Question

A firm is attempting to evaluate the quality of its scale stuff and is trying to find an examination or series of tests that may reveal the potential for good perfoarmaence in scale. the firm is proposing to select a random sample of salespeople and will evalute each on 3 measures of performance: growth of scale,profitabolity of scales and new amount scale.Each of this measure will be measured on ascale for which a scoreof 100 indicates "average" performence.the firm is also proposing to give each of the subjects in the study aptitude test on creativity,Mechanical reasoning,abstract reasoning and methametical ability. Assume that you are statistical consultant and that firm has made an appointment with you to discuss the design and stastical analysis of theire study. outline a seris of question that you would ask theire represntatives to obtain detailed information and the inforamtion givenn so far indicate probable advice that you will be giving the firm.

Answer 1

This is a good project because it makes the student really think about the problems in statistics.

I think the first thing to realize is that the company wants to see how aptitude test scores correlate with sales marks. Confirm this with the company! Then, clarify various metrics that may be of use, and pitfalls that statistical laypeople might fall into. For example, you may mention the obvious Pearson (or even Concordance) correlation between a given test score and a given performance measure. However, you'd need to then realize that the Pearson measure will test the tightness, but not the strength of that correlation (i.e., mathematical ability may strongly correlate with profitability of sales, but it may only change the profitability by a small amount [low variability, low slope], whereas creativity is more loosely correlated, but can provide massive gains when lucky [high variability, high slope]). In light of this, it may behoove the company to use a Rank-Sum type non-parametric test for correlation. Similarly, you may want to use a multi-group ANOVA (or something like that) to compare how the test scores interact--but then again, it may be better to use something like Fisher's Linear Discriminant using a scalar cost function... that's probably too advanced for this class, but the idea is to determine what you think would be the most informative statistical tests AND QUANTITATIVE MEASURES and go from there.

Be creative and confident! And it's common for students in statistics classes to limit themselves to hypothesis testing, but there are more advanced metrics out there that don't just output a "p value" which you might look into