Anaysis of variance (ANOVA) is the method which performs the testing the difference of the mean from over-3-populations ================================================================================ When there are 1 population or 2 populations, you can calculate the difference manually. But when you have over-3-populations, it's difficult to manually calculate every joint cases. So, in that cases, you can use ANOVA for simplicity ================================================================================ * Suppose arbitrary pointt $$$\bar{x}_{ij}$$$ * Entire deviation: $$$\bar{x} - \bar{x}_{ij}$$$ * Population deviation: $$$\bar{x} - \bar{x}_{i}$$$ * inner-popuplation deviation: $$$\bar{x}_{i} - \bar{x}_{ij}$$$ ================================================================================ Deviation in ANOVA $$$F \\ = \dfrac{\text{changes between classes}}{\text{changes in classes}} \\ = \dfrac{\text{mean squre between classes}}{\text{mean squre in classes}}$$$ ================================================================================ One-way ANOVA Convenient store A,B,C Satisfaction rate ================================================================================ Two-way ANOVA (cross checking) Convenient store A,B,C Region 1,2,3 Satisfaction rate ================================================================================ Multi-way ANOVA Convenient store A,B,C Region 1,2,3 Country 1,2,3 Satisfaction rate ================================================================================ Multivariate ANOVA Convenient store A,B,C Satisfaction rate Revisiting rate ================================================================================ Column: Separation, name, number of independent variable, number of dependet variable ================================================================================ * Preassumptions for ANOVA * Each population should have Gaussian normal distribution * Each population should have same variance * Each feature should be independent For example, independent between Convenient store and region in sampling * You should have enough number of feature vector data