ANOVA stands for analysis of variance and was developed by Ronald Fisher in 1918. Thus, some researchers also call it the statistics fisher analysis of variance. ANOVA is a statistical method that is used to do the analysis of variance between n groups. T-test is the test used when the researcher wants to compare two groups. For example, if a researcher wants to compare the income of people based on their gender, they can use the t-test. Here, we have two groups: male and female. To compare the two groups, T-test is the best test. However, there is sometimes a problem when comparing groups that are more than two groups. In these cases, when we want to compare more than two groups, we can use the T-test as well, but this procedure is long. For example, first we would have to compare the first two groups. Then we would have to compare the last two groups. Finally, we would have to compare the first and the last group. This would take more time and there would be more possibility for mistakes. Thus, Fisher developed a test called ANOVA that can be applied to compare the variance when groups are more than two. ANOVA statistics also belong to the parametric test family, because ANOVA has some assumptions. When data meets these specific assumptions, then ANOVA is a more powerful test than the nonparametric test.
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Assumptions in ANOVA:
1. Normality: The first assumption in ANOVA is that the data should be normally distributed or the distribution of the particular data should be normal. There are many statistical tests that are applied to know the distribution of the ANOVA data. More commonly, many researchers use Kolmogorov-Smirnov, Shapiro-Wilk, or the histogram test to test the normality of the data.
2. Homogeneity: The second important assumption in ANOVA is that homogeneity or variance between the groups should be the same. In SPSS, Levene’s test is applied to test the homogeneity of the ANOVA data.
3. The third assumption is ANOVA is independence of case. This means that the grouping variables should be independent of each other or there should not be any pattern between the cases.
In research, after the regression technique, ANOVA is the second technique that is the most commonly used by the researcher. It is used in business, medicine or in psychology research. For example, in business, ANOVA is used to know the sales difference of different regions. A Psychology researcher can use ANOVA to compare the behavior of different people. A medical researcher can use ANOVA statistics in the experiment of a drug as he or she can test whether or not the drug cures the illness.
Procedure of ANOVA:
Set up hypothesis: To perform ANOVA statistics, a researcher has to set up the null and alternative hypothesis.
Calculation of MSB, MSW and F ratio: After set up, the researcher must calculate the hypothesis and the variance between the samples. In the calculation of variance between the samples, first we calculate the grand mean from the all the samples. Then, the researcher must make the deviation from individual mean to the grand mean for each sample, and square the deviation and divide the square deviation of all the samples by their degree of freedom. This is called MSB, which stands for the mean sum of square between the samples. The second component of ANOVA statistics will be the variance within the sample. To calculate the variance within the sample, take each deviation sample from the respective sample means, find the square of each sample, and divide it by the respective degree of freedom. This is called MSW, which stands for the mean sum of the square within the sample. The ratio of the MSB and MSW is called the F ratio.
Testing of hypothesis in ANOVA: In ANOVA statistics, the calculated F ratio value is compared to the standardized table value. If the calculated F ratio value is greater than the table value, we will reject the null hypothesis and conclude that the means of the groups are different. If the calculated value is less than the table value, then we will accept the null hypothesis and conclude that the means of all the groups are the same.
ANOVA and SPSS: Manual calculation of ANOVA statistics is a long procedure. These days, almost all statistical computer software has the option for calculating ANOVA statistics. In SPSS, ANOVA can be performed by using the “analysis menu” and the “compare means option.” Select “one way ANOVA” from the compare means option. In SPSS, the hypothesis probability value is used to accept or reject the null hypothesis.
