Two-way analysis of variance with no replication (ANOVA)
The non-parametric equivalent to this test is the Friedman ANOVA by ranks test.
Script operation
This tool operates in a slightly different way to most of the others. Sample data should be entered as multiple samples but the column titled 'Subject' in the example below must also be included within the input range. The title of this column may be anything you wish. In the example below, the column headers 'A', 'B', etc. should also be included in the input range. The reason for this is that this information represents the two factors within the analysis.
Click here for information about general script usage.
Raw data: Subject A B C D 1 31 42 14 80 2 42 26 25 106 3 84 21 19 83 4 26 60 36 69 5 14 35 44 48 6 16 80 28 76 7 29 49 80 39 8 32 38 76 84 9 45 65 15 91 10 30 71 82 39 Spreadsheet output: ANOVA-Two Way:No Replication Subject Count Total Mean Variance 1 4 167 41.75 782.9167 2 4 199 49.75 1466.9167 3 4 207 51.75 1344.9167 4 4 191 47.75 404.25 5 4 141 35.25 230.25 6 4 200 50 1072 7 4 197 49.25 486.9167 8 4 230 57.5 691.6667 9 4 216 54 1030.6667 10 4 222 55.5 621.6667 A 10 349 34.9 390.9889 B 10 487 48.7 388.9 C 10 419 41.9 751.8778 D 10 715 71.5 513.6111 ANOVA Source of Sum of Degrees of Variance F Ratio Variation Squares Freedom Estimate Rows 1565 9 173.8889 0.2787 Columns 7553.1 3 2517.7 4.0359 Remainder 16843.4 27 623.8296 Total 25961.5 39 P(F Column <=f) one-tail: 0.017098 F-Critical (95%): 2.9606 F-Critical (99%): 4.6011
Interpretation