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

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In This Topic

Sum of squares
Degrees of freedom
Mean squares
F
p-value

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.

SS_Operator

Term	Description
a	number of parts
n	number of replicates
	mean for each operator
	grand mean

SS_{Part (Operator)}

Term	Description
n	number of replicates
	mean for each part, i, within operator, j
	mean for operator j

SS_{Repeatability}

Term	Description
	each observation
	mean for each part, i, within operator, j

SS_Total

SS_Total = SS_Operator + SS_{Part (Operator)} + SS_{Repeatability}

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.

DF_Operator

Term	Description
b	number of operators

DF_{Part (Operator)}

Term	Description
a	number of parts measured by each operator
b	number of operators

DF_{Repeatability}

Term	Description
a	number of parts
b	number of operators
n	number of replicates

DF_Total

Term	Description
a	number of parts
b	number of operators
n	number 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.

MS_Operator
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.

F_Operator
F_{Part(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.