Hypothesis Testing got Simple ... ANOVA Part 2

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Two way ANOVA test


Suppose we have two factors ( 2 categorical variable), we can test them together along with their interaction.

Let us understand it by the same example ( One way ANOVA). In the data, there are three variables :

1.  Sales value of  XYZ category
2.  Media Spend as  High, Medium and Low ( based on how many $ were spent on promotion)
3.  Festive Season Flag ( Yes or No)

Now suppose, we have a hypothesis that Sales is independent of media spend and Festivity.

So the null hypothesis is equality of means:

H0 :    Mean sales is same across categories
H1 :    Mean sales of at least one category is significantly different

Let's perform the test in SAS.

Proc anova data = a.sales;
Class Media_Spend Festive_season  ;
Model Sales = Media_Spend Festive_season  Media_Spend * Festive_season  ;
Run;
Quit;



As the p value is < 0.01in case of Media Spend, Festive_Season and their interaction as well, it means:

1.  Mean of Sales across Media Spend brackets is different
2.  Mean of sales in Festive and Non Festive season is different
3.  Considering categories with both Media Spend and Festive Season, Sales is different across the categories. Even their interaction is significant.

Just one thing : When interactions are present, the main effects of the independent variables don't have their usual interpretations.




Coming Next in the series:  Errors in hypothesis testing


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