ANOVA is a statistical method that stands for analysis of variance. ANOVA was developed by Ronald Fisher in 1918 and is the extension of the T and the Z test. Before the use of ANOVA, the T-test and Z-test were commonly used. But the problem with the T-test is that it cannot be applied for more than two groups. In 1918, Ronald Fisher developed a test called the analysis of variance. This test is also called the Fisher analysis of variance, which is used to do the analysis of variance between and within the groups whenever the groups are more than two.
These days, researchers are using ANOVA in many ways. The use of ANOVA depends on the research design. Commonly, researchers are using ANOVA in three ways: one way ANOVA, two way ANOVA and n way ANOVA. When we compare more than two groups, based on one factor, this is called one way ANOVA. For example, it is used if a manufacturing company wants to compare the productivity of three or more employees based on working hours. This is called one way ANOVA. When a company wants to compare the employee productivity based on two factors, then it said to be two way ANOVA. For example, based on the working hours and working conditions, if a company wants to compare employee productivity, it can do that through two way ANOVA. When the factor comparison is taken, then it said to be n way ANOVA. For example, in productivity measurement if a company takes all the factors for productivity measurement, then it is said to be n way ANOVA.
Data level and assumption plays a very important role in ANOVA. In ANOVA, the dependent variable can be continuous or on the interval scale. Factor variables in ANOVA should be categorical. Like the T-test, ANOVA is also a parametric test and has some assumptions, which should be met to get the desired results. ANOVA assumes that the distribution of data should be normally distributed. ANOVA also assumes the assumption of homogeneity, which means that the variance between the groups should be equal. ANOVA also assumes that the cases are independent to each other or there should not be any pattern between the cases.
ANOVA is used very commonly in business, medicine or in psychology research. In business, ANOVA can be used to compare the sales of different designs based on different factors. A psychology researcher can use ANOVA to compare the different attitude or behavior in people and whether or not they are the same depending on certain factors. In medical research, ANOVA is used to test the effectiveness of a drug.
The procedure of ANOVA is the same as the T-test, but the calculation is different. In ANOVA, a researcher first sets up the null and alternative hypothesis. The null hypothesis assumes that there is no significant difference between the groups. The alternative hypothesis assumes that there is a significant difference between the groups. After setting up the hypothesis, data must be cleaned and made free of outlier and missing values. After cleaning the data, the researcher must test the above assumptions and see if the data meets them. They must then do the necessary calculation and calculate the F-ratio. After this, the researcher must compare the critical value of the F-ratio with the table value. If the calculated critical value is greater than the table value, the null hypothesis will be rejected and the alternative hypothesis is accepted. Rejecting the null hypothesis, we will conclude that the mean of the groups are not equal. If the calculated value is less than the table value, we will accept the null hypothesis and reject the alternative hypothesis.
These days, researchers have extended ANOVA in MANOVA and ANCOVA. MANOVA stands for the multivariate analysis of variance. MANOVA is used when the dependent variable in ANCOVA are two or more than two. ANCOVA stands for analysis of covariance. ANCOVA is used when the researcher includes one or more covariate variables in the independent variable. SAS, SPSS, STATA and many more software applications are used to perform ANOVA.
