Business Analytics Part 6- Two Way Analysis of variance (ANOVA) | Two Way ANOVA

In the last chapter about one way ANOVA, we studied how one way ANOVA is used to measure a variable or output or factor for more than two groups at different interval or level. Suppose we instead of one variable, we have two variables. In that case, we will two way ANOVA.

Welcome to part 6 of this Business Analytical tutorial where we will learn two ways ANOVA.


As mentioned earlier, two way ANOVA is used to measure two factors. In last chapter, we used example of measuring drug impact on a group at different stages based on dosage quantity. Let’s add one more factor to it, the gender. So now we need to measure;

  • The impact of drugs for different dosage
  • And impact of drugs for male and female

In this case we are going to use Two Way ANOVA.

Two Way ANOVA is used when we have two factors to evaluate and to check if there is any interaction between them.

Two Way ANOVA helps in evaluating two factors simultaneously whereas with One Way you may have to conduct two different experiments to measure their impact on the common variable, but still you will not be able to find out their interaction with each other. Therefore, Two way ANOVA is a better statistic technique to use when you have two factors to play.

In our case, above experiment will validate if there is impact of the increasing dosage on the treatment and if gender, as factor plays any role in it.


Assumptions used in two way anova are similar to one way anova, they are;

  • Population used for sampling purpose had normal distribution of variable.
  • Variables are regularly monitored and measured at continues level.
  • Dependent variable has same variance and normally distributed.
  • Errors are independent.
  • Factors/variables which you use for the study should be relevant to the overall experiment like dosage of the medicine is a relevant factor if you are looking to study its effect.

Essentially Two way ANOVA is similar to one way ANOVA but it helps when there is a additional factor to evaluate. Let’s go through a Two ANOVA Calculation Example to see how above mentioned factors like dosage and gender play it out in real Two Way ANOVA.

Two Way ANOVA Calculation

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