Hypothesis testing aims to determine whether a statement about a phenomenon or condition is reasonable.
Hypothesis testing is the process carried out to analyze whether a condition detected in a certain universe is compatible with what is observed in a sample of the statistical population in question. That is, it seeks to demonstrate whether a hypothesis is a reasonable statement and to do so it is based on two fundamental pillars such as probability theory and sample evidence .
Before moving forward, it is important to know the etymological origin of the two main words that give shape to the concept:
- Proof derives from the Latin probus , which can be translated as "good."
- Hypothesis , for its part, emanates from Greek, since it is made up of the sum of two differentiated parts: the prefix hypo- , which is synonymous with "underneath" , and the noun thesis , which is equivalent to "conclusion" .
What is a hypothesis test
A test can be a test, an experiment, an evaluation or a sample: its meaning depends on the context in which it is used. Hypothesis , on the other hand, is a conjecture or presumption that has a certain probability of being true or real.
A hypothesis is generally considered to be untestable true or false. What is done is to support an argument based on evidence that arises from scientific research. The greater the amount of scientific evidence , the greater certainty there will be about the status of a hypothesis. In other words: if twenty or thirty experiments are carried out that confirm that a hypothesis is true, there is a good chance that it is actually true.
A hypothesis test requires working with scientific evidence.
An example
Let's look at an example of a hypothesis test. A man suspects that a die has been manipulated so that, when thrown, it offers values greater than 4 . The person thinks, therefore, every time he rolls the die, it is very likely that he will get a 4 , a 5 , or a 6 .
To perform a hypothesis test, roll the die one hundred times and note the results. At the end of his experiment, he discovers that in 93% of the cases he obtained a result equal to or greater than 4 . There is sufficient evidence, therefore, to affirm that his hypothesis is true .
Hypothesis testing and statistics
Specifically, the procedure that shapes any hypothesis test is undertaken following these fundamental steps: formulation of the null and alternative hypotheses, selection of the significance level, identification of the relevant test statistic, establishment of the decision rule, sample taking and decision based on the results.
When the aforementioned test is carried out within the field of statistics , it must be taken into account that two fundamental results can be given:
- Error I : the null hypothesis turns out to be true and is therefore rejected.
- Error II : the null hypothesis is false and, therefore, it is accepted as a consequence of the test. The probability of this type of error occurring will depend on what the true value of the parameter in question is.