hypothesis test

(noun)

A test that defines a procedure that controls the probability of incorrectly deciding that a default position (null hypothesis) is incorrect based on how likely it would be for a set of observations to occur if the null hypothesis were true.

Related Terms

Examples of hypothesis test in the following topics:

  • Student Learning Outcomes

    • Conduct and interpret hypothesis tests for two population means, population standard deviations known.
    • Conduct and interpret hypothesis tests for two population means, population standard deviations unknown.

  • Student Learning Outcomes

  • Student Learning Outcomes

    • Conduct and interpret hypothesis tests for a single population mean, population standard deviation known.
    • Conduct and interpret hypothesis tests for a single population mean, population standard deviation unknown.

  • Introduction

    • This process is called "hypothesis testing. " A hypothesis test involves collecting data from a sample and evaluating the data.
    • In this chapter, you will conduct hypothesis tests on single means and single proportions.
    • Hypothesis testing consists of two contradictory hypotheses or statements, a decision based on the data, and a conclusion.
    • To perform a hypothesis test, a statistician will:
    • NOTE: To do the hypothesis test homework problems for this chapter and later chapters, make copies of the appropriate special solution sheets.

  • Summary of the Hypothesis Test

    • The hypothesis test itself has an established process.
    • Draw a graph, calculate the test statistic, and use the test statistic to calculate the p-value.
    • (A z-score and a t-score are examples of test statistics. )
    • Notice that in performing the hypothesis test, you use α and not β. β is needed to help determine the sample size of the data that is used in calculating the p-value.
    • If the power is low, the null hypothesis might not be rejected when it should be.

  • The Null and the Alternative

    • The alternative hypothesis and the null hypothesis are the two rival hypotheses that are compared by a statistical hypothesis test.
    • In statistical hypothesis testing, the alternative hypothesis and the null hypothesis are the two rival hypotheses which are compared by a statistical hypothesis test.
    • The concept of an alternative hypothesis forms a major component in modern statistical hypothesis testing; however, it was not part of Ronald Fisher's formulation of statistical hypothesis testing.
    • Modern statistical hypothesis testing accommodates this type of test, since the alternative hypothesis can be just the negation of the null hypothesis.
    • A hypothesis test begins by consider the null and alternate hypotheses, each containing an opposing viewpoint.

  • Elements of a Hypothesis Test

    • A statistical hypothesis test is a method of making decisions using data from a scientific study.
    • A statistical hypothesis test is a method of making decisions using data from a scientific study.
    • Statistical hypothesis testing is a key technique of frequentist inference.
    • The typical line of reasoning in a hypothesis test is as follows:
    • Derive the distribution of the test statistic under the null hypothesis from the assumptions.

  • Steps in Hypothesis Testing

    • Be able to state the null hypothesis for both one-tailed and two-tailed tests
    • The first step is to specify the null hypothesis.
    • For a two-tailed test, the null hypothesis is typically that a parameter equals zero although there are exceptions.
    • For a one-tailed test, the null hypothesis is either that a parameter is greater than or equal to zero or that a parameter is less than or equal to zero.
    • Failure to reject the null hypothesis does not constitute support for the null hypothesis.

  • Does the Difference Prove the Point?

    • In statistical hypothesis testing, tests are used in determining what outcomes of a study would lead to a rejection of the null hypothesis for a pre-specified level of significance; this can help to decide whether results contain enough information to cast doubt on conventional wisdom, given that conventional wisdom has been used to establish the null hypothesis.
    • The critical region of a hypothesis test is the set of all outcomes which cause the null hypothesis to be rejected in favor of the alternative hypothesis.
    • Unless a test with particularly high power is used, the idea of "accepting" the null hypothesis may be dangerous.
    • Alternatively, if the testing procedure forces us to reject the null hypothesis ($H_0$), we can accept the alternative hypothesis ($H_1$) and we conclude that the research hypothesis is supported by the data.
    • Hypothesis testing emphasizes the rejection which is based on a probability rather than the acceptance which requires extra steps of logic.

  • Directional Hypotheses and One-Tailed Tests

    • When putting together a hypothesis test, consideration of directionality is critical.
    • The vast majority of hypothesis tests involve either a point hypothesis, two-tailed hypothesis or one-tailed hypothesis.
    • A one-tailed hypothesis is a hypothesis in which the value of a parameter is specified as being either:
    • An appropriate hypothesis test would look for evidence that $B$ is better than $A$ not for evidence that the outcomes of treatments $A$ and $B$ are different.
    • Formulating the hypothesis as a "better than" comparison is said to give the hypothesis directionality.