Single Factor ANOVA Example

The null hypothesis in single factor ANOVA is that the means of the various samples are equal.

Each of the following four columns (stored in the waves f1to f4) represents instrument recording of some arbitrary property consisting of 6 samples.

Samplef1f2f3f4
119222021
221212219
319202022
420222219
519222120
618192018

H0: there is no difference in the values recorded by the four instruments.

Ha: there is sufficient difference in the values recorded by the four instruments.

To run the test, execute the following command:

StatsAnova1Test/T=1/Q/W/BF  f1,f2,f3,f4

The results are displayed in three tables. Straight ANOVA results are in the table "ANOVA1 Results":

DFSSMSFFcP
Groups311.53.83333
Error20291.45
Total2340.51.760872.643683.098390.077207

Here the critical value Fc>F so H0 can't be rejected. Note also that P>alpha which is set by default to 0.05.

The second table titled "Welch Test" contains the following results:

N13
N28
Fp0.45153
Fpc4.06618
Pp0.723258

Here Fp is the Welch test statistic associated with degrees of freedom N1 and N2, Fpc is the critical value and Pp is the P-value.

The third table "Brown and Forsythe Test" contains the following results:

N13
N218
Fp2.64368
Fpc3.15991
Pp0.0805162

Here again Fp is the test statistic associated with degrees of freedom N1 and N2, Fpc is the critical value and Pp is the P-value.