Analysis Of Variance Method

Example (cont.): The sum-of-squares for the interaction between the appraisers and the parts, SSAB, is

Squaring all 60 individual reading and summing the values gives 457,405.8. The total sum-of-squares is

There are 2 degrees-of-freedom for the appraisers, the number of appraisers minus one; 9 degrees-of-freedom for the parts, the number of parts minus one, 18degrees-of-freedom for the interaction between the appraisers and the parts, the number

of appraisers minus one multiplied by the number of parts minus one; 59 total degrees of-freedom; the total number of readings minus one, and 30 degrees-of-freedom for the gage, total degrees-of-freedom minus the degrees-of-freedom for the appraisers minus the degrees-of-freedom for the parts minus the degrees-of-freedom for the interaction.

The significance listed in Table 9 represents the probability of Type I error .Stated another way, if the statement is made “the appraisers are a significant source of measurement variability”, the probability of this statement being incorrect is 0.000057.

This significance is the area under the F probability density function to the right of the computed F-statistic. This value can be found using the function FDIST(F-statistic,d1,d2)in Microsoft Excel or Lotus 123, where d1 and d2 are the appropriate degrees of freedom. Continuing with the example, the repeatability is