If you go through scientific publications, you freely realize that descriptive statistics for categorical variables are presented as frequency and proportion but in two different ways.
A) 50(30%)
B) 30%(50)
Which one would you recommend and why?
If you have to use just either frequency or proportion/percentage you give priority to which one?
It's always better to mention the frequency first and then the percentage. This is because the frequency is the actual number, which is what most readers are interested in knowing. In my publications, I have adopted this manner of presentation.
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Both articles have been published in reputed scopus as well as web of science indexed journals.
Let us consider a cohort of 40 male researchers and a cohort of 60 female researchers to whom the following question is asked:
Do you fear statistics?
Following data collection, entry and exploration, FASTDAM obtained the following statistics: 20 male researchers as against 30 female researchers fear statistics.
FASTDAM then took the opportunity in the statistical classroom and asks the students.
Do male and female researchers have equal interest in statistics considering the above findings while clearly indicating that 40 males were sampled as against 60 females making up the total population of 100 researchers in the targeted research center.
Out of the 10 students at FASTDAM, 7 said female researchers fear statistics more than their male colleagues, two refused to answer and one said they have equal interest in statistics.
In fact, if we go by frequency, we have 30 female researchers that fear statistics as against 20 male thus clearly indicating that the female fear statistics more than the male.
If we go by percentage/proportion, we have (20/40)*100 males making un 50% and (30/60)*100 females making up 50%. Based on percentage, we can resolve that male and female researchers have equal interest in statistics thus accepting the hypothesis 'Male and female researchers have equal interest in statistics'.
By weighting the frequencies on equal scale of 100, we make them conservative thus compensating for sampling bias.
Percentage/proportion as we can all realize gives the true statistical map of this context as 20 males against 40 makes half of the males and 30 females against 60 makes half of the females, thus males and females are 50 and 50% thus indicating equal interest.
If we go by differentiation or matrically, we freely arrive at the same conclusion: 30/20 gives us 1.5 indicating a deviation while 50/50 gives 1 indicating no deviation thus reflecting the true picture of the context because percentages are conservative unlike the frequencies.
So if we have to prioritize, percentage/proportion shall be.
Frequency now tends to mislead in the interpretation.
Given the fact that people naturally tend to give priority to the first thing, in this presentation 30(50%), the tendency is to value 30 because what is in brackets is always considered secondary or explanatory.
Moreover in applied statistics, priority is generally given to conservative figures.
Reason why the presentation 50%(20) male researchers fear statistics as against 50%(30) for the females is recommended by applied statisticians.
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