# Hypothesis Test with more than two distributions

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This topic contains 11 replies, has 8 voices, and was last updated by The Force 12 years, 6 months ago.

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- March 30, 2007 at 5:00 am #46582
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!

0March 30, 2007 at 7:12 am #154199

Bower ChielParticipant@Bower-Chiel**Include @Bower-Chiel in your post and this person will**

be notified via email.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

0March 30, 2007 at 3:11 pm #154209Yes, I have. But now, i want prove it statistically that difference is not significant. Any idea?

Thanks!

Rick0March 30, 2007 at 3:19 pm #154211

harathiParticipant@harathi**Include @harathi in your post and this person will**

be notified via email.You can do comparison of means in minitab…

0March 30, 2007 at 5:35 pm #154221Rick,

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….0March 30, 2007 at 9:09 pm #154231Thank you that sounds right!!!

Rick0March 30, 2007 at 9:30 pm #154232

Jim ShelorParticipant@Jim-Shelor**Include @Jim-Shelor in your post and this person will**

be notified via email.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.0March 31, 2007 at 6:50 am #154235

Adrian P. SmithParticipant@Adrian-P.-Smith**Include @Adrian-P.-Smith in your post and this person will**

be notified via email.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 :

PLATE0March 31, 2007 at 6:50 am #154236

Adrian P. SmithParticipant@Adrian-P.-Smith**Include @Adrian-P.-Smith in your post and this person will**

be notified via email.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 :

PLATE0March 31, 2007 at 6:54 am #154237

Adrian P. SmithParticipant@Adrian-P.-Smith**Include @Adrian-P.-Smith in your post and this person will**

be notified via email.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.

Rgds,Adrian

0March 31, 2007 at 9:45 am #154238Toshi,

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 :-)

Toshi0April 3, 2007 at 7:01 pm #154362

The ForceMember@The-Force**Include @The-Force in your post and this person will**

be notified via email.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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