Business Analytics Part 5- One Way Analysis of Variance (ANOVA)

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As we have already seen been through t test and f test in previous chapters, it is a good time to look at ANOVA in detail. In this chapter we will go through One Way ANOVA.

In the last chapter, we have mentioned that t test for independent variable is equivalent to ANOVA if you are looking to measure the two groups/sample and it will produce similar results. ANOVA is used when you have to evaluate more than two sample groups.

If you are interested in ANOVA analysis with R, Anova in R


One way ANOVA is used to measure a variable or output or factor for more than two groups at different interval or level. It basically means you are measuring the same variable at different levels across all of these groups.

One Way ANOVA is used when there is one factor which need to be evaluated or measured.

As mentioned earlier, ANOVA is widely used in psychological experiments, so let’s assume that you are looking to measure the impact of a medicine at different time/level.

So you will create a group of patient based on certain factor and measure the impact of the medicine’s impact on desired ailment, say stress (or whatever medicine is targeting) at different stages of the medication life cycle. In this case, it could be based on dosage, like;

  1. x mg
  2. 2x mg
  3. 3x mg

In our case; factor is medicine’s effect and level are dosage.

So you will be measuring the impact of a medicine on different groups based on dosage.

You use these results to compare the final output and measure how drug treatment benefited the patients over a period of time.

In short, one way ANOVA is used to compare the means of more than 3 samples using the F distribution. If you haven’t read the F test, please read the previous chapter.

Under F test, test value should exceed the critical value in order to reject the null hypothesis which simply means that occurrence or the change in the variable’s value is not out of coincidence.

Assumption Validation in One Way ANOVA

Assumptions are integral part of ANOVA, therefore ANOVA assumptions should be validated before accepting the findings. These assumptions are;

  • Population used for sampling purpose had normal distribution of variable.
  • Dependent variable has same variance and normally distributed.
  • Errors are independent.

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