References to the Hypothesis testing

 

After our understanding of the inferential statistics and understanding the concept of hypothesis, let us look further in the details of these tests.



We will plot a hypothesis testing roadmap:


We are only going to cover some of the important tests definitions from above.

What Is a One-Tailed Test?

A one-tailed test is a statistical test in which the critical area of a distribution is one-sided so that it is either greater than or less than a certain value, but not both. If the sample being tested falls into the one-sided critical area, the alternative hypothesis will be accepted instead of the null hypothesis.

Example of a One-Tailed Test

Let's say an analyst wants to prove that a portfolio manager outperformed the S&P 500 index in a given year by 16.91%. They may set up the null (H0) and alternative (Ha) hypotheses as:

H0: μ ≤ 16.91

Ha: μ > 16.91

The null hypothesis, is the measurement that the analyst hopes to reject. The alternative hypothesis, is the claim made by the analyst that the portfolio manager performed better than the S&P 500. If the outcome of the one-tailed test results in rejecting the null, the alternative hypothesis will be supported. On the other hand, if the outcome of the test fails to reject the null, the analyst may carry out further analysis and investigation into the portfolio manager’s performance.

What Is a Two-Tailed Test?

In statistics, a two-tailed test is a method in which the critical area of a distribution is two-sided and tests whether a sample is greater than or less than a certain range of values. It is used in null-hypothesis testing and testing for statistical significance. If the sample being tested falls into either of the critical areas, the alternative hypothesis is accepted instead of the null hypothesis.

  • In statistics, a two-tailed test is a method in which the critical area of a distribution is two-sided and tests whether a sample is greater or less than a range of values.
  • It is used in null-hypothesis testing and testing for statistical significance.
  • If the sample being tested falls into either of the critical areas, the alternative hypothesis is accepted instead of the null hypothesis.
  • By convention two-tailed tests are used to determine significance at the 5% level, meaning each side of the distribution is cut at 2.5%.


What Is a Z-Test?

A z-test is a statistical test used to determine whether two population means are different when the variances are known and the sample size is large. The test statistic is assumed to have a normal distribution, and nuisance parameters such as standard deviation should be known in order for an accurate z-test to be performed.

A z-statistic, or z-score, is a number representing how many standard deviations above or below the mean population a score derived from a z-test is.

 

What Is a P-test?

A P-test is a statistical method that tests the validity of the null hypothesis, which states a commonly accepted claim about a population. Though the term null is a bit misleading, the objective is to test accepted fact by attempting to disprove, or nullify, it. The P-test can provide the evidence that can either reject or fail to reject (statistics speak for 'inconclusive') a widely accepted claim.

The result of a P-test is a p-value. The p-value is used as a heuristic of the smallest level of significance at which the null hypothesis would be rejected. A smaller p-value means that there is stronger evidence in favor of the alternative hypothesis and that the null should be rejected.

Reference for the z test and the t test.

https://www.analyticsvidhya.com/blog/2020/06/statistics-analytics-hypothesis-testing-z-test-t-test/

 

The link below gives an in-detailed information about which test to be used and when.

https://towardsdatascience.com/statistical-tests-when-to-use-which-704557554740


In upcoming sessions, we will just look into some codes of these statistical learning. Later will jump into the details of Machine learning and AI.

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