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    Comparing standard deviations of different means




    Hey y'all, I'm a total rookie when it comes to statistics, so please forgive my ignorance/laymen's terms.

    I want to know when CONSISTENCY is more valuable than a higher mean for a range of numbers. For instance, if one range of sales figures from employee A is a lower average but has a lower standard deviation, and employee B has a range of sales figures with a higher average but also a higher deviation. Most week, employee A is better, but B can pull some big numbers to make up for it. Again, I want to know when steady production is more valuable than overall average production.

    I can give you examples, but I don't know what numbers you'd need.

    Thanks!

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    Re: Comparing standard deviations of different means

    Are you interested in a statistical comparison of the dispersion in two samples? If so, Bartlett's test would work (assuming your data are normally distributed): http://en.wikipedia.org/wiki/Bartlett%27s_test. If you don't have normally distributed data, Levene's test will work. You can get SPSS to give you Bartlett's if you ask for it in the factor analysis procedure, and you can get Levene's test in SPSS by using the two-sample t-test. These tests will allow you to evaluate if one group of data is more consistent than another.

    As far as which is more valuable... valuable in terms of what? If we are talking about like which salesperson makes more sales, a t-test takes the dispersion of the data into account when comparing the means, so it could be used to see which is more valuable in terms of sales.
    Last edited by marchhare; 05-20-2011 at 10:00 PM.

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    Re: Comparing standard deviations of different means

    Well, from what I've read it seems like the T-test can help me- but to be sure, here's a sample of two numbers I'm trying to compare:

    Here are the weekly units sold by Employee A vs Employee B. I put an asterisk (*) next to the month's leader in sales.

    A
    43*
    32*
    37*
    58*
    77*
    57
    41*
    53
    61*
    42*
    48
    45*

    B
    41
    17
    12
    47
    46
    126*
    34
    113*
    47
    12
    101*
    17

    SUM for A: 594
    SUM for B: 613
    AVG for A: 49.50
    AVG for B: 51.08
    ST DEV for A: 12.30
    ST DEV for B: 40.19


    Now, B has a better average and a higher number of units sold, but a worse consistency (st. dev.). Also, Employee A outsold Employee B 9 out of the 12 months.

    Let's say I have to give one of them a promotion- how can I test whether the consistency is more valuable than the total output?
    Last edited by cpaavola; 05-22-2011 at 02:24 AM.

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    Re: Comparing standard deviations of different means

    Hi!

    Please, see the attached files.

    First, I believe that you should consider to use the median instead of the mean as measure of central tendency, due to the presence of some outliers values in both samples (Employees).
    Using this robust measure, the story remains the same as you rightly pointed out. A stands out for two reasons: 1) because he sold a slightly greater median amount of units (46,5); 2) because the amount of sold units is less variable (as the IQR, Norm IQR, and Robust Coefficient of Variation show). On this respect, it is true that B managed to sell 126 units, but it is also true that he is featured by lower peak of sold units (compare the 1 quartiles).

    So, all thing considered, I believe that A performed better than B as far as median values of sold units, and variability of sold units, are concerned.

    Best Regards,
    Gm
    Attached Images
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    Re: Comparing standard deviations of different means


    To answer whether consistency is more important than mean performance, you need to do a cost-benefit analysis. How much does it hurt the company to have a few cases of very low performance? Often, even a single instance of very low performance can cause irreparable damage to the company. In that case, you should prefer consistency. If the low performances can be corrected with a few instances of high performance, you should probably prefer the worker with a better average.

    Without knowing the details of the business, we can't really answer this question.
    Last edited by squareandrare; 05-23-2011 at 03:03 PM.

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