Statistics can seem daunting but they cannot be avoided in medical research. If we don’t understand statistical concepts, like ratio data, we are at the mercy of the author’s conclusions. While there are guidelines and peer review processes that help to maintain the integrity of how studies are conducted or reported, there are gaps.
Perhaps you’ve heard of John Carlisle whose skill in statistical analysis has led to the retraction and correction of hundreds of publications including randomized controlled trials and studies published in the New England Journal of Medicine. The concerns raised were both from mistakes but some were also because of misconduct. You can read more about the work of John Carlisle here. It will undoubtedly impart the importance of having a working knowledge of statistics.
The goal here is not to become a statistician. At the most basic level we should be able to look at the main outcomes of the study and determine if the numbers support the conclusions of the author. Let’s start with understanding ratios.
Statistical Tests
Statistical tests are tools that we use to analyze data and make predictions. They are mathematical formulas that are based on validated assumptions. One of those assumptions is the type of data that is being studied. Statistical tests are like mathematical recipes. The recipe was created to use specific ingredients. If you deviate from that you will not get the mathematical “cake” intended by the test.
One of those mathematical ingredients needed for statistical tests is the type of data.
It is important to understand the difference between the type of data and calculations that use a specific type of data. Some of the terminology is very similar. Taking the time to tease out those small differences will make it easier to actually understand statistical concepts.
Ratio Data vs Ratio Calculations
The term ratio descriptive. It tells you the characteristics of the type of data that was used for the calculation or to obtain a result.
Often, you will hear, “there are 2 kinds of ratio: risk ratio and odds ratio”.
In reality, there is only one type of data set that can be referred to as ratio but there are multiple ratio calculations (risk ratio or odds ratio) that can be derived from ratio data.
It is a small but simple distinction that can resolve a lot of confusion when trying to understand statistics.
Ratio is a type of data. Odds ratio and risk ratio are ratio calculations.
Odds ratio and risk ratio are calculations of probability using ratio data points.
Properties of Ratio Data
When the term ratio is used this automatically implies 4 properties of the data.
Ratios can only be used to describe data that is quantitative, continuous, equidistant order with a true zero.
This is a mouthful but each those components are important. Once we break down what each means, it will be easy to remember.
Knowing whether the data used to calculate the probability of risk is ratio (i.e. quantitative, continuous, equidistant order with a true zero) is the very first step is knowing that the correct calculation was done. It is how we know that the right ingredients were used for a particular statistical test.
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Quantitative Data
Quantitative simply means that the variable has a value or number that can be measured. It is not descriptive like white or black, yes or no. Is it quantitative data? Ask yourself: Can I measure this variable and assign it a numerical value? Ratio data, used in ratio calculations must be quantitative.
Continuous Data
Continuous data means that it can take any value within a range. You could not predict what the value could be because there are an infinite number of options. For example, if I ask you to pick a number from 1-5 that number can be: 1, 4, 1.25, 3.6, 1.678, 0.004, 2.99984.
Considering the opposite of continuous data will help make it clear.
Discrete data is the opposite of continuous data. Discrete data is a finite or countable number of options. For example, if I asked you to choose 1 of 5 people, then that would be discrete because it can only be a whole person, there is no in between, no half person.
In both cases you’re choosing from 1-5 but what you are choosing is what makes it continuous versus discrete. How can you remember what is continuous versus discrete data? Ask yourself: Can I break the variable into smaller units?
Can I breakdown number of people/patients into smaller units? No! Therefore number of people/patients is discrete data.
Can I break down length of time (time to an event like occurrence of a heart attack) down into smaller units? Yes! Did it occur after 2 years or 2 months (i.e. 0.67 years)? If the variable can be a expressed as a decimal or fraction it is continuous data. Ratio data, used in ratio calculations must be continuous.
Equidistance
Equidistant order means that there is a established hierarchy of the data points AND there is an equal distance/measurement as you move along the hierarchy.
Let’s use the same example of 1-5. We all agree that after 1 comes 2, then 3, then 4, then 5. As we move from one to the other the difference is consistently 1. This the basis of measurement tools like rulers.
Let’s consider college degrees as a data point. There is a clear, established hierarchy there. Associate degree, to bachelor’s, to master’s degree, to doctoral degree.
What is the numerical value that can be measured between those degrees? There is none! They are ordered but not equidistant and therefore cannot be ratio data or be used in ratio calculations.
True Zero
If at point 0 of your data, nothing exists then your data set has a true zero. True zero means we can get to a point where nothing would exist i.e. a point of nothing. There are no negative values because there nothing less than zero with ratio data.
Why is it called true zero instead of just zero? Because in some cases, specifically temperature in Celsius, zero degrees does not create a point of nothing. In fact zero Celsius will create something… ice! There must be a complete absence at point zero for it to be considered true zero.
This includes data points like number of patients or objects. We can get down to zero patients but not a negative number of patients.
Weight: at 0 kg, nothing exists. Change is weight can also be zero. Height: at 0 inches, there is nothing. Time: at 0 seconds, no time has past.
For whatever variable (X) you are considering ask yourself: if I have zero of X, do I have nothing? If yes, then your data has a true zero. True zero must exist for your data to be considered ratio and used in ratio calculations.
If you are presented with results of a study that utilizes ratio calculations like risk ratio and odds ratio, you can verify that the correct mathematical ingredient (ratio data) has been used. Look at the variable that was used in those calculations and ask yourself: is it quantitative, continuous, equidistant AND has a true zero?
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The information on this website is intended to be used solely for educational and informational purposes. While the content may be about specific medical and health care issues, it is not a substitute for or replacement of personalized medical advice and is not intended to be used as the sole basis for making individualized medical or health-related decisions.
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