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(NOTE: the question and data explained here is not based on a real experiment; it has been randomly generated for the sake of explanation)

Let’s say I wanted to compare 3 different coin types—a US quarter dollar coin (25¢), British one pound coin (1£), and a euro coin (€1)—to see which one, if any, would produce the most ‘random’ outcome in a coin toss. Participants flip each coin 30 times and record the number of times each coin landed on heads vs the times it landed on tails.

While collecting data, I was looking at the results from the US quarter. I could say (again, this is all hypothetical data) that a participant landed on heads 12 times (tails 18 times) OR I could say that they landed on heads 40% of the time (tails 60% of the time). Both technically represent the same value–albeit, in different formats–, and if you were to do data analysis with them, you'll get fairly similar results…...but is there one method that is more preferred or accepted in academia?

Overall, it seems like the percentage format makes more sense for comparison reasons and in case where you don't have an equal number of measurements from each group. However, it seems like the percentage format really only works for when you have two levels of a dependent variables. This would become more confusing if you were looking at a dependent variable with more than two levels; for example, a 6-sided die instead of a 2-sided coin. In the coin example, if 70% of the coin flips were heads, then you know the other 30% had to be tails. However, if you are given the information that 30% of the dice rolls were 5s, you only know that the other 70% are not 5s (they could be 1s, 2s, 3s, 4s, or 6s).

Anyways, this is just a question that has been bothering me for some time and I've always wondered what the best answer to it is. Is it better to use percentages/proportions in some cases and raw number data in others? Is there one that is always preferable over the other? Or does it just vary case by case?

(Also, anyone would like to see the randomly generated data from the coin flip example, let me know and I'll edit this question so that I can include it. I felt that it was just cluttering up this question, so I took it out, but I can always add it back.)

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I could say (again, this is all hypothetical data) that a participant landed on heads 12 times (tails 18 times) OR I could say that they landed on heads 40% of the time (tails 60% of the time). Both technically represent the same value–albeit, in different formats–, and if you were to do data analysis with them, you'll get fairly similar results…..

If you report your results only in percentage format, then 12 heads and 18 tails is the same as 2 heads and 3 tails or 200 heads and 300 tails.

If you were interested in estimating the probability of heads, you would definitely be interested in the number of coin flips that you performed. How much would you trust the probability estimate from 2 heads and 3 tails vs. 200 heads and 300 tails?

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