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# Analysis of Variance (ANOVA)

Analysis of Variance (ANOVA)

Analysis of Variance (ANOVA) is a statistical test, which is applied to test whether there is a potential difference between two variables, or groups of variables. In simple terms, ANOVA is a technique used to compare dataset properties such as means and relative variance between them. It uis appropriately use if there are more than two samples to be compared.

Types of Analysis of Variance (ANOVA)

The application of ANOVA is dependent on the research design applied. Majorly, there are three ways ANOVA is applied, one-way ANOVA two-way ANOVA, and N-way ANOVA. The one-way and two-way implies the number of independent variables included in the analysis of variance test. The one-way ANOVA has only one independent variable with two levels of analysis, while the two-way ANOVA has two independent variables and multiple levels. The N-way ANOVA implies the use of more than two independent variables where ‘n’ implies the number of independent variables present.

For instance, a researcher may be interested in investigating the difference in IQ of students. The difference could be assessed by: country (One-way ANOVA); by country and gender (two-way ANOVA) and by country, gender, ethnicity, age-group etc. (N-way ANOVA).

Conducting Analysis of Variance (ANOVA)

When conducting ANOVA, the null and alternative hypotheses are stated as follows.

H0 (Null hypothesis): there is no significant difference among the groups

Ha (alternative hypothesis):  there is a significant difference among the groups

After cleaning the data and conducting the test, then two parameters are calculated; the F-ration and the associated probability value (p-value). The rule of thumb is that if the p-value associated with F-statistic is small than 0.05 (p-value<0.05), then the Null hypothesis is Rejected and Alternative hypothesis accepted. The conclusion in this case is that the means of the groups analysed is not equal.

Generally, when conducting analysis of variance, we are investigating whether there is a statistically significant difference among the groups considered. If the results indicate that there is a difference, then it is vital to examine the sources of the difference. In this case,the researcher could run thepost-hoc tests, which tests the mean differences between the groups considered.

Major assumptions when conducting Analysis of Variance

The first assumption is that the dependent variable should be a continuous variable (interval or ration measurement levels). The second assumption is that the independent variables should be a categorical (nominal or ordinal) variable. Thirdly, ANOVA assumes that the data is normally distributed.