The Fstatistic is the ratio of Sb2 to Sw2 where Sb2 is the v

The F-statistic is the ratio of Sb2 to Sw2, where Sb2 is the variability between the sample means and Sw2 is the variability within the samples. Why is the F-statistic constructed this way? And what does it tell us?

Solution

Z test or t test is used to test whether two sample means are sufficiently different to indicate the samples are from populations with different population means.

When more than two different groups are involved, we need to depend on ANOVA for the inference.

For example : Different parts of a test (listening, reading, vocabulary, Cloze, translation)

Priciples of ANOVA :

Two kinds of differences in a test: systematic differences and random errors

Systematic differences are caused by different experimental conditions.

Random errors are caused by any factors other than experimental conditions.

The total variance between different groups represents systematic differences

The total variance within the group is random errors.

The ratio of these two variances follows the F distribution.

F=Sb2/Sw2

The larger value of F-statistics results into rejection of null hypothesis.

where, Sb2 is the variability between the sample means and

Sw2 is the variability within the samples.

Sb2 = SSb / dfb

Sw2 = SSw / dfw

dfb=m-1

where m = number of samples

dfw=m(n-1)

m= number of the samples times

n = size of the sample minus.

Look up for F(m-1,m(n-1)) in the Table of F-distribution

where is leve of significance.