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Context:

I have a series of figures for car sales that show me (a) the usual number of car sales for particular models and (b) the number of car sales by a particular car salesperson for each model.

Let's say the values are:

Model | Sales by all Salespeople | Sales by Salesperson x
    A |                      100 |                     20
    B |                       50 |                     40
    C |                       50 |                      0

I want to find out if Salesperson x is significantly more responsible for sales of a particular model.

My first thought is to determine the rate of sales per model vs the rate of sales per model for the salesperson, i.e.:

Model | % Total Sales for all Salespeople | % Total Sales for Salesperson x
    A |                               50% |                             33%
    B |                               25% |                             66%
    C |                               25% |                              0%

However, naturally every salesperson has a significant variation in the cars they sell.

Question:

  • How do I determine if salesperson variation from the mean is statistically significant?

Initial Thoughts:

I think the Pearson correlation has some bearing, as perhaps may chi-square distribution, but I really don't have the background yet to understand why, so introductory help is appreciated.

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Chi square test, but I'd set it up as follows:

Model | this salesman | all other salesmen

A | 20 | 80

B | 40 | 10

etc.

Chi square test of independence, with expected values equal to row total * column total / grand total.

Null hypothesis: this salesman = same as all other.

Most stat books will have this test.

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