null hypothesis

(noun)

A hypothesis set up to be refuted in order to support an alternative hypothesis; presumed true until statistical evidence in the form of a hypothesis test indicates otherwise.

Related Terms

Examples of null hypothesis in the following topics:

  • Misconceptions

    • State why the probability value is not the probability the null hypothesis is false
    • Explain why a non-significant outcome does not mean the null hypothesis is probably true
    • Misconception: The probability value is the probability that the null hypothesis is false.
    • It is the probability of the data given the null hypothesis.
    • It is not the probability that the null hypothesis is false.

  • Type I and II Errors

    • Explain why the null hypothesis should not be accepted when the effect is not significant
    • Instead, α is the probability of a Type I error given that the null hypothesis is true.
    • If the null hypothesis is false, then it is impossible to make a Type I error.
    • Lack of significance does not support the conclusion that the null hypothesis is true.
    • A Type II error can only occur if the null hypothesis is false.

  • 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.
    • A typical null hypothesis is μ1 - μ2 = 0 which is equivalent to μ1 = μ2.
    • If the probability value is lower then you reject the null hypothesis.
    • Failure to reject the null hypothesis does not constitute support for the null hypothesis.

  • Does the Difference Prove the Point?

    • Rejecting the null hypothesis does not necessarily prove the alternative 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.
    • Rejection of the null hypothesis is a conclusion.
    • Whether rejection of the null hypothesis truly justifies acceptance of the research hypothesis depends on the structure of the hypotheses.

  • Interpreting Significant Results

    • Thus, rejecting the null hypothesis is not an all-or-none proposition.
    • If the null hypothesis is rejected, then the alternative to the null hypothesis (called the alternative hypothesis) is accepted.
    • If this null hypothesis is rejected, then the alternative hypothesis that π > 0.5 is accepted.
    • The null hypothesis is:
    • If this null hypothesis is rejected, then there are two alternatives:

  • Exercises

    • What is the null hypothesis?
    • The probability value is the probability of obtaining a statistic as different (add three words here) from the parameter specified in the null hypothesis as the statistic obtained in the experiment.
    • The probability value is computed assuming that the null hypothesis is true.
    • Assume the null hypothesis is that μ = 50 and that the graph shown below is the sampling distribution of the mean (M).

  • 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.
    • Modern statistical hypothesis testing accommodates this type of test, since the alternative hypothesis can be just the negation of the null hypothesis.
    • Since the null and alternate hypotheses are contradictory, we must examine evidence to decide if there is enough evidence to reject the null hypothesis or not.
    • Sir Ronald Fisher, pictured here, was the first to coin the term null hypothesis.

  • Using the Sample to Test the Null Hypothesis

    • We would reject the null hypothesis if the evidence is strongly against it.
    • The null hypothesis could be Ho: µ ≤15 The alternate hypothesis is Ha: µ > 15
    • The null hypothesis must contradict the alternate hypothesis.
    • Suppose the null hypothesis is true (the mean height of the loaves is no more than 15 cm).
    • The hypothesis test works by asking the question how unlikely the sample mean would be if the null hypothesis were true.

  • Elements of a Hypothesis Test

    • The null hypothesis was that the Lady had no such ability.
    • Statistical hypothesis tests define a procedure that controls (fixes) 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.
    • Derive the distribution of the test statistic under the null hypothesis from the assumptions.
    • Decide to either reject the null hypothesis in favor of the alternative or not reject it.
    • Reject the null hypothesis in favor of the alternative or not reject it.

  • The Null and Alternate Hypotheses

    • The null hypothesis is simply that all the group population means are the same.
    • The alternate hypothesis is that at least one pair of means is different.
    • The graphs help in the understanding of the hypothesis test.
    • In the first graph (red box plots), Ho : µ1 = µ2 = µ3 and the three populations have the same distribution if the null hypothesis is true.
    • If the null hypothesis is false, then the variance of the combined data is larger which is caused by the different means as shown in the second graph (green box plots).