Gage Agreement Folio Analysis Results

1. • Subject is the identifier of the measured part.

   • The Number of Readings columns show the number of observations taken of a particular part using a particular gage. The name of the gage is shown at the top of the table.

   • The Average Reading columns show the average of the measurements that were taken of a particular part by a particular gage.

   • Difference is the Average Reading from the first gage minus the Average Reading from the second.

   • Grand Average is the average of all measurements taken of a particular part.

The Difference and Grand Average values in this table are plotted in the difference vs. mean plot.

1. • The Mean column shows the mean value of the difference between the averages of the two gages.

   • Standard Deviation of Mean is the standard deviation of mean value of the difference.

   • The Lower Bound and Upper Bound columns show the confidence bounds of the mean value of the difference. The confidence level is determined by the risk level entered on the Analysis Settings page of the control panel (e.g., if the risk level is 0.1, then the 95% one-sided upper and 95% one-sided lower bounds are calculated).

   • T Value is the ratio of the absolute value of the Mean column and the Standard Deviation of Mean column. It is used to calculate the p value.

   • P Value is calculated from the T value. If the p value is less than or equal to the risk level specified on the Analysis Settings page of the control panel, then the two gages have different average readings in this study. In this case, the p value will be shown in red.

Note: If you suspect that the gages may differ in linearity (e.g., you see a trend in the difference vs. mean plot), then you should check the Regression Study table and/or the average reading plot to make sure the gages have the same accuracy.

The Individual Coefficient Test table shows the calculated coefficients for the regression line fitted to the average readings of the first vs. second gages (also shown in the Average Reading plot). It includes the following columns.

1. • Test is the null hypothesis. Two hypotheses are tested individually with this table: that b0 of the fitted regression line is 0 (i.e., no difference in bias, assuming there is no difference in linearity) and that b1 is 1 (i.e., no difference in linearity). Both of these hypotheses are true if the gages have the same accuracy. Note that if there is a difference in linearity, then there is also a difference in bias, since linearity describes how the bias changes with the size of the measured parts.

   • Coefficient is the coefficient of b0 and b1 in the regression equation.

   • Standard Error is the standard deviation of the regression coefficient.

   • The Low Confidence and High Confidence are the lower and upper confidence bounds on the regression coefficient. For example, if the bounds on b0 include 0, then the b0 = 0 null hypothesis is not false.

   • T Value is the normalized regression coefficient, which is equal to Coefficient/Standard Error.

   • P Value is the probability that the null hypothesis is true. If the p value is less than or equal to the risk level specified on the Analysis Settings page of the control panel, then the null hypothesis is considered false. In this case, the value is shown in red.

The Simultaneous Coefficient Test table shows the results of the F-test that is used to determine whether the gages have the same accuracy. It includes the following columns.

1. • Test is the null hypothesis that b0 = 0 and b1 = 1. If this is true, then the two gages have the accuracy.

   • F Value is the critical value of the F-distribution. It is used to calculate the p value.

   • P Value is the probability that the null hypothesis is true. If the p value is less than or equal to the risk level, then the two gages do not have the same accuracy. In this case, the value is shown in red. The folio's conclusion about whether the accuracy is the same is based on this value.

1. • Gage is the name of the measuring device specified on the Data tab.

   • Repeatability Variance is the repeatability of each gage (i.e., the variation when multiple readings for the same part are performed by the same operator).

   • Degrees of Freedom is the number of parts measurement by each individual gage.

   • F Ratio is the ratio of the first Repeatability Variance value to the second value. An F ratio of 1 means the gages have the same repeatability.

   • The Lower Bound and Upper Bound columns show the confidence bounds on the F ratio. If the bounds include 1, then the two gages have the same repeatability.

   • P Value is the probability that the F ratio is 1. If the p value is less than the risk level/2 and 1-(risk level/2), then the two gages do not have the same repeatability. (The risk level is specified on the Analysis Settings page of the control panel.) If the gages do not have the same repeatability, then this value is shown in red.