## 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.

 Sample f1 f2 f3 f4 1 19 22 20 21 2 21 21 22 19 3 19 20 20 22 4 20 22 22 19 5 19 22 21 20 6 18 19 20 18

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":

 DF SS MS F Fc P Groups 3 11.5 3.83333 Error 20 29 1.45 Total 23 40.5 1.76087 2.64368 3.09839 0.077207

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:

 N1 3 N2 8 Fp 0.45153 Fpc 4.06618 Pp 0.723258

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:

 N1 3 N2 18 Fp 2.64368 Fpc 3.15991 Pp 0.0805162

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.