2 O.J. Simpson trial: the situation O.J. is assumed innocent.Evidence collected
3 O.J. Simpson trial: jury decisions In criminal trial: The evidence does not warrant rejecting the assumption of innocence. Behave as if O.J. is innocent.In civil trial: The evidence does warrant rejecting the assumption of innocence. Behave as if O.J. is guilty.Was an error made in either trial?
4 Errors in TrialsIf O.J. is innocent, then an error was made in the civil trial.If O.J. is guilty, then an error was made in the criminal trial.
6 Definitions: Types of Errors Type I error: The null hypothesis is rejected when it is true.Type II error: The null hypothesis is not rejected when it is false.There is always a chance of making one of these errors. We’ll want to minimize the chance of doing so!
13 Minimize chance of Type I error... … by making significance level small.Common values are = 0.01, 0.05, or 0.10.“How small” depends on seriousness of Type I error.Decision is up to researcher.
14 P(Type I Error) in trials Criminal trials: “Beyond a reasonable doubt”. Jurors must unanimously vote guilty. Significance level set at 0.001, say. Very small chance of Type I error.Civil trials: “Preponderance of evidence.” 9 out of 12 jurors must vote guilty. Significance level set at 0.10, say. Larger chance of a Type I error.
15 Example: Serious Type I Error New Drug A is supposed to reduce blood pressure by more than 15 mm Hg.H0: μ = 15 versus HA: μ > 15Drug A can have serious side effects, so don’t want patients on it unless μ > 15.Implication of Type I error: Expose patients to serious side effects without other benefit.Set = P(Type I error) to be small 0.01
16 Example: Not so serious Type I Error Grade inflation?H0: μ = 2.7 vs. HA: μ > 2.7Type I error: claim average GPA is more than 2.7 when it really isn’t.Implication: Instructors grade harder. Students get unhappy.Set = P(Type I error) at, say, 0.10.
17 Type II ErrorType II Error is made when we fail to reject the null when the alternative is true.When Type I error is made smaller, Type II error is made larger.When Type II error is made smaller, Type I error is made larger.Inverse relationship