The paper is an application of the Analysis of Variance also know as ANOVA. a case study is picked and the values that would be used tabulated. The kind of variables adn their characteristics are defined, then the assumptions that will be taken into consideration also highlighted. The Alternative and Null hypothesis are also give.
¶ … ANOVA study
Analysis of Variance (ANOVA)
Analysis of variance is a term used in statistics which involves a collection of statistical models and procedures that are associated with them where the observed variance in a particular variable is partitioned into components that can be attributed to different sources of variations. It is therefore a statistical technique that is useful for evaluation whether there are differences between average values or mean across several population groups. This model also entails that the response variable is continuous in nature while the predictor variables can be categorized. For there to be a test for statistical significance between means then there has to be a comparison i.e. analyzing variances hence the name of the model. There are various concepts in variance analysis these are; the partitioning of sums of squares .at the core of variance analysis is the fact that variances can be divided or partitioned. This means that variance that has been computed as the sum of deviations that are squared from the overall mean then divided by the sample size minus one. Hence from a given sample, the variance is a function of the sums of deviation squares or partitioning of variance.
The identified problem here is the performance of a group of 15 students in the GLMAT test. There is need to analyze whether the type of treatment that the students are subjected to has any consequences in the performance in the GMAT test that they take. The students will be grouped into tree categories of treatments, the first group will be 3-hour review program, the second will be 1 day program and the third will be 10-week course. The test that will be used here will be the F test.
The data that will be used here is as below
Treatment
Observation
3-Hour review
1 day program
10 weeks course
The question above is suitable for the selected test which is F test since there are more than two means that will be used in the calculations. An in a situation like this where more than two means are expected to be obtained and used, the best way to manipulate such data is through ANOVA, hence the above variables fit the qualifications of the selected variable test.
The variables here are discrete, quantitative, nominal and independent.
Null Hypothesis: There is a significant difference between the treatments that the students are subjected to in relation to their performance.
Alternative Hypothesis: There is no significant difference between the treatments that the students are subjected to.
Assumptions:
It is important to note here that in this case, there are two assumptions that will be made;
1. That there is a normal population distribution.
2. The variance associated with each variable is the same.
Types of errors likely in ANOVA case
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