## (VNF) – Let’s find out with VietnamFinance what is analysis of variance? What is one-way analysis of variance (oneway ANOVA)? Steps of ANOVA analysis.

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## Analysis of variance is a statistical method for analyzing the total size of variation of a dependent variable into several parts, and each part is attributed to the variation of an individual explanatory variable or a group of explanatory variables.

## What is analysis of variance?

**Analysis of variance (analysis of variance-ANOVA)** is the way

**statistics to analyze the total variability of the dependent variable**(the sum of which the total size of variation is defined as the sum of squared deviations from its mean) into multiple parts, and each part is attributed to the variability of an individual explanatory variable or a group of variables. explain. The remainder that cannot be attributed to any variable is called the unexplained variation or residual. This method is used to test the null hypothesis to determine if the samples obtained are drawn from the same population. The test results tell us whether the samples obtained are correlated or not.

## What is Single-Factor Analysis of Variance?

**One-way analysis of variance** (also called * oneway anova*) used to

**test the hypothesis of equal mean of the sample groups with a probability of error of only 5%.**

For example: Analyze the difference between customer attributes (gender, age, occupation, income…) for a certain problem (usually chosen as a dependent factor, eg: satisfaction).

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## Steps of ANOVA . analysis

** Some assumptions** When analyzing ANOVA:

The comparison groups must be independent and randomly selected.

– The comparison groups must have a normal distribution or the sample size must be large enough to be considered asymptotically normally distributed.

The variances of the comparison groups must be the same.

Note: if the assumption that the population is normally distributed with equal variances is not met, you can use the Kruskal-Wallis non-parametric test as an alternative to ANOVA.

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* Inspection results* consists of two parts:

*Part 1*:

Levene test: used to test whether variance is equal or not between groups

Ho: “Equal variance”

Sig 0.05: accept Ho -> eligible for further analysis anova

*Part 2*:

ANOVA test: Test anova

Ho: “Equal average”

Sig is qualified to confirm that there is a difference between groups for the dependent variable

Sig > 0.05: accept Ho -> not qualified to confirm the difference between groups for dependent variable

When there is a difference, it can be analyzed further to find out how the difference is between the groups of observations by the Tukey, LSD, Bonferroni, Duncan tests as shown below. The anova depth test is called the Post-Hoc test.

*(References: Nguyen Van Ngoc, Dictionary of Economics, National Economics University)*

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