Example of a Variability Chart
Suppose that you have data containing part measurements. Three operators, Cindy, George, and Tom, each took measurements of 10 parts. They measured each part three times, making a total of 90 observations. You want to identify the variation between operators.
1. Select Help > Sample Data Library and open Variability Data/2 Factors Crossed.jmp.
2. Select Analyze > Quality and Process > Variability / Attribute Gauge Chart.
3. For Chart Type, select Variability.
4. Select Measurement and click Y, Response.
5. Select Operator and click X, Grouping.
6. Select part# and click Part, Sample ID.
7. Click OK.
Figure 8.2 Example of a Variability Chart
Looking at the Std Dev chart, you can see that Cindy and George have more variation in their measurements than Tom, who appears to be measuring parts the most consistently. George seems to have the most variation in his measurements, so he might be measuring parts the most inconsistently.
Launch the Variability/Attribute Gauge Chart Platform
Launch the Variability/Attribute Gauge Chart platform by selecting Analyze > Quality and Process > Variability/Attribute Gauge Chart. Set the Chart Type to Variability.
Figure 8.3 The Variability/Attribute Gauge Chart Launch Window
Chart Type
Choose between a variability gauge analysis (for a continuous response) or an attribute gauge analysis (for a categorical response, usually “pass” or “fail”).
Note: The content in this chapter covers only the Variability chart type. For details about the Attribute chart type, see the “Attribute Gauge Charts” chapter.
Model Type
Choose the model type (Main Effect, Crossed, Nested, and so on). See “Statistical Details for Variance Components”.
Analysis Settings
Specify the method for computing variance components. See “Analysis Settings”.
Specify Alpha
Specify the alpha level used by the platform.
Y, Response
Specify the measurement column. Specifying more than one Y column produces a separate variability chart for each response.
Standard
Specify a standard or reference column that contains the “true” or known values for the measured part. Including this column enables the Bias and Linearity Study options. These options perform analysis on the differences between the observed measurement and the reference or standard value. See “Bias Report” and “Linearity Study”.
X, Grouping
Specify the classification columns that group the measurements. If the factors form a nested hierarchy, specify the higher terms first. If you are doing a gauge study, specify the operator first and then the part.
Freq
Identifies the data table column whose values assign a frequency to each row. Can be useful when you have summarized data.
Part, Sample ID
Identifies the part or sample that is being measured.
By
Identifies a column that creates a report consisting of separate analyses for each level of the variable.
For more information about the launch window, see the Get Started chapter in the Using JMP book.
The Variability Gauge Chart
The variability chart and the standard deviation chart show patterns of variation. You can use these charts to identify possible groups of variation (within subgroups, between subgroups, over time). If you notice that any of these sources of variation are large, you can then work to reduce the variation for that source.
Follow the instructions in “Example of a Variability Chart” to produce the results shown in Figure 8.4.
Figure 8.4 Variability Gauge Chart
The charts show the response on the y-axis and a multilevel, categorized x-axis.
In Figure 8.4, the Measurement chart shows the range of measurements for each operator by part. Each measurement appears on the chart. Maximum and minimum bars indicate the range of values for each cell, and a cell means bar indicates the median value for each combination of values. The Std Dev chart plots the standard deviation of the measurements taken on each part by operator.
You can add features to the charts, as illustrated in Figure 8.4. See “Variability Gauge Platform Options”.
To replace variables in charts, do one of the following:
• Swap existing variables by dragging a variable from one axis label to the other axis label. When you drag a variable over a chart or click on an axis label, the axis labels are highlighted. This indicates where to drop the variable.
• Click on a variable in the Columns panel of the associated data table and drag it onto an axis label.
In other platforms, rows that are excluded in the associated data table still appear on the charts or plots. However, in variability charts, excluded rows do not appear on the charts.
Variability Gauge Platform Options
Use the red triangle options to modify the appearance of the chart, perform Gauge R&R analysis, and compute variance components.
Note: Figure 8.4 illustrates some of these options.
Tip: To set the default behavior of these options, select File > Preferences > Platforms > Variability Chart.
Vertical Charts
Changes the layout to horizontal or vertical.
Variability Chart
Shows or hides the variability chart.
Show Points
Shows or hides the points for individual rows.
Show Range Bars
Shows or hides the bars indicating the minimum and the maximum value of each cell.
Show Cell Means
Shows or hides the mean mark for each cell.
Connect Cell Means
Connects or disconnects cell means within a group of cells.
Show Separators
Shows or hides the separator lines between levels of the X, Grouping variables.
Show Group Means
(Available only if you have two or more X, Grouping variables or one X, Grouping variable and one Part, Sample ID variable) Shows or hides the mean for groups of cells, represented by a horizontal solid line. A window appears, prompting you to select one of the grouping variables.
Show Grand Mean
Shows or hides the overall mean, represented by a gray dotted line across the entire graph.
Show Grand Median
Shows or hides the overall median, represented by a blue dotted line across the entire graph.
Show Box Plots
Shows or hides box plots.
Mean Diamonds
Shows or hides mean diamonds. The confidence intervals use the within-group standard deviation for each cell.
XBar Control Limits
Shows or hides lines at the UCL and LCL on the variability chart.
Points Jittered
Adds some random noise to the plotted points so that coincident points do not plot on top of one another.
Show Bias Line
(Available only if you have specified a Standard variable) Shows or hides the bias line in the main variability chart.
Show Standard Mean
(Available only if you have specified a Standard variable) Shows or hides the mean of the standard column.
Variability Summary Report
Shows or hides a report that gives the mean, standard deviation, standard error of the mean, lower and upper confidence intervals, and the minimum, maximum, and number of observations.
Std Dev Chart
Shows or hides a separate graph that shows cell standard deviations across category cells.
Mean of Std Dev
Shows or hides a line at the mean standard deviation on the Std Dev chart.
S Control Limits
Shows or hides lines showing the LCL and UCL in the Std Dev chart.
Group Means of Std Dev
Shows or hides the mean lines on the Std Dev chart.
Heterogeneity of Variance Tests
Performs a test for comparing variances across groups. See “Heterogeneity of Variance Tests”.
Variance Components
Estimates the variance components for a specific model. Variance components are computed for these models: main effects, crossed, nested, crossed then nested (three factors only), and nested then crossed (three factors only). See “Variance Components”.
Gauge Studies
Contains the following options:
‒ Gauge RR interprets the first factors as grouping columns and the last factor as Part, and creates a gauge R&R report using the estimated variance components. (Note that there is also a Part field in the launch window). See “Gauge RR Option”.
‒ Discrimination Ratio characterizes the relative usefulness of a given measurement for a specific product. It compares the total variance of the measurement with the variance of the measurement error. See “Discrimination Ratio”.
‒ Misclassification Probabilities show probabilities for rejecting good parts and accepting bad parts. See “Misclassification Probabilities”.
‒ Bias Report shows the average difference between the observed values and the standard. A graph of the average biases and a summary table appears. This option is available only when you specify a Standard variable in the launch window. See “Bias Report”.
‒ Linearity Study performs a regression using the standard values as the X variable and the bias as the Y variable. This analysis examines the relationship between bias and the size of the part. Ideally, you want the slope to equal 0. A nonzero slope indicates that your gauge performs differently with different sized parts. This option is available only when you specify a Standard variable in the launch window. See “Linearity Study”.
‒ Gauge RR Plots shows or hides Mean Plots (the mean response by each main effect in the model) and Std Dev plots. If the model is purely nested, the graphs appear with a nesting structure. If the model is purely crossed, interaction graphs appear. Otherwise, the graphs plot independently at each effect. For the standard deviation plots, the red lines connect 
for each effect.
for each effect.‒ AIAG Labels enables you to specify that quality statistics should be labeled in accordance with the AIAG standard, which is used extensively in automotive analyses.
See the JMP Reports chapter in the Using JMP book for more information about the following options:
Local Data Filter
Shows or hides the local data filter that enables you to filter the data used in a specific report.
Redo
Contains options that enable you to repeat or relaunch the analysis. In platforms that support the feature, the Automatic Recalc option immediately reflects the changes that you make to the data table in the corresponding report window.
Save Script
Contains options that enable you to save a script that reproduces the report to several destinations.
Save By-Group Script
Contains options that enable you to save a script that reproduces the platform report for all levels of a By variable to several destinations. Available only when a By variable is specified in the launch window.
Heterogeneity of Variance Tests
The Heterogeneity of Variance Tests option performs a test for comparing variances across groups. The test is an Analysis of Means for Variances (ANOMV) based method. This method indicates whether any of the group standard deviations are different from the square root of the average group variance.
To be robust against non-normal data, the method uses a permutation simulation to compute decision limits. For complete details about this method, see Wludyka and Sa (2004). Because the method uses simulations, the decision limits can be slightly different each time. To obtain the same results each time, hold down CTRL and SHIFT and select the option, and then specify the same random seed.
The red triangle menus for the test reports contain the following options:
Set Alpha Level
Sets the alpha level for the test.
Show Summary Report
Shows or hides a summary report for the test. The values in the report are the same values that are shown in the plot.
Note: The values in the plots and the Summary Reports are the values used in performing the test, not the group standard deviations.
Display Options
Shows or hides the decision limits, shading, center line, and needles.
Variance Components
The Variance Components option models the variation from measurement to measurement. The response is assumed to be a constant mean plus random effects associated with various levels of the classification.
Note: Once you select the Variance Components option, if you did not select the Model Type in the launch window (if you selected Decide Later), you are prompted to select the model type. For more information about model types, see “Launch the Variability/Attribute Gauge Chart Platform”.
Figure 8.5 Example of the Variance Components Report
The Analysis of Variance report appears only if the EMS method of variance component estimation is used. This report shows the significance of each effect in the model.
The Variance Components report shows the estimates themselves. See “Statistical Details for Variance Components”.
Analysis Settings
From the launch window, click Analysis Settings to choose the method for computing variance components.
Figure 8.6 Analysis Settings Window
Choose best analysis (EMS, REML, or Bayesian)
Chooses the best analysis from EMS, REML, or Bayesian, using the following logic:
‒ If the data are balanced, and if no variance components are negative, the EMS (expected mean squares) method is used to estimate the variance components.
‒ If the data are unbalanced, the REML (restricted maximum likelihood) method is used, unless a variance component is estimated to be negative, then the Bayesian method is used.
‒ If any variance component is estimated to be negative using the EMS method, the Bayesian method is used.
‒ If there is confounding in the variance components, then the bounded REML method is used, and any negative variance component estimates are set to zero.
Choose best analysis (EMS or REML)
Chooses the best analysis from EMS or REML, using the same logic as the Choose best analysis (EMS, REML, or Bayesian) option. However, this option never uses the Bayesian method, even for negative variance components. The bounded REML method is used and any negative variance component is forced to be 0.
Use REML analysis
Uses the bounded REML method, even if the data are balanced. The bounded REML method can handle unbalanced data and forces any negative variance component to be 0.
Use Bayesian analysis
Uses the Bayesian method. The Bayesian method can handle unbalanced data and forces all variances components to be positive and nonzero. If there is confounding in the variance components, then the bounded REML method is used, and any negative variance component estimates are set to zero. The method implemented in JMP computes the posterior means using a modified version of Jeffreys’ prior. For details, see Portnoy (1971) and Sahai (1974).
Maximum Iterations
(Applicable only for the REML method) For difficult problems, you might want to increase the number of iterations. Increasing this value means that JMP will try more times to find a solution in the optimization phase.
Convergence Limit
(Applicable only for the REML method) For problems where you want greater precision, you might want to change the convergence limit to be smaller. Decreasing this value means that JMP will find the solution to a higher level of accuracy in the optimization phase. However, this can increase the time taken to find a solution. Providing a larger convergence value returns quicker results, but is less precise.
Number of Iteration Abscissas
(Applicable only for the Bayesian method) For greater accuracy, you might want to increase the number of iteration abscissas. However, this can increase the time taken to find a solution. Providing a smaller number returns quicker results, but is less precise.
Maximum Number of Function Evaluations
(Applicable only for the Bayesian method) For greater accuracy, you might want to increase the maximum number of function evaluations. However, this can increase the time taken to find a solution. Providing a smaller number returns quicker results, but is less precise.
About the Gauge R&R Method
The Gauge R&R method analyzes how much of the variability in your measurement system is due to operator variation (reproducibility) and measurement variation (repeatability). Gauge R&R studies are available for many combinations of crossed and nested models, regardless of whether the model is balanced.
Tip: Alternatively, you can use the EMP method to assess your measurement system. See the “Measurement Systems Analysis” chapter.
Before performing a Gauge R&R study, you collect a random sample of parts over the entire range of part sizes from your process. Select several operators at random to measure each part several times. The variation is then attributed to the following sources:
• The process variation, from one part to another. This is the ultimate variation that you want to be studying if your measurements are reliable.
• The variability inherent in making multiple measurements, that is, repeatability. In Table 8.1, this is called the within variation.
• The variability due to having different operators measure parts—that is, reproducibility.
A Gauge R&R analysis then reports the variation in terms of repeatability and reproducibility.
|
Variances Sums
|
Term and Abbreviation
|
Alternate Term
|
|
V(Within)
|
Repeatability (EV)
|
Equipment Variation
|
|
V(Operator)+V(Operator*Part)
|
Reproducibility (AV)
|
Appraiser Variation
|
|
V(Operator*Part)
|
Interaction (IV)
|
Interaction Variation
|
|
V(Within)+V(Operator)+V(Operator*Part)
|
Gauge R&R (RR)
|
Measurement Variation
|
|
V(Part)
|
Part Variation (PV)
|
Part Variation
|
|
V(Within)+V(Operator)+ V(Operator*Part)+V(Part)
|
Total Variation (TV)
|
Total Variation
|
A Shewhart control chart can identify processes that are going out of control over time. A variability chart can also help identify operators, instruments, or part sources that are systematically different in mean or variance.
Gauge RR Option
The Gauge RR option shows measures of variation interpreted for a gauge study of operators and parts.
Once you select the Gauge RR option, if you have not already selected the model type, you are prompted to do so. Then, modify the Gauge R&R specifications.
Note: The Platform preferences for Variability include the Gauge R&R Specification Dialog option. The preference is selected by default. Deselect the preference to use the spec limits that are defined in the data table.
Enter/Verify Gauge R&R Specifications
The Enter/Verify Gauge R&R Specifications window contains these options:
Choose tolerance entry method
Choose how to enter the tolerance, as follows:
Select Tolerance Interval to enter the tolerance directly, where tolerance = USL – LSL.
Select LSL and/or USL to enter the specification limits and then have JMP calculate the tolerance.
K, Sigma Multiplier
K is a constant value that you choose to multiply with sigma. For example, you might type 6 so that you are looking at 6*sigma or a 6 sigma process.
Tip: Modify the default value of K by selecting File > Preferences > Platforms > Variability Chart.
Tolerance Interval, USL-LSL
Enter the tolerance for the process, which is the difference between the upper specification limits and the lower specification limits.
Spec Limits
Enter upper and lower specification limits.
Historical Mean
Computes the tolerance range for one-sided specification limits, either USL-Historical Mean or Historical Mean-LSL. If you do not enter a historical mean, the grand mean is used.
Historical Sigma
Enter a value that describes the variation (you might have this value from history or past experience).
The Gauge R&R Report
Figure 8.7 Example of the Gauge R&R Report
Note: To generate the reduced Gauge R&R report, select File > Preferences > Platforms > Variability Chart > Reduced Gauge RR Report.
In this example, the values in the Variation column are the square roots of sums of variance components scaled by the value of k (6 in this example).
Table 8.2 shows guidelines for measurement variation, as suggested by Barrentine (1991).
|
< 10%
|
excellent
|
|
11% to 20%
|
adequate
|
|
21% to 30%
|
marginally acceptable
|
|
> 30%
|
unacceptable
|
Note the following:
• If you have provided a Tolerance Interval in the Enter/Verify Gauge R&R Specifications window, a % of Tolerance column appears in the Gauge R&R report. This column is computed as 100*(Variation/Tolerance). Also, a Precision-to-Tolerance ratio appears at the bottom of the report. This ratio represents the proportion of the tolerance or capability interval that is lost due to gauge variability.
• If you have provided a Historical Sigma in the Enter/Verify Gauge R&R Specifications window, a % Process column appears in the Gauge R&R report. This column is defined as follows: 100*(Variation/(K*Historical Sigma)).
• The Number of Distinct Categories (NDC) is defined as (1.41*(PV/RR)), rounded down to the nearest integer.
Discrimination Ratio
The discrimination ratio characterizes the relative usefulness of a given measurement for a specific product. Generally, when the discrimination ratio is less than 2, the measurement cannot detect product variation, implying that the measurement process needs improvement. A discrimination ratio greater than 4 adequately detects unacceptable product variation, implying that the production process needs improvement.
See “Statistical Details for the Discrimination Ratio” for more information.
Misclassification Probabilities
Due to measurement variation, good parts can be rejected and bad parts can be accepted. This is called misclassification. Once you select the Misclassification Probabilities option, if you have not already done so, you are prompted to select the model type and enter specification limits.
Figure 8.8 Example of the Misclassification Probabilities Report
Note the following:
• The first and second values are conditional probabilities.
• The third and fourth values are joint probabilities.
• The fifth value is a marginal probability.
• The first four values are probabilities of errors that decrease as the measurement variation decreases.
Bias Report
The Bias Report shows a graph for Overall Measurement Bias with a summary table and a graph for Measurement Bias by Standard with a summary table. The average bias, or the differences between the observed values and the standard values, appears for each level of the X variable. A t test for the bias is also given.
The Bias Report option is available only when a Standard variable is provided in the launch window.
The Measurement Bias Report contains the following red triangle options:
Confidence Intervals
Calculates confidence intervals for the average bias for each part and places marks on the Measurement Bias Report by Standard plot.
Measurement Error Graphs
Produces a graph of Measurement Error versus all grouping columns together. There are also graphs of Measurement Error by each grouping column separately.
Linearity Study
The Linearity Study performs a regression analysis using the standard variable as the X variable and the bias as the Y variable. This analysis examines the relationship between bias and the size of the part. Ideally, you want to find a slope of zero. If the slope is significantly different from zero, you can conclude that there is a significant relationship between the size of the part or variable measured as a standard and the ability to measure.
The Linearity Study option is available only when a Standard variable is provided in the launch window.
The report shows the following information:
• Bias summary statistics for each standard.
• An ANOVA table that tests if the slope of the line is equal to zero.
• The line parameters, including tests for the slope (linearity) and intercept (bias). The test for the intercept is useful only if the test on the slope fails to reject the hypothesis of slope = 0.
• The equation of the line appears directly beneath the graph.
The Linearity Study report contains the following red triangle options:
Set Alpha Level
Changes the alpha level that is used in the bias confidence intervals.
Linearity by Groups
Produces separate linearity plots for each level of the X, Grouping variables that you specified in the launch window.
Additional Examples of Variability Charts
This section contains additional examples of variability charts.
Example of the Heterogeneity of Variance Test
Suppose that you have data containing part measurements. Three operators (Cindy, George, and Tom) each took measurements of 10 parts. They measured each part three times, making a total of 90 observations. You want to examine the following:
• whether the variance of measurements for each operator are the same or different
• whether the variance for each part is the same or different
• whether the variance for each Operator*part combination is the same or different
Ideally, you want all of the variances for each of the groups to be considered the same statistically.
1. Select Help > Sample Data Library and open Variability Data/2 Factors Crossed.jmp.
2. Select Analyze > Quality and Process > Variability / Attribute Gauge Chart.
3. Select Measurement and click Y, Response.
4. Select Operator and click X, Grouping.
5. Select part# and click Part, Sample ID.
6. Set the Chart Type to Variability.
7. Click OK.
8. From the red triangle menu, select Heterogeneity of Variance Tests.
9. Select Crossed.
10. Click OK.
You see a message that JMP will change your ordinal effect to a nominal one. Click OK to dismiss it.
Figure 8.9 Heterogeneity of Variances Tests Report
Note: Because the method uses simulations, the decision limits can be slightly different each time.
In the Operator Variance test, all three levels exceed the upper and lower decision limits. From this, you conclude that each operator has a different variability from the square root of the average group variance. You might want to examine why the variation between each operator is different.
For the part# Variance test and the interaction (Operator*part#) Variance test, none of the levels exceed the decision limits. From this, you conclude that the variances are not statistically different from the square root of the average group variance. Each part has a similar variance to the other parts, and each Operator*part# combination has similar variance to the other Operator*part# combinations.
Example of the Bias Report Option
Note: This data comes from the Automotive Industry Action Group (AIAG) (2002), Measurement Systems Analysis Reference Manual, 3rd edition, 94.
Assume that as a plant supervisor, you are introducing a new measurement system into your process. As part of the Production Part Approval Process (PPAP), the bias and linearity of the measurement system needs to be evaluated. Five parts were chosen throughout the operating range of the measurement system, based on documented process variation. Each part was measured by layout inspection to determine its reference value. Each part was then measured twelve times by the lead operator. The parts were selected at random during the day. In this example, you want to examine the overall bias and the individual measurement bias (by standard).
1. Select Help > Sample Data Library and open Variability Data/MSALinearity.jmp.
2. Select Analyze > Quality and Process > Variability / Attribute Gauge Chart.
3. Select Response and click Y, Response.
4. Select Standard and click Standard.
5. Select Part and click X, Grouping.
6. Set the Chart Type to Variability.
7. Click OK.
8. From the red triangle menu, select Gauge Studies > Bias Report.
Figure 8.10 Measurement Bias Report
The bias (Response minus Standard) is calculated for every measurement. The Overall Measurement Bias Report shows a histogram of the bias and a t-test to see whether the average bias is equal to 0. You can see that the Average Bias is not zero, it is -0.0533. However, zero is contained within the confidence interval (-0.1152,0.0085), which means that the Average Bias is not significantly different from 0. Using a significance level of 0.05, you can see that the p-value is greater than 0.05, which also shows that the Average Bias is not significantly different from 0.
The Measurement Bias Report by Standard shows average bias values for each part. The bias averages are plotted on the graph along with the actual bias values for every part, so that you can see the spread. In this example, part number 1 (with a standard value of 2) is biased high and parts 4 and 5 (with standard values of 8 and 10) are biased low.
Tip: To see confidence intervals for the bias, right-click in the table and select Columns > Lower 95% and Upper 95%.
Example of a Linearity Study
Using the same data and scenario as the Bias Report option, you can now examine the linearity to determine whether there is a significant relationship between the size of the parts and the operator’s ability to measure them.
1. Select Help > Sample Data Library and open Variability Data/MSALinearity.jmp.
2. Select Analyze > Quality and Process > Variability / Attribute Gauge Chart.
3. Select Response and click Y, Response.
4. Select Standard and click Standard.
5. Select Part and click X, Grouping.
6. Set the Chart Type to Variability.
7. Click OK.
8. From the red triangle menu, select Gauge Studies > Linearity Study.
9. In the window that prompts you to Specify Process Variation, type 16.5368.
Figure 8.11 Linearity Study
Note the following:
• The slope is -0.131667. This value appears as part of the equation below the graph, and also in the third table.
• The p-value associated with the test on the slope is quite small, <.0001. The t test for the slope is testing whether the bias changes with the standard value.
Because the p-value is small, you can conclude that there is a significant linear relationship between the size of the parts and the operator’s ability to measure them. You can also see this in the graph. If the part or standard value is small, the bias is high, and vice versa.
Statistical Details for Variability Charts
This section contains statistical details for variance components and the discrimination ratio.
Statistical Details for Variance Components
The exact model type that you choose depends on how the data was collected. For example, are the operators measuring the same parts (in which case you have a crossed design) or are they measuring different parts (in which case you have a nested design)? To illustrate, in a model where B is nested within A, multiple measurements are nested within both B and A, and there are na•nb•nw measurements, as follows:
• na random effects are due to A
• na•nb random effects due to each nb B levels within A
• na•nb•nw random effects due to each nw levels within B within A:
.The Zs are the random effects for each level of the classification. Each Z is assumed to have a mean of zero and to be independent from all other random terms. The variance of the response y is the sum of the variances due to each z component:
.Table 8.3 shows the supported models and what the effects in the model would be.
|
Model
|
Factors
|
Effects in the Model
|
|
Main Effects
|
1
2
unlimited
|
A
A, B
and so on, for more factors
|
|
Crossed
|
1
2
3
4
unlimited
|
A
A, B, A*B
A, B, A*B, C, A*C, B*C, A*B*C
A, B, A*B, C, A*C, B*C, A*B*C, D, A*D, B*D, A*B*D, C*D, A*C*D, B*C*D, A*B*C*D,
and so on, for more factors
|
|
Nested
|
1
2
3
4
unlimited
|
A
A, B(A)
A, B(A), C(A,B)
A, B(A), C(A,B), D(A,B,C)
and so on, for more factors
|
|
Crossed then Nested
|
3
|
A, B, A*B, C(A,B)
|
|
Nested then Crossed
|
3
|
A, B(A), C, A*C, C*B(A)
|
Statistical Details for the Discrimination Ratio
The discrimination ratio compares the total variance of the measurement, M, with the variance of the measurement error, E. The discrimination ratio is computed for all main effects, including nested main effects. The discrimination ratio, D, is computed as follows:
where:
P = estimated variance for a factor
T = estimated total variance
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