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

Select the method or formula of your choice.

## Sum of squares (SS)

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

SSPart

TermDescription
bnumber of operators
nnumber of replicates
mean for each part
grand mean
SSOperator

TermDescription
anumber of parts
nnumber of replicates
mean for each operator
grand mean
SSPart*Operator

SSPart*Operator = SSTotal – (SSPart + SSOperator + SSRepeatability)

SSRepeatability
When the interaction term is in the ANOVA table, use the following formula for the sum of squares for repeatability:

When the interaction term is not in the ANOVA table, use the following formula for the sum of squares for repeatability:
TermDescription
each observation
mean of each factor level
SSTotal

TermDescription
each observation
grand mean

## Degrees of freedom (DF)

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

DFPart

TermDescription
anumber of parts
DFOperator

TermDescription
bnumber of operators
DFPart*Operator

TermDescription
anumber of parts
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 (MS)

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.

MSPart

MSOperator

MSPart*Operator

MSRepeatability

## F

The F-statistic is used to determine whether the effects of Operator, Part, or Operator*Part are statistically significant.

FPart

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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