What Are Confidence Intervals? Can They Be Made Simple
Confidence intervals are where the reasonable estimate of the size of the effect lies. Can you figure this out? Let ThinkWell help!
Most of us would like to be better at maths and when someone flashes big numbers with confidence it is sometimes easier to admire them and assume they are right without really looking at the numbers. Confidence Intervals help us see past this but first we need to understand what they are. This kind of assumption leads to health research error because people with conflicts of interest pass on wrong information and others just assume it is true.
For instance I just read a paper where an author tried to make out hurt people were faking their injuries because the “test” they use has very good specificity of 50%! Well lots of people would not know this is not good at all provides less information than tossing a coin. I was curious and wanted to know if the authors made a simple mistake or did this on purpose to slant the numbers in their favor. I found out that the same authors had done this on other papers and they were working for insurance companies that did not want to pay damages to injured beneficiaries. To find the true story we need to have confidence in the work that produced the numbers. For this to actually happen we need concrete ways to understand the numbers. Here you will find teaching videos and written explanations and links because we all learn different ways.
Who is the better student? You or your friend?
You and your friend attempt five class tests and in one of those tests you both fail. Your risk of failure is 1/5 (=0.2). Lets assume that your friend had attempted another five tests before you, your friend’s risk of failure, similarly is only 1/10 (= 0.1).
The ratio of the risk (Risk ratio, also known as relative risk) gives us an idea to how much worse you are in relation to your friend (0.2/0.1 = 2). More accurately, it gives the probability of failure given the existing data. This allows us to predict how you might fare in the future. In this case RR=2, which means that you are twice more likely to fail in comparison to your friend.
You look worse! but both of you failed only in one test. (…read more about Absolute risks)
However the tests that you attended might not have accurately measured your knowledge. You might have failed or passed the tests by chance because the questions given to you were either easy or difficult for you by luck/bad luck. Hence, if you took more tests, even without studying more, you might end up with a different risk. So, in reality, you might not exactly be 2 times worse than your friend, you might actually be better or even worse than 2. Hence to be more confident in your relative abilities we need to have a range of possible relative risks.
We can calculate the statistical dispersion of the possible results, or confidence Intervals from the available data. 100% of the possible results would include all possible values, and would not help us. But we can assume that most or 95% of possible values will lie somewhere close to the calculated relative risk of 2. So, we calculate the 95% Confidence intervals. For example the value ‘2’ calculated from the above example has a 95% CI of 0.15 to 25.76 (try it here). This means that you might be actually fail less than your friend by 0.15 times or fail more by 25.76 times. As you can see this is quite a wide range, and this shows that we cannot really conclude that you are worse than your friend even though your risk of failure is two. There is a possibility that you may outshine your friend (RR = 0.15 to 0.99). In other words your risk of failure might become smaller than your friends rate in the next series or next-to-next series of tests, you may be the same as him (RR=1) or you may do worse (RR = 1.1 to 25.76).
In other words the given RR of ‘2’ from the data from a total of 15 tests, is not very dependable to judge which one of you is necessarily a better student. This would have been possible if we had sufficient number (‘n’) of tests so that the 95% CI is narrow enough and does not touch/cross an RR of 1 (the point of no difference). e.g RR = 2 (95% CI 1.1 to 4.7).
Okay this is all good for class tests!! But how does one make an interpretation when it comes to a treatment outcome??
– Well.. try it out for yourself, by plugging in your own numbers, risks and calculating confidence intervals. Try using the calculator here.
Need more information? Check out this short video too
Give us your examples and your interpretation in the comments below.
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