# T test statistical hypothesis testing and mean

This analysis is appropriate whenever you want to compare the means of two groups, and especially appropriate as the analysis for the posttest-only two-group randomized experimental design. Idealized distributions for treated and comparison group posttest values. Figure 1 shows the distributions for the treated blue and control green groups in a study. Actually, the figure shows the idealized distribution -- the actual distribution would usually be depicted with a histogram or bar graph. Early use[ edit ] While hypothesis testing was popularized early in the 20th century, early forms were used in the s. Ronald Fisher began his life in statistics as a Bayesian Zabellbut 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. 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.

## S Hypothesis Testing (P-Value Approach) | STAT ONLINE

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. Neyman wrote a well-regarded eulogy. Great conceptual differences and many caveats in addition to those mentioned above were ignored. 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. 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.

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.

We are testing the hypothesis that the population means are equal for the two samples. We assume that the variances for the two samples are equal. For our two-tailed t-test, the critical value is t 1- Two-sample t-tests are available in just about all general purpose statistical software programs. 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). 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 following shows a worked out example of a hypothesis test.

When the null hypothesis is predicted by theory, a more precise experiment will be a more severe test of the underlying theory.

When the null hypothesis defaults to "no difference" or "no effect", a more precise experiment is a less severe test of the theory that motivated performing the experiment.

Pierre Laplace compares the birthrates of boys and girls in multiple European cities. Karl Pearson develops the chi squared test to determine "whether a given form of frequency curve will effectively describe the samples drawn from a given population.

He uses as an example the numbers of five and sixes in the Weldon dice throw data. Karl Pearson develops the concept of " contingency " in order to determine whether outcomes are independent of a given categorical factor. Here the null hypothesis is by default that two things are unrelated e.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.

 Statistics Online 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. Student's t-test - Wikipedia What assumptions are made when conducting a t-test? S Hypothesis Testing Examples | STAT ONLINE The other two sets of hypotheses Sets 2 and 3 are one-tailed testssince an extreme value on only one side of the sampling distribution would cause a researcher to reject the null hypothesis. Formulate an Analysis Plan The analysis plan describes how to use sample data to accept or reject the null hypothesis. Breadcrumb In the t-test comparing the means of two independent samples, the following assumptions should be met: Each of the two populations being compared should follow a normal distribution. S Hypothesis Testing (P-Value Approach) | STAT ONLINE Specifically, the four steps involved in using the P-value approach to conducting any hypothesis test are:

«Previous S Hypothesis Testing (Critical Value Approach). the statistical test (=, , etc.). 6. Determine the critical value. Hypothesis Testing of a Single Mean (Normally Distributed) 42 Known Variance 43 Example: Two-Tailed Test 1.

A simple random sample of 10 people from a certain population has a mean age of Can we conclude that. The t-test is any statistical hypothesis test in which the test statistic follows a Student's t-distribution under the null hypothesis. A t -test is most commonly applied when the test statistic would follow a normal distribution if the value of a scaling term in the test statistic were known.

The t-test does just this. Statistical Analysis of the t-test. The formula for the t-test is a ratio. The top part of the ratio is just the difference between the two means or averages.

The bottom part is a measure of the variability or dispersion of the scores. The t-value will be positive if the first mean is larger than the second and. If the engineer set his significance level α at and used the critical value approach to conduct his hypothesis test, he would reject the null hypothesis if his test statistic t* were greater than (determined using statistical software or a t-table).

What is the meaning of p values and t values in statistical tests? hypothesis-testing t-test p-value interpretation intuition. share | cite | improve this question. The one-sample t-test and the likelihood of a sample mean when the population standard deviation is unknown (replete with stories about the secret identity of a certain.

Hypothesis Test for Mean