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

Select the method or formula of your choice.

In This Topic

Sum of squares (SS)
Degrees of freedom (DF)
Mean squares (MS)
F
p-value

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.

SS_Part

Term	Description
b	number of operators
n	number of replicates
	mean for each part
	grand mean

SS_Operator

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

SS_{Part*Operator}

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

SS_{Repeatability}

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:

Term	Description
	each observation
	mean of each factor level

SS_Total

Term	Description
	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.

DF_Part

Term	Description
a	number of parts

DF_Operator

Term	Description
b	number of operators

DF_{Part*Operator}

Term	Description
a	number of parts
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 (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.

MS_Part

MS_Operator

MS_{Part*Operator}

MS_{Repeatability}

F

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

F_Part

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.