# Methods and formulas for ANOVA table in Nested Gage R&R Study

Select the method or formula of your choice.

## Sum of squares

The sum of squares (SS) is the sum of squared distances, and is a measure of the variability that is from different sources.

SSOperator TermDescription
anumber of parts
nnumber of replicates mean for each operator grand mean
SSPart (Operator) TermDescription
nnumber of replicates mean for each part, i, within operator, j mean for operator j
SSRepeatability TermDescription each observation mean for each part, i, within operator, j
SSTotal
SSTotal = SSOperator + SSPart (Operator) + SSRepeatability

## Degrees of freedom

The degrees of freedom (DF) for each SS (sums of squares). In general, DF measures how much information is available to calculate each SS.

DFOperator TermDescription
bnumber of operators
DFPart (Operator) TermDescription
anumber of parts measured by each operator
bnumber of operators
DFRepeatability TermDescription
anumber of parts
bnumber of operators
nnumber of replicates
DFTotal TermDescription
anumber of parts
bnumber of operators
nnumber of replicates

## Mean squares

The mean squares (MS) is the variability in the data from different sources. MS accounts for the fact that different sources have different numbers of levels or possible values.

MSOperator MS Part (Operator) MS Repeatability ## F

The F-statistic is used to determine whether the effects of Operator or Part (Operator) significantly impact the measurement.

FOperator FPart(Operator) ## p-value

The p-value is the probability of obtaining a test statistic (such as the F-statistic) that is at least as extreme as the value that is calculated from the sample, if the null hypothesis is true.

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