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Let's asume we have a dataframe with 100 clients, 70 males and 30 females, where 10% of them buys the product and 90% doesn't.

Case 1: 7 males and 3 females buys the product = Same distributions

If you do a counting for males and females who buys the product, you would see a higher bar of males than females (7 vs 3), and much people (e.g. kaggle kernels EDAs) reaches to the conclusion of "more males tends to buy the product than females" when actually it's the distribution of one classification ("Buy") is the same than the distribuion of the dataframe. So, you can't conclude than males tend to buy more than females, because they have the same distribution.

Case 2: 5 males and 5 females buys the product = Different distributions.

Same than case 1, having equal counting bars (5 males vs 5 females) usually people reach to the conclusion of "both genres have the same tendency to buy the product" when actually, if you consider the distribution of the dataframe, more females than males tend to buy the product.

Percentages

If we do a percentage (males who buys / total males; females who buys / total females) we would have:

Case 1:

  • 7/70 = 10% of males buys
  • 3/30 = 10% females buys

Case 2:

  • 5/70 = 7.2% of males buys
  • 5/30 = 16.7% of females buys

As we can see, this calculation considers the difference/equality between the distributions of the dataframe and the distribution of each class (buy/don't buy). If we plot these percentages, we would see 10% for each genre for Case 1, and 7.2% for males and 16.7% for females for Case 2, where we could reach the next conclusions:

  • Case 1: Males and females have the same tendency to buy the product
  • Case 2: More females than males tends to buy the product.

However, I'm looking to reach a step forward:

  • How more likely are females to buy the product than males for Case 2?
  • How could I plot this insights for non-technical people in order to not have to explain the differences between the distributions? How would you do that computation and how would you show/present it in a straightforward manner?
  • And any idea why the absolute counting method is very used given that it doesn't show the difference between the distributions?
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    $\begingroup$ If your goal is simply to determine how more likely females are to buy a product than males, why not simply perform a logistic regression analysis? I think it's rare among people who understand data to use absolutely counting methods in the situation I think you are describing, if I understand you correctly, but your question is a bit unclear and difficult to understand. $\endgroup$ – StatsStudent Aug 22 '20 at 7:39
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It's generally always a good idea to use rates or proportions (or percentages) to describe data when there are different numbers of populations in your data as you describe. To answer your questions:

  1. How more likely are females to buy the product than males for Case 2?
    Using your method, you could simply divide the proportion of females who bought the product by the proportion of males who bought the product to determine how much more likely they are to buy the product. In this case: $0.167/0.072\approx 2.319$. So females are about 2.3 times more likely to purchase the product than males in this population. Worded another way, females are about 131.9% more likely than males to buy the product than males.

  2. How could I plot this [sic] insights for non-technical people in order to not have to explain the differences between the distributions? How would you do that computation and how would you show/present it in a straightforward manner?
    This is straight forward. You simply graph the percentages, instead of the absolute numbers. For example, a simple graphic can be created in R by the following code (graph output follows). This is certainly simple enough for nearly anyone to understand:

#Create Example Variables
gender<-c(rep("Males", 70), rep("Females", 30))
buys<-c(rep("Buy", 5), rep("Doesn't Buy", 65), rep("Buy", 5), rep("Doesn't Buy", 25))

#Create Example Dataset
buyingdata<-data.frame(gender, buys)

#Compute Percentage of Purchases by Gender
percentages<-table(buyingdata)/rowSums(table(buyingdata))*100
percentages.buy<-percentages[,1]

#Graph the Results
barplot(percentages.buy, ylim=c(0,20), xlab="Gender", ylab="Percent", main="Perctage of Purchases by Gender")

enter image description here

  1. And any idea why the absolute counting method is very used [sic] given that it doesn't show the difference between the distributions?
    It's not. Anyone with a basic understanding of data should understand that it's important to describe the data using rates/proportions instead of absolute values when encountering populations of different sizes. This is why for example you see statistics like murder rates when comparing the amount of murder across cities instead of the total number of murders, because larger cities would be expected to have a greater number of murders simply because they have more people. Taking another example from the recent news, there have been media reports of increasing absolute number of people testing positive for COVID-19, but a criticism that usually follows is that this is because more testing for the illness is being performed. Of course, when more testing is performed, there will be more positive cases (because you're looking harder for instances of COVID-19). To gain a better sense of whether relatively more people have COVID-19 now versus some time period in the past, it's always better to compare the number of positive cases divided by the total number of tests. This adjusts the number of positive cases for the amount of testing done, providing a more accurate comparison.
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