Two-Way ANOVA

Two-Way ANOVA

Two-Way ANOVA

Description

It analyzes the effect of independent variables on the expected outcome along with their relationship to the outcome itself.

Why to use

To perform analysis of variance.

When to use

To know how two independent variables, in combination, affect a dependent variable.

When not to use

When the number of dependent variables is more than one.

Prerequisites

  • The dependent variable should be continuous.
  • One independent variable should be categorical.
  • One independent variable should be numerical.
  • All the independent variables should be taken from a normally distributed population.

Input

Any dataset that contains numerical data.

Output

  • Degrees of Freedom
  • Sum of Squares
  • Mean Sum of Squares
  • F-Ratio

Statistical Methods used

  • Shapiro Wilk Test
  • Bartlett Test of homogeneity

Limitations

  • It cannot be used on any data other than numerical.
  • It cannot be used for more than one dependent variable.

Two-Way ANOVA is a statistical analysis method. It is used to determine if there are any statistical differences in two or more samples' mean values.

In Two-Way ANOVA,

Null Hypothesis –

  • There is no difference in group means of the first independent variable.
  • There is no difference in group means of the second independent variable.

Alternative Hypothesis – All the samples do not have equal means.

Two Way ANOVA tests the Null Hypothesis (H0),

H0: µ0 = µ1 = µ2 = µ3 = … = µk

Where,

µ = the group mean

k = number of samples

A two-way ANOVA is used to estimate how the mean of a quantitative variable changes according to the levels of two categorical variables. Use a two-way ANOVA when you want to know how two independent variables, in combination, affect a dependent variable.

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