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I have been doing some reading about gage R&R and I have a simple application for it. I will be using ANOVA for performing my gage R&R. From my standpoint, most people seem to be using gage R&R to determine the relative contribution that various sources make to the total variation. However, when I read about ANOVA I usually think in terms of hypothesis testing and answering a question.

In gage R&R, what is the question my ANOVA will be answering?

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Let us take this example.

Three parts were selected that represent the expected range of the process variation. Three operators measured the three parts, three times per part, in a random order.

  Part   Operator  Response    Trial
    3      3       413.75       3
    3      3       268.75       2
    3      3       420.00       1
    3      2       426.25       3
    3      2       471.25       2
    3      2       432.50       1
    3      1       368.75       3
    3      1       270.00       2
    3      1       398.75       1
    2      3       386.25       3
    2      3       478.75       2
    2      3       436.25       1
.
.
.

This is Gage R&R Study - ANOVA Method output

Two-Way ANOVA Table With Interaction

Source           DF      SS       MS        F      P
Part              2   38990  19495.2  2.90650  0.166
Operator          2     529    264.3  0.03940  0.962
Part * Operator   4   26830   6707.4  0.90185  0.484
Repeatability    18  133873   7437.4
Total            26  200222

The ANOVA table shows which sources of variation were statistically significant. Factors with p-values less than .05 in the ANOVA table below are statistically significant.

The high p-values for Part, Operator and Part*Operator interaction indicate that these three sources of variation are not statistically significant, and therefore will not be of concern when trying to reduce the variability of the measurement system.

This link is for your reference. I hope this helps !

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    $\begingroup$ In addition to what the ANOVA table tests,the ANOVA table is also used to create tables of the sources of variation, such as the % contribution of repeatability, reproducability (a combination of operator and operator*part), and part-to-part variation as ratios of the $MS$. It can also be used to create a table of the Study Variation, which in turn is used to calculate the number of distinct categories. $\endgroup$
    – Tavrock
    Feb 17 '17 at 21:06
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The ANOVA in a gage R&R helps to answer if you can refuse or accept the null hypothesis which is: 'There is no significant difference among the groups'. If there is a significant (you can refuse H0) difference among groups then you might want to reconsider your (measurement) methods or instruction to the operator(s). Therefore F-statistics helps you cut a line between what is "acceptable" and what is "not acceptable" given your criteria and data. The P-value gives an idea of the certain of the data or more precisely: the probability of obtaining results at least as extreme as the observed results of a statistical hypothesis test, assuming that the null hypothesis is correct.

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