# anova - Mean wheat Treatment 1 Treatment 2 Treatment 3...

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Treatment 1 5 bushels/acre Treatment 2 7 bushels/acre Treatment 3 6 bushels/acre Treatment 4 8 bushels/acre Mean wheat x

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Is there any significant difference in means ? or Are the obtained means due to chance only ?
Definition of ANOVA Definition: Analysis of the variance is the simultaneous testing of two or more treatment means by examinations of the variances within groups (treatments). The t-test can test the difference between two means of two groups, but not more than two. Even though the ANOVA is an analysis of variances among data, its primary use is the test of differences among the group means.

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ANALYSIS OF VARIANCE 1. One way classification or one factor experiments 2. Two way classification or two factor experiments
One-Way Classification (Fixed-Effect) • The term “one way classification” refers to the fact that only one factor is being studied in the experiment. • The term “fixed effect” refers to the fact that the treatments of the factor involved are specifically selected by experimenter because they are of particular interest.

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1. One way classification ……………………………… …………. .. Treatment a Treatment 2 Treatment 1 b x x x 1 12 11 ..... .......... b x x x 2 22 21 ..... .......... ab a a x x x ..... .......... 2 1 . 1 x . 2 x . a x
a j x b x b k jk j ....... , , 2 , 1 , 1 1 . = = = ∑∑ = = = == k j jk a j b k jk x ab a j x ab x , 11 1 ....... , , 2 , 1 , 1

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( ) () = = + = = j j B k j j jk W B W k j jk x x b V x x V V V x x V 2 , 2 2 , . . where Total Variation
Problem 1. Table below shows the yields in bushels per acre of a certain variety of wheat grown in a particular type of soil treated with chemicals A, B or C.

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anova - Mean wheat Treatment 1 Treatment 2 Treatment 3...

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