October 9,2012-Lesson about ANOVA (Analysis of Variance)

Next week will be the schedule for our second departmental test, so we are now going fast with our lessons so that we will be able to take the whole coverage of Advanced Statistics.

Now we’re having the lesson about Analysis of Variance (ANOVA). This lesson will be useful for our Advanced Research next school year so we should understand the lesson well. Here are some key points for this lesson:

*The z-test and t-tests should not be used when three or more means are compared, instead, F-test can be used to compare three or more means. (ANOVA)

*The most commonly used tests are the Scheffe test and Tukey test.

*Between-Group variance (S_B²)– one of the first estimates, involves finding the variance of means.

*Mean Square of the Between Group (MS_B) – one of the first estimates, made by computing the variane using all the data and is not affected by differences in the means.

*Within-Group Variance (S_W²) or Mean Square of the Within-Group (MS_W) – the second estimates, is made by computing the variance using all the data and is not affected by differences in the means.

*Analysis of variance used to compare three or more means which contains only one variable. (One-Way Analysis of Variance)

*ANOVA that involve two variables. (Two Way Analysis of Variance)

*No difference in the means: the between group variance estimate will approximately equal to the within group variance estimate; F test value will be approximately equal to one; Null hypothesis will not be rejected.

*Means differ significantly: the between-group variance will be much larger than the within-group variance; F test value will be significantly greater than 1; the Null hypothesis will be rejected.

*k=number of groups

*N=sum of the sample sizes for groups

*SS_B =sum of squares between groups

*SS_w=sum of squares within groups/ (sum of squares for the error)

*MS_B =Between group variance (S_B²)=SS_B/k-1)

*MS_W =Error variance

*Scheffe Test = one must compare the means two at a time, using all possible combination of means.

*Tukey Test can also be used after the analysis has been completed to make pairwise comparisons between means when the groups have the same sample size. The symbol for the Tukey test is q.

Analysis of Variance includes a wide range of symbols, ideas and needs a lot of understanding. Our knowledge of ANOVA will be used for our studies when we are already in 4^th year.

Posted by: Kent Spencer Manalo Mendez