# Hypothesis Testing to Compare Lead Times

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• #56045

Stephen Coath
Participant

Good afternoon

We have recently finished implementing a transactional process change.
The Lead Time before the change was 8400 minutes and there was no target.
The revised process Lead Time is now 6000 minutes.

After submitting the project documentation, it was returned asking for documented hypothesis testing comparing the Lead time before vs the Lead time after and also asking us to analyse a null hypothesis of Lead time before = Lead time after.

To be honest we are struggling with this and unsure how to procede.
Anyone able to offer some guidance please?

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#202816

Robert Butler
Participant

If we are assuming the lead times you have provided are averages then the quickest way to answer both of the questions would be for you to run a two sample t-test. You would need to have the sample size for both of the lead time calculations and the associated standard deviations. The t-test would answer the question concerning statistically significant differences in the two lead times and the null the t-test is examining is that there is no difference between before and after lead times.

There is a caution here – if they really mean for you to test the equivalence of the before and after lead times (Lead time before = Lead time after) then you will have to run an equivalence test which is a Two One Sided t-test (TOST) and you will have to do some reading to make sure you are running the analysis correctly

Given what you are doing I would recommend also providing at least a histogram with both the before and after data overlaid on the same graph. This will help everyone visualize what you have done and what you are comparing. There are any number of graphical packages that will do this for you.

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#202819

Chris Seider
Participant

are you sure the lead times recorded are precise/accurate?

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#202820

Mike Carnell
Participant

@CI-Mentor Just a curious question. You said it was “returned” asking for the hypothesis test. Who (not necessarily a name) returned it? You have a difference of 40 hours. I assume that is a mean shift? I would think they would really want to understand the homogeneity of variance.

Absolutely agree with Robert Butler’s comment.

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#202821

Stephen Coath
Participant

Hi Mike

This project is being conducted by a member of my team as her six sigma project.
It was the external certifying company who asked for the hypothesis test.

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#202823

Mike Carnell
Participant

@CI-Mentor If it is for the purposes of training I can understand the question. They want to see them use the tool. Assuming it is a mean shift in the data the difference is actually obvious.

To run a 2 Sample t test you need to check the variances to know which formula to use for the t test. so either way you will need to test the variance. In real life the question that would seem to be the most critical is if the variance is equal or less (homoscedasticity -preferred state). What you don’t want, most likely, is to shift the mean and have the variance get larger (heteroscedasticity).

You need to understand your sample sizes on this. Large sample sizes affect the sensitivity of the test. A large sample size can force the test to show statistical significance when there is no practical difference. Just a thought.

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