Non-Parametric Testing for Widget Defectivity: Sample Size Considerations

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Discussion Overview

The discussion revolves around determining whether the defectivity of a specific widget is significantly different from the usual defectivity observed in widgets. The focus is on the application of non-parametric testing methods, particularly in the context of small sample sizes derived from batches of widgets.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the appropriateness of using a non-parametric test given the variance in defectivity within and between batches, particularly with only three batches available for analysis.
  • Another participant seeks clarification on what constitutes 'different' defectivity, suggesting that the initial question lacks specificity regarding the types of defects.
  • A later reply clarifies that the focus is on the number of defective parts in each widget, rather than the nature of the defects themselves.
  • There is a request for information regarding the number of parts in a widget and the usual defect count, indicating a need for more context to address the original question.
  • One participant advises against generalizing statistical problems, emphasizing the importance of contextual expertise over abstract problem-solving.

Areas of Agreement / Disagreement

Participants express varying levels of clarity and understanding regarding the initial question, with some seeking more detail while others challenge the framing of the problem. No consensus is reached on the appropriateness of the statistical approach or the definitions involved.

Contextual Notes

The discussion highlights limitations in the initial problem statement, including missing details about the types of defects and the usual defect count, which may affect the choice of statistical methods.

Who May Find This Useful

Readers interested in non-parametric statistical methods, quality control in manufacturing, and those dealing with small sample sizes in defect analysis may find this discussion relevant.

DeShark
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Hi all. I'm trying to come up with a way to determine if the defectivity of a particular widget is 'different' to the usual defectivity of a widget. The difficulty comes from the fact that widgets are made in batches of 25. We'd like to investigate any widgets which have a higher (or lower) defect count than should be expected.

Is it Ok to use a non-parametric test on the widget defect count, despite the fact that the variance of defectivity within a batch is less than the variance between batches. E.g. if only 3 batches have been made, what is the sample size? 75? This doesn't seem right to me...

Any insight or suggestion is very welcome. Thank you!
 
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DeShark said:
I'm trying to come up with a way to determine if the defectivity of a particular widget is 'different' to the usual defectivity of a widget.

It isn't clear what that means. Taken literally it implies that there is a variable type of defectivity in widgets, but you didn't elaborate on what would make one type of defect different than another and without getting into those details, I don't think there is a general answer to your question.
 
Sorry for not being clearer: each widget itself is made up of parts, each of which can be 'working' or 'defective'. The exact manner in which the parts are defective is unimportant; just the number of defective parts (or equivalently, the proportion of parts which is defective).
 
I should have said:

I'm trying to come up with a way to determine if the defect count of a particular widget is 'different' to the usual defect count of a widget.
 
How many parts make up a widget and what is the usual defect count?
 
Last edited:
My general advice is not to approach real life statistical problems as general problems! Textbooks pose problems involving widgets and being an expert on astronomy or strength of materials etc.doesn't help you solve them. In real life, if you have expertise in a situation, you shouldn't lobotomize yourself by thinking of it as a problem with "widgets".
 

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