Analysis of variance, ANOVA, is a statistical technique used to analyze the variation between two or more groups so as to discover the disparity among the group means. Analysis of variance is used to examine the general variation instead of a specific variation between means.
The assumptions that involve the use of ANOVA are:
- The population is normally distributed
- The population is mutually exclusive
- All population should have equal variance
- The measurement of the dependent variable is at
the internal/ratio level
- Each observation of the samples are independent
ANOVA consists of two types of measurements: first, one-way ANOVA and second, two-way ANOVA. The one-way ANOVA is measuring variations among different
groups, comparing two groups or more. The one-way ANOVA is the preferred statistical test when examining two or more groups. An example of using one-way
ANOVA is the analysis of a particular sport but on different education levels like sophomore, junior, or senior. The two-way ANOVA is used when the variations analysis is comparing a much more complicated pair of groupings. An example of two-way ANOVA could be analyzing the grades of an American senior student to the grades of a student who is studying in America on the exchange student program.
Analysis of variance refers to the differences between two, three, or more groups. The textbook says two or more groups, while the visual learner says three or more groups (Grove & Cipher, 2017, p. 179); (The Visual Learner, 2018). There are different versions of the analysis of variance (ANOVA) tests but the most basic form, is a one-way ANOVA. The one-way ANOVA has only one dependent variable and one independent variable. The variable is dependent if it is being tested and measured. The independent variable is the variable that is changed to see how it affects the dependent variable. The outcome of the ANOVA provides an F-ratio that is an average of the differences between the groups. There will also be a F-critical value. If the F-critical value is not more than the F-ratio, the null hypothesis would be rejected at the given alpha level.
The test must meet certain guidelines. The distributions of the populations should be very near normal. The variance of the population should be the same. The samples must be quantitative and taken from simple random samples and the samples must not be dependent on one another (The Visual Learner, 2018).
The repeated-measures analysis of variance can be used to measure changes in the dependent variable over extended periods of time.
Post hoc analysis can then be used to find the location of the variance. These tests include the Dunnett test, Newman-Keuls test, the Scheffe test and the Tukey Honestly Significant Difference (HSD) test (Grove & Cipher, 2017).
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