Type I error

(noun)

Rejecting the null hypothesis when the null hypothesis is true.

Related Terms

  • data snooping
  • Kruskal-Wallis test
  • significance criterion
  • Hotelling's T-square statistic
  • chi-squared distribution
  • null hypothesis
  • ANOVA
  • F-Test
  • type II error

(noun)

An error occurring when the null hypothesis ($H_0$) is true, but is rejected.

Related Terms

  • data snooping
  • Kruskal-Wallis test
  • significance criterion
  • Hotelling's T-square statistic
  • chi-squared distribution
  • null hypothesis
  • ANOVA
  • F-Test
  • type II error

(noun)

An error occurring when the null hypothesis (H0) is true, but is rejected.

Related Terms

  • data snooping
  • Kruskal-Wallis test
  • significance criterion
  • Hotelling's T-square statistic
  • chi-squared distribution
  • null hypothesis
  • ANOVA
  • F-Test
  • type II error

Examples of Type I error in the following topics:

  • Type I and II Errors

    • This type of error is called a Type I error.
    • The Type I error rate is affected by the α level: the lower the α level, the lower the Type I error rate.
    • It might seem that α is the probability of a Type I error.
    • If the null hypothesis is false, then it is impossible to make a Type I error.
    • Unlike a Type I error, a Type II error is not really an error.
  • Outcomes and the Type I and the Type II Errors

    • The decision is to reject Ho when, in fact, Ho is true (incorrect decision known as a Type I error).
    • α = probability of a Type I error = P(Type I error) = probability of rejecting the null hypothesis when the null hypothesis is true.
    • The following are examples of Type I and Type II errors.
    • Type I error: The emergency crew thinks that the victim is dead when, in fact, the victim is alive.
    • The error with the greater consequence is the Type I error.
  • Type I and Type II Errors

    • The two types of error are distinguished as type I error and type II error.
    • What we actually call type I or type II error depends directly on the null hypothesis, and negation of the null hypothesis causes type I and type II errors to switch roles.
    • An example of acceptable type I error is discussed below.
    • This is an example of type I error that is acceptable.
    • Distinguish between Type I and Type II error and discuss the consequences of each.
  • References

    • D. (1979) Type I error rate of the chi square test of independence in r x c tables that have small expected frequencies.
  • Summary of Formulas

    • α = probability of a Type I error = P(Type I error) = probability of rejecting the null hypothesis when the null hypothesis is true.
    • β = probability of a Type II error = P(Type II error) = probability of not rejecting the null hypothesis when the null hypothesis is false.
  • Elements of a Designed Study

    • The problem of comparing more than two means results from the increase in Type I error that occurs when statistical tests are used repeatedly.
    • 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 $\alpha$.
    • These methods provide "strong" control against Type I error, in all conditions including a partially correct null hypothesis.
    • These methods have "weak" control of Type I error.
    • Discuss the increasing Type I error that accompanies comparisons of more than two means and the various methods of correcting this error.
  • Student Learning Outcomes

  • Multiple Comparisons of Means

    • ANOVA is useful in the multiple comparisons of means due to its reduction in the Type I error rate.
    • These errors are called false positives, or Type I errors.
    • Doing multiple two-sample $t$-tests would result in an increased chance of committing a Type I error.
    • where $T_i$ is the total of the observations in treatment $i$, $n_i$ is the number of observations in sample $i$ and CM is the correction of the mean:
    • The sum of squares of the error SSE is given by:
  • Sample size and power exercises

    • (a) The standard error of ¯ x when s = 120 and (I) n = 25 or (II) n = 125.
    • (d) The probability of making a Type 2 error when the alternative hypothesis is true and the significance level is (I) 0.05 or (II) 0.10.
    • (b) Decreasing the significance level (α) will increase the probability of making a Type 1 error.
    • (d) If the alternative hypothesis is true, then the probability of making a Type 2 error and the power of a test add up to 1.
    • If the null hypothesis is harder to reject (lower α), then we are more likely to make a Type 2 error.
  • Decision errors

    • What does a Type 1 Error represent in this context?
    • What does a Type 2 Error represent?
    • How could we reduce the Type 1 Error rate in US courts?
    • How could we reduce the Type 2 Error rate in US courts?
    • A Type 2 Error means the court failed to reject H 0 (i.e. failed to convict the person) when she was in fact guilty (H A true).
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