# ANOVA practical application

#### New to statistics

##### Involved In Discussions
Hello guys.
Quality control bought a profil-meter to measure the inner grouved for aluminum tubes (attached pic).

From the sample they measure random 10 h, 10tb & 10γ (total numbers of each 100).

They gave 10 samples, 9 operators with 3 repetitions.

Cause the machine picks random (10 h, 10tb & 10γ) geometries of the total i could not perform a GRR analysis, so i run a simple ANOVA just to see if the operator is an important factor.

The analysis gave the below result

and

How you consider this approach?
Do you have an additional suggestion?
Presentation need also the residual plots (in order to show that the statistical model i use is right?)

Thank you.

#### Miner

##### Forum Moderator
It appears that you are using Minitab for this analysis. If I understand your concern regarding the random selection of geometries, you can use Minitab's Gage R&R Study (Nested). You are correct in judging that this did not meet the criteria for a Crossed study, but it does meet the criteria for a nested study.

Having said that, you can manually duplicate this using other means. Unfortunately, Minitab's ANOVA would make assumptions that are the same as with a crossed study, so you would have to use the General Linear Model (GLM) instead, so you can specify the nested structure. Also, Operators are typically specified as Random, unless these are all of the operators that would use this measurement device, in which case they are Fixed.

Using the Nested R&R study is much easier and less prone to making an error, so I recommend using that option.

#### Bev D

##### Heretical Statistician
Super Moderator
Most experimental statistics requires a study design that determines what kind of data and in what order it is collected to answer the question at hand.

I have said it a million times: A random pile of data is just that - no amount of statistical analysis can save a flawed study design. You must first determine what question you are trying to answer, then what study design (experimental structure) will answer that question. Then run the experiment and collect the data. Then plot the raw data. then you can apply the appropriate statistical analysis.

I am not trying to be rude or insulting just blunt: you seem to be substituting statistical software for statistical analysis. You say you are new to statistics. what training have you actually had? was it in statistics or how to use statistical software? Hint: who was the teacher, a statistics teacher or a statistical software instructor?

Think about the requirements for ANOVA. I will give you a hint: the data you have does not meet the requirements for a real ANOVA analysis that can determine if the operator matters. First of all operator to operator can only be determined once good repeatability has been established. repeatability is completely lacking from your study. (a nested design can help with this but not after the fact of random data collection)

a few quotes that apply here:
“The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from a given body of data.” - John Tukey

“It must be emphasized that it is the design techniques that are of primary importance to the troubleshooter, rather than the strictly statistical methodology. Too many people have the attitude that statistical analysis is merely a refined method of arriving at conclusions and that statistics will somehow compensate for a shoddy experimental design.” - Leonard Seder, “A New Science of Troubleshooting”, Industrial and Engineering Chemistry, Vol. 43 No.9 pp. 2053-2059

“To call in the statistician after the experiment is done may be no more than asking him to perform a postmortem examination: he may be able to say what the experiment died of.” - R. A. Fisher

The manipulation of statistical formulas is no substitute for knowing what one is doing. - Hubert M. Blalock, Jr., Social Statistics

#### New to statistics

##### Involved In Discussions
Hello again i will check nest tomorrow.. background is engineering ms is statistics.
I received the data...to be honest.
Assumptions of ANOVA you mean Normal distribution, equal variances etc?
But why i need repeatability to the operator's.
Operator's just put the sample at the machine and choose the module depending the sample.. they wait and take the results. In case that a characteristic tb is out of spec they just check if the machine is drawn the line correct, if it not they just drag the line to sit on the edge of the Shadow...no more interaction than that

#### Miner

##### Forum Moderator
Assumptions of ANOVA you mean Normal distribution, equal variances etc?
No. While those are true, I mean the balanced ANOVA in Minitab assumes that it is a crossed study (which it is not) and that all factors are fixed (which they are not).

I'll let Bev explain her thoughts on the repeatability. I will say that from your description that the operators could potentially have some impact though slight.

#### Bev D

##### Heretical Statistician
Super Moderator
ANOVA is fairly robust against non-normality and with the small sizes typical of an ANOVA it is difficult to determine if the variances are unequal unless the inequality is large. These are not the most important requirements of ANOVA. The important requirements are the assignment of controlled and uncontrolled factors and how each subgroup is created - are the within subgroup data independent or not…it is not sufficient to remember the mathematical formulas (or worse rely on statistical software to do that); it is essential that you understand how the formulas work - and how they do not.

As for repeatability think about how reproducibility is determined. Repeatability is within each unit and each operator. IF the repeatability is too large you will not statistically ‘see’ operator difference (unless they are larger than the repeatability error) since the within operator repeatability will overwhelm the operator to operator variability. MSA is essentially a paired analysis not a grouped analysis. I don’t know if you actually have pairable (or nested) data

In the case of the data you were given you would need to KNOW that the measurements you decide to nest are in fact physically nested. In this case the paired measurements must be physically close to each other. (Same side of the same tooth.). . Profilometer measurements are considered non-repeatable tests.

Next you need to plot the results by operator and measurement pair. and forget the residual plots - they tell you nothing. Look up multi-vari - you need to understand components o variation and nesting order…even tho I eschew p values you have a .84 p value for operator. Give up on this data.you can torture it all you want but it has already told you all it can.

1. Question
2. Study design to answer question
3. Run the experiment and collect the data
4. Plot the data in multi-variate format(s)
6. Then - if necessary - calculate some statistics.

What you are continually doing is getting some data first then trying to do something with it. That is putting the cart before the horse.

#### New to statistics

##### Involved In Discussions
Okay.
If it was you guys, what you will do. Suppose you start from the beginning.

#### Bev D

##### Heretical Statistician
Super Moderator
That is what I have been saying.

If you want to just practice using MINITAB keep taking whatever data you can find and slice it and dice it all you want. You’ll get lots of exercise for your button pushing finger.

If you want to actually practice industrial statistics, start with a real world quality question that you want to answer. (See my post above).

Good luck

#### New to statistics

##### Involved In Discussions
The truth is do know for sure if the data is nested or crossed or both maybe??!!
Bev (i read repetitive times your answer) and i am not sure i am fully understand you.
I will check yours and Miner posts next week.

Just asking if in the research every operator have unique samples would be more correct the approach?

Samples are random factors.
Operators are fixed factors (used them all).
From Minitab i used GLM (function)

#### Miner

##### Forum Moderator
The truth is do know for sure if the data is nested or crossed or both maybe??!!

Just asking if in the research every operator have unique samples would be more correct the approach?

Samples are random factors.
Operators are fixed factors (used them all).
From Minitab i used GLM (function)
If I understand your initial description that the machine randomly selects the location in which to measure, then this is a non-replicable study and location is nested within the part. Giving each operator a unique sample would add an additional layer of nesting (part nested within operator). This would add another layer of unnecessary complexity.

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