null

(noun)

A non-existent or empty value or set of values.

Related Terms

Examples of null 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.

  • A Geometrical Picture

    • Any vector in the null space of a matrix, must be orthogonal to all the rows (since each component of the matrix dotted into the vector is zero).
    • Therefore all the elements in the null space are orthogonal to all the elements in the row space.
    • In mathematical terminology, the null space and the row space are orthogonal complements of one another.
    • Similarly, vectors in the left null space of a matrix are orthogonal to all the columns of this matrix.
    • This means that the left null space of a matrix is the orthogonal complement of the column $\mathbf{R}^{n}$ .

  • 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.

  • Simulating a difference under the null distribution

    • Suppose the null hypothesis is true.
    • Next we generate many more simulated experiments to build up the null distribution, much like we did in Section 6.5.2 to build a null distribution for a one sample proportion.
    • Caution: Simulation in the two proportion case requires that the null difference is zero
    • The technique described here to simulate a difference from the null distribution relies on an important condition in the null hypothesis: there is no connection between the two variables considered.
    • Simulated results for the CPR study under the null hypothesis.

  • 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.
    • It is important to note the philosophical difference between accepting the null hypothesis and simply failing to reject it.
    • 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.

  • 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.
    • A hypothesis test begins by consider the null and alternate hypotheses, each containing an opposing viewpoint.
    • 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.
    • Differentiate between the null and alternative hypotheses and understand their implications in hypothesis testing.

  • 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.
    • The null hypothesis is:
    • If this null hypothesis is rejected, then there are two alternatives:
    • The two null hypotheses are then

  • Using simulation for goodness of fit tests

    • This distribution will be a very precise null distribution for the test statistic X2 if the probabilities are accurate, and we can find the upper tail of this null distribution, using a cutoff of the observed test statistic, to calculate the p-value.
    • Since the minimum bin count condition was satisfied, the chi-square distribution is an excellent approximation of the null distribution, meaning the results should be very similar.
    • Figure 6.21 shows the simulated null distribution using 100,000 simulated values with an overlaid curve of the chi-square distribution.
    • The distributions are almost identical, and the p-values are essentially indistinguishable: 0.115 for the simulated null distribution and 0.117 for the theoretical null distribution.
    • The precise null distribution for the juror example from Section 6.3 is shown as a histogram of simulated $X^2_{sim}$ statistics, and the theoretical chi-square distribution is also shown.

  • The Null and Alternate Hypotheses

    • The null hypothesis is simply that all the group population means are the same.
    • 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).