Null and Alternative Hypothesis is used extensively in Machine Learning. Before we answer what is null and alternative hypothesis, let us understand what is Hypothesis Testing.
Hypothesis Testing is used to assess if the difference between samples taken from population are representative of actual difference between populations themselves.
Now why do we even conduct hypothesis testing? Suppose we are comparing the efficacy between two different exercises on 10 patients who underwent the same kind and complexity of knee replacement surgery. This should not be too difficult to do with real data. E.g. 5 patients are asked to do exercise1 and other 5 are asked to do exercise 2, 15 mins a day for 1 month after surgery. After a month, they are tested for the angle at which they can bend their knee. This comparison between patients is not difficult to make.
Now let us imagine if the same comparison is between two groups of patients from two different hospitals. The comparison quickly becomes unwieldy and introduces multiple random events which can easily affect the data. E.g. some patients do exercise after a shower, or after food, or some patients were on different medication which affected their musculoskeletal system etc. Now imagine if the comparison is not across these two groups, but across the population of the whole state of California. Here it is extremely difficult, if not impossible, to compare every single patient in the state of California. Lets park this thought for a second.
Now what is Null Hypothesis (H0):
Null hypothesis H0 is also described as “no difference” hypothesis. i.e. There is no difference between sample sets from different populations. Here we mostly see an equality relationship.
So for the example above about sample of patients from state of California, we start by assuming that null hypothesis H0 is true. i.e. all the samples from different population set are same and that there is no difference between them. We then calculate the probability of such an event (occurrence of null-hypothesis) using the a number between 0 and 1 called as p-value. Generally a value less than 0.05 is considered low probability and therefore we say that chance of having null-hypothesis is very less. Thus we reject null-hypothesis in that scenario. For a p-value greater than 0.05 we fail to reject null-hypothesis (Basically a roundabout way of saying that null-hypothesis is true). For p<0.05, when null-hypothesis is rejected, an alternative hypothesis must be adopted in its place.
What is Alternative Hypothesis (Ha) :
Alternative hypothesis is a scenario in which if you have a new claim against the default hypothesis using current data and therefore it is sort of a new news and requires data to back up this claim. You basically say that you disagree with the data at hand and that there is something new happening. The alternative hypothesis does not have a statement of equality and also uses data from pre-established success rate given in the problem statement.
In the above example of efficacy of exercise comparison for patients, a p-value < 0.05 will reject null-hypothesis and thus an alternative hypothesis takes place. From hereon, we get an opportunity to dig more deeper into the available data and see how the sample sets are different ( Remember, if null-hypothesis was true then we would have concluded that sample data are all the same and that both exercises help patients equally. Only after p-value being less than 0.05 we rejected null-hypothesis ) . We can use various statistical calculations e.g. mean angle of knee bent amongst people of exercise1 set vs mean angle of knee bent amongst people of exercise2 set. This may help us determine which exercise turned out to be better.
Why do we use null-hypothesis?
Null-hypothesis seems to be an extremely simple way to start. And that is exactly what we want in statistical inference. A starting point. Null hypothesis provides an easy starting point. It is easy to describe our expectation from data when null hypothesis exist. An then by using p-value we land on to alternative hypothesis, if it is available or inferred using the data. Null and alternative hypothesis are mutually exclusive.
Bibliography:
- Walker J. (2019). Hypothesis tests. BJA education, 19(7), 227–231.
https://doi.org/10.1016/j.bjae.2019.03.006 - Khan S., “Simple Hypothesis Testing” (video). Khan Academy. Accessed December 11, 2023. http://www.khanacademy.org/math/statistics-probability/significance-tests-one-sample/idea-of-significance-tests/v/simple-hypothesis-testing
- Starmer J., “Hypothesis Testing and The Null Hypothesis, Clearly Explained!!!” (video). StatQuest. Accessed December 11, 2023. https://youtu.be/0oc49DyA3hU?si=o5IO4WcSVGUy7E6g