Variance: Analysis Of Means

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Analysis of Variance (ANOVA) is a statistical method used to test differences between two or more means. Though it is called "Analysis of Variance" but actually it is "Analysis of Means."
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. 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. If the Type one error is set to be .05, and there are several groups, each time a mean is tested against another there would be a .05 probability
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You compare the differences in the samples to see if they are the same or statistically different while still accounting for sampling error.

For example, a teacher might have data on student performance in non-assessed tutorial exercises as well as their final grading. The teacher is interested in knowing if tutorial performance is related to final grade. ANOVA allows breaking up the group according to the grade and then knowing if performance is different across these grades.

Types of ANOVA

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
• N-way Multivariate ANOVA.

One-Way: When we compare more than two groups, based on one factor (independent variable), 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
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For example, in productivity measurement if a company takes all the factors for productivity measurement, then it is said to be n-way ANOVA.

Related Statistical Tests
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.

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. ANOVA is also used in medical research to test the effectiveness of a
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