Anova

Format: A[nova] [N] [column]

The one-way analysis of variance is equivalent to an unpaired t test except that the comparison is performed between more than two groups. It measures whether there is a tendency for the groups of values to have different means, or whether they might all be drawn from the same population. The values lie in one column and the groups are defined by conditions. If the option N (for nonparametric) is chosen then the Kruskal-Wallis one-way analysis of variance by ranks test is performed instead.

Example:

Enter command - A

- One-way analysis of variance -
Enter column for dependent variable
c15
Input number of groups:   5
Enter condition for group A:    c5=1
Enter condition for group B:    c5=2
Enter condition for group C:    c5=3
Enter condition for group D:    c5=4
Enter condition for group E:    c5=5

Output:

One-way analysis of variance with C15 (GHQ) as dependent variable
Group A:  C5=1
Group B:  C5=2
Group C:  C5=3
Group D:  C5>3

Between pairs of groups: t tests (96 df)
    A               B               C
    t      p        t      p        t      p
B  -1.111  0.2692
C  -0.400  0.6897   1.456  0.1487
D  -1.940  0.0553  -1.353  0.1793  -4.231  0.0001

Overall significance: F = 6.463 3,96 df, p = 0.0005

The analysis of variance outputs an F ratio which gives the overall significance representing the probability that all the group means could have varied so much by chance. It also computes a t statistic and two-tailed probability value for the difference between the means for each pair of groups. This latter differs from performing an ordinary unpaired t test between the two groups only in that the whole sample is used to provide an estimate of the overall variance of the measure, rather than only relying on the values in the pair of groups under consideration.

Example:

Enter command - A N

- One-way analysis of variance -
Enter column for dependent variable
c15
Input number of groups:   4
Enter condition for group A:    c5=1
Enter condition for group B:    c5=2
Enter condition for group C:    c5=3
Enter condition for group D:    c5>3

Output:

Kruskal-Wallis test with C15 (GHQ) as dependent variable
Group A:  Number = 3     Mean rank = 35.00        C5=1
Group B:  Number = 12    Mean rank = 52.88        C5=2
Group C:  Number = 41    Mean rank = 38.71        C5=3
Group D:  Number = 25    Mean rank = 59.66        C5=4
Group E:  Number = 19    Mean rank = 64.84        C5=5

Between pairs of groups comparisons of mean ranks
(Two-tailed, corrected for multiple comparisons)
   A              B              C              D
   Ru-Rv     p    Ru-Rv     p    Ru-Rv     p    Ru-Rv     p
B   17.88    NS
C    3.71    NS   -14.17    NS
D   24.66    NS     6.78    NS    20.95  0.0887
E   29.84    NS    11.97    NS    26.13  0.0235   5.18    NS

Overall significance: KW (corrected for ties) = 14.880,  4 df
p = 0.0050

For the Kruskal-Wallis test the column and groups are selected in the same way as for the parametric analysis of variance, and the output reports the overall differences between the group ranks and between pairs of groups comparisons as described in Nonparametric Statistics for the Behavioural Sciences by Siegel.