Percentages
Do you often struggle with statistics?
In this Chalk Talk series, we’ll be providing you with the basics of statistics over several
episodes.
This will not only help you understand the various types of epidemiological studies but
also enables you to interpret data correctly.
Some of the questions that we’ll be addressing include:
How are risk scores calculated?
What’s the relationship between the attributable risk and the number needed to harm?
We’ll also clarify the following question, which often creates confusion:
What’s the difference between relative risk and odds ratio?
In this first episode, we’d like to start by providing you with an overview of fractions
and proportions.
Let’s take a look at the following three examples:
The first example is the relative frequency.
Let’s imagine that we have a study with 100 participants.
Of these, 60 are female.
The proportion of female study participants is 60 out of 100, or 60 percent.
This is an example of relative frequency.
Let’s look at an example of another fictional study posing the following question:
What’s the probability of a smoker developing lung cancer?
Let’s assume that the study included 100 smokers and of these, 20 developed lung cancer.
In other words, a proportion of 20 out of 100 smokers or 20 percent of study participants
developed lung cancer.
This would lead us to conclude that the risk of developing lung cancer in smokers is 20%.
So, as you can also see in this example, the proportion is represented as a percentage.
However, in this context, the percentage is called risk.
Now, on to the third example.
A study was performed evaluating a diagnostic test for pulmonary embolism.
One hundred patients with pulmonary embolism were recruited.
The proportion of patients correctly identified with pulmonary embolism using the test was
90 of 100 patients.
This value represents the sensitivity of the test; therefore, the diagnostic test sensitivity
would be 90%.
Or, in other terms: The probability of the test detecting pulmonary embolism is 90%.
OK.
So, these three examples represent various ways of how percentages can be used in statistics.
Finally, we’d like to give you a few tips on the terms used.
As you’ve seen, there are different terms that have the same meaning.
Let’s go back to the example of relative frequency: 60 out of 100 study participants
are women.
This information can be written in three different forms.
The first form is as a fraction, or 60 divided by 100.
The second form is obtained by calculating the fraction: 60 divided by 100 is 0.6.
This represents the decimal number.
The third means is by multiplying the decimal number by 100, resulting in a percentage.
0.6 times 100 is 60, thus 60 equals 60%.
Decimal numbers can also be used for the other two examples mentioned earlier in this episode.
Namely, the risk is 0.2 and the sensitivity is 0.9.
As you can see in these three examples, the results can be presented in different forms;
however, they all share the same meaning.
The three examples provided were calculated as simple fractions and expressed as a percentage.
With this information, you’re already well prepared for the next Chalk Talk episode in
this series on statistics, which focuses on risk.
But before we move on, we’ve prepared a quiz for you.
A diagnostic study from 1991 examined the association between prostate specific antigen,
in short PSA, and prostate cancer.
Two hundred and thirty-five patients were analyzed to determine whether measuring PSA
levels represents a potential diagnostic test for screening prostate cancer.
Of the 235 participants, 61 had prostate cancer.
Of these, 48 patients had elevated PSA levels.
Now, we’d like to ask you to calculate the test sensitivity of elevated PSA levels for
detecting prostate cancer.
48 patients with a positive test result / 61 patients with cancer = 48/61 = 0.79 = 79%