ANOVA Test (Analysis of Variance)

ANOVA (Analysis of Variance)

Introduction ANOVA (Analysis of Variance)

Analysis of Variance(ANOVA) is an extremely important tool for data analysis. Two types of ANOVA one is One Way and anothe is Two Way ANOVA used.

It is a statistical method to compare the population means of two or more groups by analyzing variance. 

ANOVA (Analysis of Variance)

ANOVA is a statistical tool used for comparing the dependant and the independent variables.ANOVA technique that uses a sample of observations to compare the number of means.t is similar to that of t-test and z-test, which are used to compare mean along with relative variance. However, in ANOVA, it is best suited when two or more populations/samples are compared. An ANOVA test is to find if you need to reject the null hypothesis or accept the alternate hypothesis.

Types of ANOVA

One-way ANOVA

One-way has one independent variable (with 2 levels). The one-way ANOVA compares the means between the groups you are interested in and determines whether any of those means are statistically significantly different from each other. Specifically, it tests the null hypothesis.


µ = group means 

k = number of groups. 

Example: You have a group of individuals randomly split into smaller groups and completing different tasks. For example, you might be studying the effects of tea on weight loss and form three groups: green tea, black tea, and no tea.

  • Two-way ANOVA

Two-way ANOVA is used to compare two or more factors (i.e.check the effect of two independent variables on a single dependent variable.) Both types of ANOVA have a single continuous response variable. Use a two way ANOVA when you have one measurement variable (i.e. a quantitative variable) and two nominal variables

Assumptions for Two Way ANOVA

  • N-way ANOVA

If more multiple independent variables then use N-way analysis of variance.

The N-way ANOVA can show whether there are effects of the independent variable and interactions between them. Interactions are usually seen when one independent variable depends on the second independent variable.

  • What are “Groups” or “Levels”?

Groups or levels are different groups within the same independent variable. In the above example, your levels for “brand of cereal” might be Lucky Charms, Raisin Bran, Cornflakes — a total of three levels. Your levels for “Calories” might be sweetened, unsweetened — a total of two levels.

Uses of ANOVA

  • To test correlation and regression.
  • To study the homogeneity in the case of two-way classification.
  • To test the significance of the multiple correlation coefficient.
  • To test the linearity of regression.


  • Suitable for multidimensional variables.
  • Analysis of various factors at a time.
  • Can be used in 3 or more than 3 groups


  • It is difficult to analyze ANOVA under strict assumptions regarding the nature of data.
  • It is not so helpful in comparison with the t-test that there is no special interpretation of the significance of two means.
  • The requirement of the post-ANOVA t-test for further testing.


  • Lean-Six Sigma/operational efficiency.
  • Comparing the gas mileage of different vehicles, and also the same vehicle under different fuel types.
  • Understanding the impact of temperature, pressure, or chemical reaction (power reactors, chemical plants, etc).
  • Understanding the performance, quality, or speed of manufacturing processes based on the number of cells.


ANOVA-based approaches require at least interval data for the dependent variable. 


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