varianceComponent
Description
Examples
Variance Components for Two-Way ANOVA
Load the sample car data.
load carsmall
Data for the country of origin, model year, and mileage is stored in the variables Origin
, Model_Year
, and MPG
, respectively.
Perform a two-way ANOVA to test the null hypothesis that mean mileage is not affected by the country of origin or model year. The factors Origin
and Year
are random because the data was sampled from a larger population.
aov = anova({Origin, Model_Year},MPG,RandomFactors=[1 2],FactorNames=["Origin" "Year"])
aov = 2-way anova, constrained (Type III) sums of squares. Y ~ 1 + Origin + Year SumOfSquares DF MeanSquares F pValue ____________ __ ___________ ______ __________ Origin 1078.1 5 215.62 10.675 5.3303e-08 Year 2638.4 2 1319.2 65.312 5.5975e-18 Error 1737 86 20.198 Total 6005.3 93 Properties, Methods
The p-values for Origin
and Year
indicate that the country of origin and model year have statistically significant effects on mileage.
Display the variance component estimates for the error and random factors with confidence intervals. Use the default confidence level of 95%.
vtbl = varianceComponent(aov)
vtbl=3×3 table
VarianceComponent VarianceComponentLower VarianceComponentUpper
_________________ ______________________ ______________________
Origin 21.337 6.1257 139.94
Year 44.031 11.176 1765.7
Error 20.198 15.298 27.909
The variance components for Origin
and Year
are due to the random sampling of the data. The variance of MPG
is the sum of the variance components for Origin
, Year
, and Error
. The table output shows that the variance components for Origin
and Year
are responsible for the majority of the variance in MPG
.
Obtain 99% Confidence Interval of Variance Component
Load the sample car data.
load carsmall
Data for the model year and mileage is stored in the variables Model_Year
and MPG
, respectively.
Perform a two-way ANOVA to test the null hypothesis that mean mileage is not affected by the model year. Year
is a random factor because it contains a randomly selected subset of all possible model years.
aov = anova(Model_Year, MPG, RandomFactors=[1],FactorNames=["Year"])
aov = 1-way anova, constrained (Type III) sums of squares. Y ~ 1 + Year SumOfSquares DF MeanSquares F pValue ____________ __ ___________ _____ __________ Year 3190.1 2 1595.1 51.56 1.0694e-15 Error 2815.2 91 30.936 Total 6005.3 93 Properties, Methods
Display the variance component estimates for Year
and the error with confidence intervals. Specify a confidence level of 99%.
vtbl = varianceComponent(aov,Alpha=0.01)
vtbl=2×3 table
VarianceComponent VarianceComponentLower VarianceComponentUpper
_________________ ______________________ ______________________
Year 50.026 8.1282 10177
Error 30.936 21.74 46.915
The output shows that Year
contributes more to the sample variance than Error
.
Input Arguments
aov
— ANOVA results
anova
object
ANOVA results, specified as an anova
object.
The properties of aov
contain the factors and response data used by
varianceComponent
to compute the variance component estimates and their
confidence intervals.
alpha
— Significance level
0.05
(default) | scalar value in the range (0,1)
Significance level for the estimates, specified as a scalar value in the range (0,1).
The confidence level of the confidence intervals is . The default value for alpha
is
0.05
, which returns 95% confidence intervals for the
estimates.
Example: Alpha=0.01
Data Types: single
| double
Output Arguments
v
— Variance component estimates
table
Variance component estimates and their confidence intervals, returned as a table.
The varianceComponent function assumes that coefficients for dummy variables corresponding to
the same random factor have equal variance. The table v
has rows
for the error term and for each of the random terms in aov.Formula
.
The columns of v
correspond to the following variables:
VarianceComponent
— The estimated variance component.VarianceComponentLower
— A lower confidence bound of the variance component. You can specify the confidence level usingalpha
.VarianceComponentUpper
— An upper confidence bound of the variance component.
You can use the variance component estimates to determine if the random sampling has a significant effect on the mean squares of a term.
Data Types: table
References
[1] Dunn, O. J., and V. A. Clark. Applied Statistics: Analysis of Variance and Regression. New York: Wiley, 1974.
[2] Goodnight, J. H., and F. M. Speed. Computing Expected Mean Squares. Cary, NC: SAS Institute, 1978.
[3] Seber, G. A. F., and A. J. Lee. Linear Regression Analysis. 2nd ed. Hoboken, NJ: Wiley-Interscience, 2003.
Version History
Introduced in R2022b
See Also
MATLAB Command
You clicked a link that corresponds to this MATLAB command:
Run the command by entering it in the MATLAB Command Window. Web browsers do not support MATLAB commands.
Select a Web Site
Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .
You can also select a web site from the following list:
How to Get Best Site Performance
Select the China site (in Chinese or English) for best site performance. Other MathWorks country sites are not optimized for visits from your location.
Americas
- América Latina (Español)
- Canada (English)
- United States (English)
Europe
- Belgium (English)
- Denmark (English)
- Deutschland (Deutsch)
- España (Español)
- Finland (English)
- France (Français)
- Ireland (English)
- Italia (Italiano)
- Luxembourg (English)
- Netherlands (English)
- Norway (English)
- Österreich (Deutsch)
- Portugal (English)
- Sweden (English)
- Switzerland
- United Kingdom (English)