Linearity and Bias Folio Analysis Results
When accessed from a linearity and bias folio, the Analysis
Summary window will contain detailed information about the
gage's bias and linearity.
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 Analysis of Variance (ANOVA)
table provides general information about the effects of
the reference value on the bias.
ANOVA Table Columns
- Source of Variation
is the source that caused the difference in the measurements.
Sources displayed in red are considered to be significant.
-
The number of Degrees
of Freedom for the Reference
is the number of regression coefficients for the reference
value in the model. The number of degrees of freedom
for the Residual
is the total number of observations minus the number
of parameters being estimated.
- Sum of Squares
is the amount of difference in measurements caused
by this source of variation.
- Mean Squares
is the average amount of difference caused by this
source of variation. This is equal to Sum of Squares/Degrees
of Freedom.
- F Ratio
is the ratio of Mean Squares of this source of variation
and Mean Squares of pure error. A large value in this
column indicates that the difference in the output
caused by this source of variation is greater than
the difference caused by noise (i.e., this source
affects the output).
- P Value
(alpha error or type I error) is the probability that
an equal amount of variation in the measurements would
be observed in the case that this source does not
affect the output. This value is compared to the risk
level (alpha) that you specify on the Analysis Settings
page of the control panel. If the
p
value is less than alpha, this source of variation
is considered to have a significant effect on the
output (e.g., if Reference has a significant effect,
then the gage has a linearity issue). In this case,
the term and its p
value will be displayed in red.
-
The following values are shown underneath the
ANOVA table:
- S
is the standard error of the noise. It represents
the magnitude of the difference caused by noise.
- R-sq
is the percentage of total difference in the measurements
that is attributable to differences in the reference
values. It is equal to Sum of Squares(Reference)/Total
Sum of Squares.
- R-sq(adj)
is an R-sq value that is adjusted for the number
of parameters in the model.
The Linearity Analysis table
provides specific information about the linearity of the measurement
device.
Linearity Analysis
Table Columns
- Term
is the intercept or slope of the fitted regression
model. The slope represents the measurement device's
linearity. Terms displayed in red are considered to
be significant (e.g., if "Slope" is displayed
in red, then the device has a linearity issue).
-
Coefficient is the
regression coefficient of the term, which represents the contribution
of the term to the variation in the response.
-
Standard Error is
the standard deviation of the regression coefficient.
-
Low Confidence and
High Confidence
are the lower and upper confidence bounds on the regression coefficient.
-
T Value is the normalized
regression coefficient, which is equal to Coefficient/Standard
Error.
-
P Value (alpha error
or type I error) is the probability that an equal amount of variation
in the output would be observed in the case that this term does
not affect the output. This value is compared to the risk level
(alpha) that you specify on the Anaysis Settings page of the control
panel. If the p value
is less than alpha, this source of variation is considered to
have a significant effect on the output. In this case, the term
and its p value will
be displayed in red.
- Additional values will be shown underneath the
Linearity Analysis table:
- If you specified the process standard deviation
on the Analysis Settings page of the control panel,
these values will be shown.
- Process
Variation is the total variation of
the parts' reference values (i.e., the "true"
process variation). It is equal to the specified
process standard deviation * 6.
- Linearity
is the variation in measurements due to gage
linearity.
- The % Linearity
value is always shown. It is the percentage of
the variation in measurements that is due to gage
linearity.
The Bias Analysis table
provides specific information about the bias of the measurement
device.
Bias Analysis Table
Columns
- Reference is
the reference value entered in the data sheet. It
represents the "true" value of the part
when it was measured. If a reference value is displayed
in red, then there is a significant bias for measurement
taken at that value.
- Bias
is the average bias for measurements at the given
reference value.
- % Bias
is the ratio of the bias to the process variation
at the given reference value. This column is available
only when the process standard deviation is specified
on the Analysis Settings page of the Data tab control
panel.
- Std. of Mean
is the standard deviation of the bias at each reference
value. If there are multiple parts with the same reference
value, it is the pooled standard deviation of all
the parts.
- T Value
is the ratio of the absolute value of the Bias column
and the Std. of Mean column. It is used to calculate
the p value.
- P Value
is calculated from the T
value and the corresponding degree of freedom for
each reference value. If the
p
value is smaller than the risk level specified on
the Analysis Settings page of the control panel, then
the corresponding row has significant bias. In this
case, the p
value will be shown in red.
- Average
shows the mean of all the values in the given column.
If "Average" is displayed in red, then the
gage's average bias is significant.