Statistical hypotheses

Statistical hypothesis testing is the process by which an analyst or other professional tests a hypothesis based on a distribution parameter.

Hypothesis testing is a statistical technique used to make statistical decisions using experimental data. However, the methodology used by the analyst depends on the nature of the data and the reasons for the analysis. Statistical hypothesis testing is used to assess the likelihood of a hypothesis using a sample.

In statistical analysis, we must make decisions about a hypothesis, which include deciding whether to accept or reject the null hypothesis. Each hypothesis test gives a significance value for a particular test.

The null hypothesis is usually a hypothesis that the data parameters are equal; for example, the null hypothesis might assert that the average return on a complete distribution is zero.

The alternative hypothesis is actually the opposite of the null hypothesis; for example, the average return by distribution is not zero.

Thus, they are unique, and there can only be one true. When testing hypotheses, if the significance criterion value exceeds the given significance level, we accept the null hypothesis. If the significance value is less than the specified value, then we must reject the null hypothesis.

For example, if we want to see the degree of relationship between two price distributions and the significance of the correlation coefficient is greater than a given significance level, then we can accept the null hypothesis and conclude that there was no relationship between the two distributions.

Consider the steps of statistical hypothesis testing:

  1. Formulation of the null hypothesis

The null hypothesis is generally considered the opposite of an assumption. Why not just test a working hypothesis directly? It’s about Popper’s falsification principle. Karl Popper discovered that we cannot conclusively confirm the hypothesis, but we can definitively refute it.

  1. Formulation of an alternative hypothesis

This is the only statement that logically denies the null hypothesis. H1– there is a connection between the signs.

  1. Setting the probabilistic error a
  2. Data collection

Determine whether data is collected through experimental planning or observation.

  1. Calculation of the test value F
  2. Construction of the area of ​​acceptance or rejection of the hypothesis

Based on the F values ​​of the critical and F test.

Graph 1. Probability distribution

Where in the field inside the the a hypothesis is rejected.

7. Conclusion about H0

In the next article, we will select data, criteria, and demonstrate in practice testing statistical hypotheses using Python and CaseWare IDEA.