# Statistical Hypothesis Testing to prove signficant quality improvement or decline

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#### Kelly Speiser

Statistical Hypothesis Testing

Is statistical hypothesis testing used by our Quality professionals to help "prove" signficant quality improvements/declines? It seems to be a valueable tool but I do not see or hear much about it, especially since focus has been on 'QS/ISO system' quality.

Is there interest from anyone to learn more about hypothesis testing if were easy to learn? The reason I'm asking is this: an easy-to-use workbook has been writen and the author needs feedback and peer reviews.

I find hypothesis testing fun and exciting. It is not so hard to do as DOE and one step above control charting.

Kelly Speiser

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#### Don Winton

I use hypothesis testing a lot. I find it an invaluable tool in determining significant difference between processes and performance. It is relatively simple (t-test, ANOVA, ANOM, F, Chi-square, etc)and the results are easily presented. I would love to have a peek at the book referenced. Write me at [email protected] or [email protected].

Regards,
Don

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Re: Statistical Hypothesis Testing

Hi Don and all other forum members,

I have a question related to hypothesis testing. I tried to find out in the book but couldn't get it. Hope any Statistic Champion would help me in finding the answer.

A hypothesis which contains 20 items and all these items are tested by using paired-samples t-test. If one or two items show significant difference whereas rest of the items are not statistically significant. In this case, should we reject the null hypothesis as a whole or we need some more items to be statistically significant. If yes, then how many items out of 20 should be statistically significant to reject the null hypothesis as a whole.

Thanks for any input or response.

Regards,

#### Tim Folkerts

Trusted Information Resource
Re: Statistical Hypothesis Testing

> A hypothesis which contains 20 items and all these items are tested by
> using paired-samples t-test.

So it sounds like you have 10 pairs of data (or perhaps 20 pairs, but that isn't really important.) You want to know if the first hafl of each pair is different than the second half of each pair.

> If one or two items show significant difference whereas rest
> of the items are not statistically significant. In this case,
> should we reject the null hypothesis as a whole

With a paired t-test, you aren't really interested in any specific pairs. The test is already designed to examine the data as a whole. If you already have a good idea about statistical significance, then I think some other tests might be more informative, but it is hard to know without more info.

Tim

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Re: Statistical Hypothesis Testing

Tim,

Thanks for taking time to respond my question that I had and my apologies for a bit late reply. Actually, I came to the conclusion that there isn't any clear answer for the hypothesis based on items. IMU, we should look for whether these items are interlinked with each other or not and how much impact would be on the whole hypothesis of an item that is significant. In my case the items are interlinked to each other. Therefore, rejecting the null hypothesis on the basis of one or two items that are significant would not be wrong.

Regards,

#### Steve Prevette

##### Deming Disciple
Super Moderator
Dr. Deming was very much against hypothesis testing. I am formally trained (as an Operations Researcher) in hypothesis testing, and I teach statistics for City University where I am required by curriculum to teach hypothesis testing.

The big flaws to look out for are:

1. People tend to play games with significance levels. We'll specify 5%, but when the data comes in at 6%, well that was close enough.

2. People use 10% significance levels, and do hundreds of tests on the data to see what they can find. Well, 10% of what they find will be "significant".

3. Hypothesis testing (and ANOVA) both lose the time series aspect of the data. If the data have occurred in a time sequence, you are much better off with SPC.

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Dr. Deming, really a BIG name in Quality and Statistics. One can not neglect his argument. In my research, the data was gathered one time and then analysis was made to interpret the outcomes. Therefore, hypothesis testing was plausible to analyze the data to accept or reject the formulated hypotheses.

Agreed, if this were the case on production line where the data is collected at a regular interval of time, then SPC would be a better choice of analyzing data.

There is a thread about 'Deming vs. Hypothesis Testing' which can provide you more thoughts about this topic. IMU, this issue needs an extensive research based on data to make any concrete findings.

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