hello Sinh

i would like to refer you for this post it might be helpful for you

https://www.abs.gov.au/websitedbs/a3121120.nsf/home/statistical+language+-+describing+frequencies

There are simply so many ways of characterising frequencies that without a knowledge of the purpose of the description, I can offer no insight.

Simple percentages may be point or period prevalences, incidence densities or cumulative incidences, sensitivities or specificities, positive or negative predictive values, accuracy… the list seems endless to me, even as I write.

A statistic is the answer to a question, so unless we know the question, there is no way of recommending a statistic.

I tell my students that a descriptive statistic is like any other description. If I were meeting you at the airport, I would give you a description of what I look like. But if I on a date with someone, this would be silly. I would instead describe my background and interests.

Does that make sense?

Hello, with regards to the specifics of your question, I would like to refer you to a chapter of a book (that is available online, Principles of Epidemiology in Public Health Practice, Third Edition: An Introduction to Applied Epidemiology and Biostatistics) that made it easy for me to understand these concepts when I was in college: https://www.cdc.gov/csels/dsepd/ss1978/lesson3/section1.html.

These are my own understanding of the three concepts you mentioned, ratio, proportion and rate. If you feel that they do not agree well with the contents of the link I shared above, do not mind my explanations below and focus on what the book says:

1. Ratio, in its simplest sense, is one numerical value or parameter relative to another numerical value or parameter. That's it. There is even no need for one of the values/parameters to be related or not to the other. The best example in epidemiology is the sex ratio: the ratio of males to females in a population. In mathematical terms: Sex Ratio = (number of males)/(number of females). For instance, is the sex ratio is 2, it means that the number of males in the population is twice that of the number of females. If the sex ratio is 0.5, it means that the number of males in the population is half of the number of females. In algebraic terms, Ratio = A/B.

2. Proportion, in theory, is a special/unique type of ratio. While the two values/parameters in a ratio need not to be related or not to one another, the two components of a proportion must be related to one another. In particular, the numerator value must be a sensible portion or part of the denominator value. The sex ratio mentioned above is not and cannot be a proportion, because the numerator (number of males) is not a sensible portion or part of the denominator (number of females). There are a lot of examples of proportions in our day-to-day lives, and it cannot be helped if we take some examples for granted. A proper example is the proportion of diabetics in a population. The numerator (number of diabetics) is a sensible portion or part of the denominator (the entire population). In algebraic terms, Proportion = A/(A+B), please compare this with the algebraic equation for Ratio in item #1.

3. Rate, on the other hand, is the expression of relative frequency (possibly either ratio or proportion) with the additional component of a specified period or length of time. Rates give the idea/impression of how fast something occurs, so the element of time on top of the magnitude or frequency is essential. The simplest examples of rate are crude birth rate and crude death rate. Crude birth rate is the number of of live births per 1,000 people in the average of the population per year, while crude death rate is the number of deaths occurring among the average of the population per year. There are nuances to the proper understanding of rates, and perhaps my explanations for the crude birth rate and crude death rate are not entirely correct, but the main point of Rate, compared to Ratio or Proportion, is the union of two concepts in one measure: the magnitude and the time component. By the way, in physics, the simplest example of a rate is perhaps speed - which is the distance (magnitude) covered or moved per unit of time.

I hope this helps. Just ask if you still need clarifications. Stay safe.

In the simplest way:

Absolute frequency = a number

Relative frequency = a percentage, rate, proportion or rate.

Example: you play badminton game 10 times with your opponent and you win 6 of 10 games.

Absolute frequency that you win = 6

Relative frequency that you win = 6/10 or 60%

In most of the epidemiological study, we will present the categorical variable as n (%). For example, let say your study sample include 300 subject where 180 of them are smoker, we will present the frequency of smoker as 180 (60%).

Hope this can help you.

Thanks.