Essay On ANOVA

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Register to read the introduction… Other methods like T-test can also be used but it will use several separate tests which will increase the overall type 1 error of the experiment. ANOVA can determine the differences of means with a single test.

Characteristics of ANOVA
There are two types of ANOVA as follows:
One way ANOVA _ it refers to situations where only one factor/ variance is considered. An example is when one is testing the differences in sales for 3 salesmen; by doing this one is considering one factor which is the salesmen’s selling ability.
Statistical significance
It is assessed by an F-test in which the variance of scores caused by the way the means differ “between” groups is compared with the variance of scores found “within” each group. The variance is called “mean square” and is represented by MS.
1 Two way ANOVA _ the response variable of interest may be affected by more than one factor. Example, the salesmen are affected by: salesmen selling ability, price charged and the extent of advertising in a given area.
2 Statistical
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It was proposed by statistician Wilcoxon in 1945. Man Whitney U test is used to test the null hypothesis that the population of distribution of the two independent groups are the same. The test is used in situations where the sets of selected samples are at least ordinal that is they can be ranked from low to high or vice versa.
Assumptions and formal statements of hypothesis.
• All samples from both groups are independent of each other
• The responses are ordinal or continous assessment
• Samples are randomly selected
Methodology
Given that the assumptions have been met, the U TEST compares distribution of rank scores for two independent groups of randomly selected subjects. Two distinct applications have been made-;
i. The first application assumes that the sample of the larger of the samples has an N between 9 and 20 individuals ii. A sample size of more than 20 subjects is assumed for the larger of the two groups. The values of the samples N1 and N2, from the lowest to the highest rank, irrespective of the groups, rank 1 to be the lowest ,rank 2 next to the lowest, and so forth. Then the ranks of the two samples are ranked individually and represented as R 1 and R2. These two U s are calculated for the formulas.

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