anova2
Performs two-way factorial (crossed) or a nested analysis of variance
(ANOVA) for balanced designs. For unbalanced factorial designs, diagnostic
plots and/or planned contrasts, use anovan instead.
anova2 requires two input arguments with an optional third and fourth:
anova2 returns up to three output arguments:
If anova2 is called without any output arguments, then it prints the results in a one-way ANOVA table to the standard output as if displayopt is ’on’.
Examples:
load popcorn; anova2 (popcorn, 3); |
[p, anovatab, stats] = anova2 (popcorn, 3, "off"); disp (p); |
See also: anova1, anovan, multcompare
Source Code: anova2
# Factorial (Crossed) Two-way ANOVA with Interaction
popcorn = [5.5, 4.5, 3.5; 5.5, 4.5, 4.0; 6.0, 4.0, 3.0; ...
6.5, 5.0, 4.0; 7.0, 5.5, 5.0; 7.0, 5.0, 4.5];
[p, atab, stats] = anova2(popcorn, 3, "on");
ANOVA Table
Source SS df MS F Prob>F
-----------------------------------------------------------
Columns 15.7500 2 7.8750 56.70 0.0000
Rows 4.5000 1 4.5000 32.40 0.0001
Interaction 0.0833 2 0.0417 0.30 0.7462
Error 1.6667 12 0.1389
Total 22.0000 17
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# One-way Repeated Measures ANOVA (Rows are a crossed random factor)
data = [54, 43, 78, 111;
23, 34, 37, 41;
45, 65, 99, 78;
31, 33, 36, 35;
15, 25, 30, 26];
[p, atab, stats] = anova2 (data, 1, "on", "linear");
ANOVA Table
Source SS df MS F Prob>F
-----------------------------------------------------------
Columns 2174.9500 3 724.9833 3.62 0.0873
Rows 8371.7000 4 2092.9250 10.45 0.0007
Error 2404.3000 12 200.3583
Total 12950.9500 19
Note: Greenhouse-Geisser's correction was applied to the
degrees of freedom for the Column factor: F(1.74,6.95)
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# Balanced Nested One-way ANOVA (Rows are a nested random factor)
data = [4.5924 7.3809 21.322; -0.5488 9.2085 25.0426; ...
6.1605 13.1147 22.66; 2.3374 15.2654 24.1283; ...
5.1873 12.4188 16.5927; 3.3579 14.3951 10.2129; ...
6.3092 8.5986 9.8934; 3.2831 3.4945 10.0203];
[p, atab, stats] = anova2 (data, 4, "on", "nested");
ANOVA Table
Source SS df MS F Prob>F
-----------------------------------------------------------
Columns 745.3603 2 372.6802 4.02 0.1416
Rows 278.0185 3 92.6728 9.26 0.0006
Error 180.1804 18 10.0100
Total 1203.5592 23
Note: Rows are a random factor nested within the columns.
The Column F statistic uses the Row MS instead of the MSE.
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