ANOVA (FPScript)
Carries out a Fisher analysis of variance. You can either calculate an ANOVA table or perform an F-test. The F-test specifies whether the mean values of several samples are significantly different or not. The ANOVA table provides characteristic quantities for the analysis of variance.
Syntax
ANOVA(Samples, ErrorProbability, Operation)
The syntax of the ANOVA function consists of the following parts:
Part |
Description |
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|---|---|---|---|---|---|---|---|---|---|
Samples |
Contains a data matrix or a signal series with the samples to be examined, which must originate from a normally distributed population. Permitted data structures are data matrix und signal series. All numeric data types are permitted. If the argument is a list, then the function is executed for each element of the list and the result is also a list. |
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ErrorProbability |
Specifies the error probability, on which the test is to be based, as a percentage. The values 1, 2.5, 5 and 10% are permitted. Permitted data structures are scalar value. All real data types are permitted, except calendar time und time span. The argument is transformed to the unit %. |
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Operation |
Specifies whether an ANOVA table is to be calculated or whether an F-test is to be performed. The argument Operation can have the following values:
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Remarks
If an F-test has been carried out, the result is a Boolean value that represents the test result. The following values are possible:
Value |
Interpretation |
|---|---|
FALSE |
The hypothesis was rejected. The samples are significantly different. |
TRUE |
The hypothesis was accepted. The samples are not significantly different. |
If an ANOVA table has been calculated, the result is a data series with eight floating point values or a list with eight named elements. The names of the elements are the same as those used in the following table:
Cause of Dispersion |
Degrees of Freedom (DF) |
Square Sum (SS) |
Mean Square Sum (MS) |
|---|---|---|---|
Differences Between the Data Series |
p - 1 |
SST |
MST = SST / (p - 1) |
Random Error |
N - p |
SSE |
MSE = SSE / (N - p) |
Total |
N - 1 |
TSS |
|
The values are passed in the sequence p-1, SST, MST, N -p, SSE, MSE, N - 1, TSS in the data series or list.
The abbreviations used stand for the following:
Abbreviation |
Meaning |
|---|---|
ANOVA |
Analysis of variance |
SST |
Sum of squares for treatments |
MST |
Mean square for treatments |
SSE |
Sum of squares for error |
MSE |
Mean square for error |
TSS |
Total sum of squares |
p |
Number of samples |
N |
Sum of the values of all of the samples |
For complex data types the absolute value is formed.
Available in
Option Enhanced Statistics
Examples
ANOVA({{9.0, 15.4, 8.2, 3.9, 7.3, 10.8}, {7.3, 15.6, 14.2, 13.0, 6.8, 9.7}, {18.0, 9.6, 11.5, 19.4, 17.1, 14.4}}, 5 %, ANOVA_FTEST)
Results in FALSE . This example checks whether there are differences in the tensile strength of three different grades of wire. There are six normally distributed samples available for each, and an error probability of five percent will be assumed.
There is a significant difference when the following applies: F = MST / MSE > Fp-1,N-p;1- (quantile of the F-distribution).
The test result thus shows a significant difference between the mean values of the three measurement series, and the following applies: MST / MSE = 54.02 / 14.44 = 3.74 > 3.682 = F2.15;0.95.
See Also
References
[1] "Hartung, Joachim": "Statistik (Statistics), 9th Edition", page 611 ff. "Oldenbourg Verlag GmbH, Munich",1993.ISBN 3-486-22055-1.