Analysis of Variance

Analysis of Variance

-used to compare three or more means which contains only one variable.

-used instead of t-test because all the means are compared simultaneously

With the F-test, two different estimates of the population variances are amde:L

1. Between-Group variance-involves finding the variance of the means

2. Within-Group variance-made by computing the variance using all thye data and is not affected by the difference of the means.

          In the analysis of variance, you will perform the hypothesis also. 

1. You will state the hypothesis

     Ho:m1=m2=m3...m4

     Hi: at least one mean is different from the others

2. Find the Critical Value

      d.f.N= k-1, where k is the number of groups

      d.f.D= N-k, where N is the sum of the sample size of the groups

3. Compute the test value

      a. Find the mean and variance of each sample.

      b. Find the grand mean(the mean of all sample) which is obtain by adding all the data and dividing it by the grand total

       c.Find the between-group variance

       d. Find the within-group variance

       e. Find the F-test value which is obtain by dividing the between-group variance by the within group variance.

4. Make the decision

5. Summarize the result

 Note: If the hypothesis is rejected or there is a significant difference, you can find where is the difference by performing the Scheffe or Tukey test.

Scheffe test

-one must compare the means two at a time, using all possible combination of means

Tukey test

-used only if the groups have the same sample size

By:DUSTIN JOSHUA A. ESQUIA III-GOLD