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 following table provides general information about the effects of the reference value on the bias.

The Analysis of Variance (ANOVA) table includes the following 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 following table provides specific information about the linearity of the measurement device.

This table includes the following 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 following table provides specific information about the bias of the measurement device.

This table includes the following 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.

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	Linearity and Bias Folio