Tareq Kheirbek, MD ScM FACS
When you design a study to answer a specific question, you are transforming your conceptual question into a statistically-testable hypothesis. This means that you are trying to see if the proposed association between your exposure and outcome is statistically more common than just random chance.
It is important to differentiate between your research “hypothesis”, which is another expression of your research question, and your statistical hypotheses, which are the null and alternative hypothesis. You will commonly clearly express your hypothesis in your manuscript, usually at the end of your background section and before your methods section. When doing so, you’ll state your research question (with all elements of PICO) either in the form of “we hypothesized that …” or “We aimed to evaluate whether…” or “Our objective was to …“, etc. This is difference than your statistical hypothesis, which you will NOT state in your manuscript. It is merely to create a framework for your statistical approach.
Now, let’s talk about elements of hypothesis testing.
When evaluating a relationship or association, the default that there is none. An association can occur between an exposure and outcome randomly (Null Hypothesis), which means it is not reproducible or reliable to make a clinical conclusion. Your goal is to assess whether there is instead a true relationship or association between the exposure and outcome of interest (Alternative Hypothesis), evaluate the direction of this relationship, and estimate its strength.
Null Hypothesis: There is NO true relationship
Alternative Hypothesis: There IS a true relationship
When you assess the relationship between the exposure and the outcome, you are actually assessing the Null Hypothesis statistically. The goal is to see if you can reject the null, i.e. to disprove that there is no relationship and that what we observe is due to more than just random chance. You do NOT prove your alternative hypothesis, you only propose one. Statistically, we then simply provide evidence that there is an association more than that occurring randomly. It’s important to also note that if your test does not allow you to reject the null, it does not mean that you accept the null, you only fail to reject the null hypothesis. That is because we are still limited by the weaknesses of our data and analysis and it does not mean that the null is absolutely true (we could have a type II error).
| Null is indeed True | Null is indeed False | |
| Reject the Null | Type I error (alpha error) | Correct Decision (power=1-beta) |
| Fail to Reject the Null | Correct Decision | Type II error (beta) |
Since P VALUE is what most people jump to make conclusions based on, I will use this to explain more. (more later on p values and why we should not rely on them as much):
When we test the hypothesis, we are choosing a statistical test of probability of random association. We set a cutoff for that probability (alpha), usually 0.05, but could be more conservative and set it at 0.01. P value is the probability of random observed association between variables, i.e. the probability that the null hypothesis is true. When the p value is less than alpha, then we reject the null hypothesis because we observe an association that is less probably than random.
The test we choose to assess the association depends on the type of data we are dealing with.