# Hypothesis Test with more than two distributions

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Viewing 12 posts - 1 through 12 (of 12 total)
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• #46582

Scott
Member

Hi!
How can I prove that 5 different distributions have the same true mean?
Here is my problem;
I have a plate with a bolt pattern of 5 holes equally space and same hole size (same drill and same machine) and i want to prove statistically that measuring one will be enough to make inference about the size of all the holes. This way i can do a capability on a single hole only, instead of all five.  How can i do this?

Thanks!

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#154199

Bower Chiel
Participant

Hi RickHave you thought of measuring all 5 on a series of plates and using an I-MR-R/S “triple” chart to investigate the variation? The charts are easily created in MINITAB.Best WishesBower Chiel

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#154209

Scott
Member

Yes, I have. But now, i want prove it statistically that difference is not significant. Any idea?
Thanks!
Rick

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#154211

harathi
Participant

You can do comparison of means in minitab…

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#154221

annon
Participant

Rick,
Yeah, something about this approach just doesnt sound right, but I cant put my finger on it….You are essentially sampling from a small batch and then making comparisons between batches…..
Could you treat each plate as a subgroup of 5 measures, collecting an adequate sample size, and then running an one-way ANOVA comparing holes 1-5 for statistical difference between averages (assuming assumptions and stability are upheld)….
I am also concerned about how you minimize the between-plate variation….
Double check, as this is just a first thought WAG…..good luck….

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#154231

Scott
Member

Thank you that sounds right!!!
Rick

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#154232

Jim Shelor
Participant

Try performing an MSA using one plate and the five holes as your parts.
When your part-to-part variation comes up near 0, you have statistical proof that if one hole measures in spec, you can infer all five are in spec.

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#154235

Participant

Here’s what I would do….
Measure all 5 holes on 10 plates (making sure they are representative of your production).
Then do a paired t-test setting up the data like this :
PLATE

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#154236

Participant

Here’s what I would do….
Measure all 5 holes on 10 plates (making sure they are representative of your production).
Then do a paired t-test setting up the data like this :
PLATE

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#154237

Participant

Problem with the TAB key trying to format the data :(
As I was saying, set up the data like this :
PLATE                             SIZE1    SIZE2
Plate1 Hole1/Hole2             X1         Y1Plate1 Hole1/Hole3             X1         Y2Plate1 Hole1/Hole4             X1         Y3Plate1 Hole1/Hole5             X1         Y4Plate2 Hole1/Hole2             X2         Y5Plate2 Hole1/Hole3             X2         Y6Plate2 Hole1/Hole4             X2         Y7
etc.
This way you are only testing whether there is a significant difference between holes on the same plate, and even if holes on different plates are different sizes it won’t matter.
Hope this helps.

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#154238

Toshi
Member

Toshi,
I would tag the plate in the orientation of drilling. I’d also label each hole before measurement. (I’m going to assume the Gage is accurate and precise.)
I’d then check for independence using a Splom Plot and if there is no discernable pattern I’d perform an Anova as suggested by the other poster, aassuming equal variance at each factor level.)
Something to consider .. a similar problem occurs on a lathe where the stability of the tool (vibration) can depend on extension the z-axis; so independence is not always a safe assumption :-)
Toshi

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#154362

The Force
Member

During your quality check, do you inspect each of the hole and were there issues in the past pointing to different holes having different defects? Take note that each hole constitute an opportunity for defect.

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