Analysis of variance (ANOVA) is a statistical test that analyzes the difference among the means of multiple groups. Analysis works by comparing the variation between groups with the variation within the groups. If the variation between the groups is much larger than the variation within the groups, then it suggests that there is a significant difference between the means of the groups.
The difference in means is due to at least one group’s distribution being different from the others. If all groups means were the same with approximately same variance, then they would be governed by the same distribution. With all groups belonging to the same distribution, the ratio (F-stat) of between-group variance and within-group variance is approximately 0. But if at least one of the groups is from a different distribution, then the ratio is larger than 0.
The null hypothesis of ANOVA is that there is no difference among group means. However, if any one of the group means is significantly different from the overall mean, then the null hypothesis is rejected.
A one-way analysis involves one factor or independent variable. The factor may have two or more categorical groups and analysis is used to establish if there is any significant difference between those categorical groups.
The TD_ANOVA function is used in a variety of contexts, such as comparing the performance of different treatments in a clinical trial, comparing the effectiveness of different marketing strategies, or comparing the mean salary of employees in different departments of a company.
To conduct an analysis, the data must meet certain assumptions, including that the data are normally distributed and that the variances of the groups are approximately equal.