 199.6 The p-value from the Minitab output is 0.000. It is less than alpha, so we reject the null hypothesis that the means of sales volume of all the salespersons are equal. We then make the conclusion that at 5% significance level, there is sufficient evidence to show that the average sales volumes of all the salespersons are unequal. This difference is evident from the Minitab output above whereby B has the highest average sales volume followed by A, D and C in that order. It, therefore, means that from the comparison of the average sales volume, salesperson B has sold the highest volume while salesperson B has sold the least amount among the four salespeople. We can, therefore, use these values to arbitrarily say that the best performing salesperson is B while C is the least performing salesperson.
However, using mean to compare performance, in the long run, cannot be appropriate. Further analysis is necessary to determine the consistency in performance of each salesperson. A sales person can be the best performing salesman at the time of evaluation or in the short run, but in the long-term, it will not be surprising to find out that the person might be performing at the lowest level possible.
The most appropriate statistical measure to determine consistency is the standard deviation. A salesperson would be said to have consistent sales if the standard deviation of the sales is small and at one point, he has maximum sales as compared to other salespersons. The descriptive statistics would be useful in determining the standard deviations and the maximum sales of each person. The Minitab output for the descriptive statistics is as follows.
Descriptive Statistics: A, B, C, D
_x0001_
Figure 1. Descriptive Statistics
From the means and standard deviations in the Minitab output, salesperson A has the highest volume of sales, 1932, as well as the minimum standard deviation, 76.2. The mean sales volume of A is 1830.8 which is also relatively high. A is thus a consistent performer among the other salespersons.Reference
Alyounes, Y. (2012). A realistic look at one way ANOVA (1st Ed.).