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I have a set of data in tabular form which records the time it takes 500 people to bake a cake. Each person is assigned a single time: it may take Tom 30 minutes, or Mike 60 minutes to bake a cake.

What statistical tools can I use to capture the fastest bakers? The hope is that by identifying the fastest bakers I can then interview them to find out their technique which can then be shared with others.

Could outlier analysis using box plots be useful, if so how?

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    $\begingroup$ This seems an unlikely dataset, that someone somehow monitored 500 people! $\endgroup$
    – Nick Cox
    Commented Oct 3, 2023 at 14:52
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    $\begingroup$ @EngrStudent I don't like violin plots, but don't care about that. How do violin plots help the OP identify the faster bakers? $\endgroup$
    – Nick Cox
    Commented Oct 3, 2023 at 15:07
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    $\begingroup$ Re "statistical tools to capture the fastest bakers:" the Lasso immediately comes to mind, because it works well on cattle ;-). $\endgroup$
    – whuber ♦
    Commented Oct 3, 2023 at 15:41
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    $\begingroup$ @NickCox 1) Could be self-report, 2) I agree that plots won't help (and I agree with your answer) but 3) Why don't you like violin plots? $\endgroup$
    – Peter Flom
    Commented Oct 3, 2023 at 18:43
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    $\begingroup$ @PeterFlom 3) I don't like the way violin plots are based on decisions that are rarely (ever?) revealed, namely the precise kernel smoother used OR the way that they smooth over what may be vital detail in the data, including sample size. $\endgroup$
    – Nick Cox
    Commented Oct 3, 2023 at 20:20

2 Answers 2

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Just sort the data and note the names of the top 5, or whatever the number is. Spreadsheets as well as any statistical programs make this easy.

Box plots are not going to be helpful here unless you see the names too, and you can get those directly.

Similarly the top few of 500 are by definition nowhere near the median or the quartiles, unless you are planning to interview the top 125, which I doubt.

(This has the flavour of an implausible assignment, but there you go.)

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First, I agree with Nick. No statistical method is needed, nor can any really help (unless you consider sorting to be a "statistical method").

Second, I'm betting this is a HW assignment, but it is a pretty bad one because there are a number of issues.

  • How did they get the times? If it was self-report (which seems likely) then you may well be measuring error. That is, not how long it takes a person to bake a cake, but how long they think it takes them, or how they interpret the question (does that include baking time? Time to set up the mise en place?) or what cake they are baking. The question "how long does it take you to bake a cake?" is preposterously vague.

  • What cake? From what recipe?

  • If you do manage to solve those issues, then the most likely factor in determining the time it takes Bob vs. Karen to bake the cake on p. 120 of XXXX cookbook, from start to finish, but not including clean up time, is going to be how many times the person has baked the cake. Also, what tools they have (stand mixers are easier to use than hand held, but take more clean up).

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