# Statistical hypothesis testing

AP stat formulas What is Hypothesis Testing? A statistical hypothesis is an assumption about a population parameter. This assumption may or may not be true. Early use[ edit ] While hypothesis testing was popularized early in the 20th century, early forms were used in the s.

Modern origins and early controversy[ edit ] Modern significance testing is largely the product of Karl Pearson p-valuePearson's chi-squared testWilliam Sealy Gosset Student's t-distributionand Ronald Fisher " null hypothesis ", analysis of variance" significance test "while hypothesis testing was developed by Jerzy Neyman and Egon Pearson son of Karl.

Ronald Fisher began his life in statistics as a Bayesian Statistical hypothesis testingbut Fisher soon grew disenchanted with the subjectivity involved namely use of the principle of indifference when determining prior probabilitiesand sought to provide a more "objective" approach to inductive inference.

Neyman who teamed with the younger Pearson emphasized mathematical rigor and methods to obtain more results from many samples and a wider range of distributions.

Fisher popularized the "significance test". He required a null-hypothesis corresponding to a population frequency distribution and a sample.

His now familiar calculations determined whether to reject the null-hypothesis or not. Significance testing did not utilize an alternative hypothesis so there was no concept of a Type II error.

The p-value was devised as an informal, but objective, index meant to help a researcher determine based on other knowledge whether to modify future experiments or strengthen one's faith in the null hypothesis.

They initially considered two simple hypotheses both with frequency distributions. They calculated two probabilities and typically selected the hypothesis associated with the higher probability the hypothesis more likely to have generated the sample.

Their method always selected a hypothesis. It also allowed the calculation of both types of error probabilities. The defining paper  was abstract.

Mathematicians have generalized and refined the theory for decades. Neyman accepted a position in the western hemisphere, breaking his partnership with Pearson and separating disputants who had occupied the same building by much of the planetary diameter.

World War II provided an intermission in the debate. The dispute between Fisher and Neyman terminated unresolved after 27 years with Fisher's death in Neyman wrote a well-regarded eulogy. Great conceptual differences and many caveats in addition to those mentioned above were ignored.

Neyman and Pearson provided the stronger terminology, the more rigorous mathematics and the more consistent philosophy, but the subject taught today in introductory statistics has more similarities with Fisher's method than theirs.

Sometime around in an apparent effort to provide researchers with a "non-controversial"  way to have their cake and eat it toothe authors of statistical text books began anonymously combining these two strategies by using the p-value in place of the test statistic or data to test against the Neyman—Pearson "significance level".

It then became customary for the null hypothesis, which was originally some realistic research hypothesis, to be used almost solely as a strawman "nil" hypothesis one where a treatment has no effect, regardless of the context. Set up a statistical null hypothesis.

The null need not be a nil hypothesis i.

## Statistical Hypotheses

These define a rejection region for each hypothesis. Report the exact level of significance e. If the result is "not significant", draw no conclusions and make no decisions, but suspend judgement until further data is available. If the data falls into the rejection region of H1, accept H2; otherwise accept H1. Note that accepting a hypothesis does not mean that you believe in it, but only that you act as if it were true. Use this procedure only if little is known about the problem at hand, and only to draw provisional conclusions in the context of an attempt to understand the experimental situation.

## Hypothesis Tests

The usefulness of the procedure is limited among others to situations where you have a disjunction of hypotheses e. Early choices of null hypothesis[ edit ] Paul Meehl has argued that the epistemological importance of the choice of null hypothesis has gone largely unacknowledged. When the null hypothesis is predicted by theory, a more precise experiment will be a more severe test of the underlying theory.The good news is that, whenever possible, we will take advantage of the test statistics and P-values reported in statistical software, such as Minitab, to conduct our hypothesis tests in this course.

«Previous S Hypothesis Testing (Critical Value Approach).

## Hypothesis testing and p-values (video) | Khan Academy

Statistical hypothesis testing is a key technique of both frequentist inference and Bayesian inference, although the two types of inference have notable differences. Statistical hypothesis tests define a procedure that controls (fixes) the probability of incorrectly deciding that a default position (null hypothesis) is incorrect. Hypothesis testing in statistics is a way for you to test the results of a survey or experiment to see if you have meaningful results. You’re basically testing whether your results are valid by figuring out the odds that your results have happened by chance. Accepting a Hypothesis The other thing with statistical hypothesis testing is that there can only be an experiment performed that doubts the validity of the null hypothesis, but there can be no experiment that can somehow demonstrate that the null hypothesis is actually valid.

This because of the falsifiability-principle in the scientific method. Mathematics and statistics are not for spectators. To truly understand what is going on, we should read through and work through several examples. If we know about the ideas behind hypothesis testing and see an overview of the method, then the next step is to see an example.

The following shows a worked out example of a hypothesis test. The P-value, , tells us it is "unlikely" that we would observe such an extreme test statistic t* in the direction of H A if the null hypothesis were true.

Therefore, our initial assumption that the null hypothesis is true must be incorrect.

Statistical Hypothesis Testing - Statistics and Scientific Research