hypothesis

NULL HYPOTHESIS (H0) the hypothesis that there are no differences between the groups that have been studied.

If we have two groups: placebo vs new diabetes medicinal.

The null hypothesis would say that for example, both groups have the same blood complications.

[THERE IS NO DIFFERENCE if you take a placebo or a medicinal]

By default H0 is set to True, until we have enough evidence to reject this hypothesis.

ALTERNATIVE HYPOTHESIS (Ha or H1) is the opposite. There is a difference between the studied groups, meaning that there's a relation.

[THERE IS A DIFFERENCE if you take a placebo or a medicinal]

This can only reject an hypothesis (say it's false) but cannot say that it's 100% true. Anytime you reject an hypothesis there's a chance that you make a mistake:

  • TYPE 1 ERROR (a - alpha) (when incorrectly reject null hypothesis) when researchers say THERE ARE differences between groups, BUT THERE ARE NOT.
  • TYPE 2 ERROR (b - beta) (when you fail to reject null hypothesis when you should have rejected it) researchers say THERE ARE NO differences between groups, BUT THERE ARE.

POWER probability of finding a difference between groups if one truly exists.

power = 1 - beta

This is the percentage chance that you will be able to reject the null hypothesis if it is really false.

This can be tought as the probability of making NOT a type 2 error.

P-VALUE (IF H0==true): the probability of obtaining a result at least as extreme as the current one (it inidicates the level of agreement/disagreement between data & null hypothesis).

Imagine a study comparing a placebo group to a treatment group that received a new blood pressure medication and the mean blood pressure in the treatment group was 20mm/Hg lower than the placebo group.

ASSUMING the null hypothesis is correct (i.e.: there's no difference between placebo or medication), (because we need to start from somewhere, then we will dimonstrate if it really is true or false):

the p-value is how probable is that if we repeated the study, the obeserved difference between the group averages would be at least 20mm/Hg.

P value is a statistical measure that helps scientists determine whether or not their hypotheses are correct.

P values are used to determine whether the results of their experiment are within the normal range of values for the events being observed.

Usually, if the P value of a dataset is below a certain pre-determined amount, scientists will reject the "null hypothesis" of their experiment.

In other words, it's not true that there are no differences between the groups' results.

To determine if a p-value is low or high, we use alpha.

ALPHA (a.k.a. Significance Level) is the probability of making a Type 1 Error.

Usually 1%(0.01), 5%(0.05), 10%(0.10), are used as default values.

p > a (difference between groups is not statistically significant)
p < a (difference between groups is statistically significant)

Using a 5% alpha implies that:

5% probability of incorrectly rejecting the null hypothesis is acceptable.


Today, p-values are usually found on a reference table by first calculating a chi square value.

If I have NO difference between the results of blood pressure (placebo vs medicament), it means that a person taking placebo or medicament is the same.

If I repeat the experiment on the same person I get at least the same blood pressure results. Let's suppose always, p = 100%.

I set my significance level to 10%. And I conclude that: p > a.
Taking placebo vs medicament is not statistically significant: they are not changing the blood pressure (results) in a significant way.

If you take a placebo or a medicament is the same.
If I have A difference between the results of blood pressure (placebo vs medicament) on a person, it means that taking placebo or medicaments makes a difference.

If I repeat the experiment (make people take placebo and medicaments) I get different blood pressure results. Let's suppose p = 5%.

We keep our Significance Level to 10%. We can conclude: p < a.

Taking a placebo or a medicament makes a difference, it is statistically significant: the blood pressure changes.
machine learning hypothesis alternative hypothesis