Gage Agreement Folio Analysis Results
When accessed from a gage agreement folio, the Analysis
Summary window will contain a detailed comparison of the gages'
accuracy and precision.
If the current response data has been analyzed, you
can open the window by clicking the View
Analysis Summary icon on the control panel.
If the current response data has not been analyzed, the icon will still
be available so you can view the folio's analysis history.
Select an item in the Available Report Items panel to display it on
the spreadsheet. Each item is described next.
Analysis Results
The Part Summary table
compares the average readings from each gage.
Part Summary Table Columns
- 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.
The Average Reading Comparison
table compares the average readings of the two gages in
the study using a paired T-test.
Average Reading Comparison Table
Columns
-
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 Regression Study
compares the accuracy (linearity and bias) of the two gages. It
includes two tables.
Regression Study Tables
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.
- 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.
- 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.
The Precision Comparison table
compares the repeatability of the two gages.
Precision Comparison Table Columns
- 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.