ANOVA - Two Factor


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



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