Boole's inequality

(noun)

a probability theory stating that for any finite or countable set of events, the probability that at least one of the events happens is no greater than the sum of the probabilities of the individual events

Related Terms

Examples of Boole's inequality in the following topics:

  • Elements of a Designed Study

    • Boole's inequality implies that if each test is performed to have type I error rate $\frac{\alpha}{n}$, the total error rate will not exceed $\alpha$.

  • Finding a sample size for a certain margin of error

    • The challenge in this case is to find the sample size n so that this margin of error is less than or equal to 4, which we write as an inequality:

  • Specific Comparisons (Independent Groups)

    • Defining α as the per-comparison error rate and c as the number of comparisons, the following inequality always holds true for the familywise error rate (FW):
    • This inequality is called the Bonferroni inequality.
    • The Bonferroni inequality can be used to control the family wise error rate as follows: Id you want the family wise error rate to be alpha, you use alpha/c as the per-comparisson error rate.

  • Goodness of Fit

    • The null and the alternate hypotheses for this test may be written in sentences or may be stated as equations or inequalities.

  • Estimating the Accuracy of an Average

    • Where the probability distribution is unknown, relationships of inequality can be used to calculate a conservative confidence interval.

  • Binomial

    • The words "at least" translate as what kind of inequality for the probability question P ( x____40 ) .

  • Goodness-of-Fit Test

    • The null and the alternate hypotheses for this test may be written in sentences or may be stated as equations or inequalities.

  • Formal testing using p-values

    • We will find it most useful if we always list the null hypothesis as an equality (e.g. µ = 7) while the alternative always uses an inequality (e.g. µ 6= 7, µ > 7, or µ < 7).