2O.J. Simpson trial: the situation O.J. is assumed innocent.Evidence collected
3O.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?
4Errors 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.
6Definitions: 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!
13Minimize 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.
14P(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.
15Example: 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
16Example: 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.
17Type 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