Research Methodology One-Way ANOVA - analysis of variance , pares the means of two or more independent groups in order to determine whether there is statistical evidence that the associated population means are significantly different.

One-way ANOVA is a parametric test. This test is also known as One-Factor ANOVA

1. M.Com- Semester-4 Research Methodology – II PB04CCOM21 Unit-3 Analysis of Variance (ANOVA)

2. Syllabus content What is ANOVA? Basic principles of ANOVA techniques t- test Short-cut method for one way ANOVA Two way ANOVA

3. Introduction Buying a new product or testing a new technique but not sure how it stacks up against the alternatives? It’s an all too familiar situation for most of us. Most of the options sound similar to each other so picking the best out of the lot is a challenge. Consider a scenario where we have three medical treatments to apply on patients with similar diseases. Once we have the test results, one approach is to assume that the treatment which took the least time to cure the patients is the best among them. What if some of these patients had already been partially cured, or if any other medication was already working on them? In order to make a confident and reliable decision, we will need evidence to support our approach. This is where the concept of ANOVA comes into play . Professor R.A. Fisher was the first man to use the term ‘Variance’* and, in fact, it was he who developed a very elaborate theory concerning ANOVA, explaining its usefulness in practical field. Later on Professor Snedecor and many others contributed to the development of this technique

4. Meaning Analysis of variance (ANOVA) is a statistical technique that is used to check if the means of two or more groups are significantly different from each other . ANOVA checks the impact of one or more factors by comparing the means of different samples . ANOVA is essentially a procedure for testing the difference among different groups of data for homogeneity . It may seem odd that the technique is called “Analysis of Variance” rather than “Analysis of Means.” As you will see, the name is appropriate because inferences about means are made by analyzing variance

5. Examples Through this technique one can explain whether various varieties of seeds or fertilizers or soils differ significantly so that a policy decision could be taken accordingly, concerning a particular variety in the context of agriculture researches. Similarly , the differences in various types of feed prepared for a particular class of animal or various types of drugs manufactured for curing a specific disease may be studied and judged to be significant or not through the application of ANOVA technique . Likewise, a manager of a big concern can analyze the performance of various salesmen of his concern in order to know whether their performances differ significantly.

6. one-way ANOVA two-way ANOVA An ANOVA conducted on a design in which there is only one factor is called a one-way ANOVA. If an experiment has two factors, then the ANOVA is called a two-way ANOVA. If we take only one factor and investigate the differences amongst its various categories having numerous possible values, we are said to use one-way ANOVA and in case we investigate two factors at the same time, then we use two-way ANOVA. In a two or more way ANOVA, the interaction (i.e., inter-relation between two independent variables/factors), if any, between two independent variables affecting a dependent variable can as well be studied for better decisions. For example, suppose an experiment on the effects of age and gender on reading speed were conducted using three age groups (8 years, 10 years, and 12 years) and the two genders (male and female). The factors would be age and gender. Age would have three levels and gender would have two levels.

7. Basic Principles of ANOVA The basic principle of ANOVA is to test for differences among the means of the populations by examining the amount of variation within each of these samples, relative to the amount of variation between the samples . Assumptions Population from which the samples are drawn are normal E ach of these populations has the same variance. Samples are random Samples are independent Errors are normally distributed with 0 mean and σ 2 Variance The total variance in the joint sample is divided into two parts A) one based on between samples variance and the other based on within samples variance. Using these two variance test statistic can be defined Fe= between samples varian ce within samples variance.

8. Hypothesis Testing H 0 = All Means of population are same H 1 = All Means of population are not same Between sample variance is large when the effect of treatment are different FC is large so null hypothesis is rejected

9. One-way (or single factor) ANOVA One-way (or single factor) ANOVA: Under the one-way ANOVA, we consider only one factor and then observe that the reason for said factor to be important is that several possible types of samples can occur within that factor. We then determine if there are differences within that factor. The technique involves the following steps:

10. I llustration 1 In a company there are four shop floors. Productivity rate for three methods of incentives and gain sharing in each shop floor is presented in the following table. Analyze whether various methods of incentives and gain sharing differ significantly at 5% and 1% F-limits.