KIN 4310 Lecture 12 Outline of Last Lecture I Exploratory Data Analysis II Probability Outline of Current Lecture III Formal Hypotheses IV Type 1 and Type 2 Errors Current Lecture Inferential statistics always starts with a claim A null hypothesis is the negation of a claim research hypothesis H 0 is the skeptical choice The research hypothesis is a formal statement of the claim H 1 is assertive positive Positive result We assume that H0 is true when we analyze our data we reject H0 if it is very unlikely to result in what we observed in research we are very conservative and skeptical We do not reject H0 unless we really have to Rejecting H0 is a positive result Not rejecting H0 is a negative result A test statistic is a value that comes from your sample data It is used to test the null hypothesis it describes how extreme the data is Scientific Method o Assume that H0 is true o Select an appropriate sample o Perform experiment or make observations o Collect Data o Given that H0 is true is it likely that you would end up with the data that you got YES Fail to reject H0 NO Reject H0 The evidence is conclusive The significance level denoted by alpha is the probability representing how rare or unusual or extreme must a test statistic be in order to reject the null hypothesis A critical value is a value of the test statistic that is used to determine the result of the hypothesis test If the test statistic has a smaller probability than the critical value the null hypothesis will be rejected Reject H0 if the test statistic falls within the critical region Fail to reject H0 if the test statistic does not fall within the critical region The p value is the probability of getting a value more extreme than the test statistic by chance assuming that the null hypothesis is actually true If the p value is less than the level of significance we reject the null hypothesis Reject H0 if the P value is less than or equal to alpha where alpha is the significance level such as 0 05 Fail to reject H0 if the P value is greater than alpha Another option Instead of using a significance level such as 0 05 simply identify the Pvalue and leave the decision to the reader A Type I error is the mistake of rejecting the null hypothesis when it is true The symbol alpha is used to represent the probability of a type I error A Type II error is the mistake of failing to reject the null hypothesis when it is false The symbol beta is used to represent the probability of a type II error For any fixed alpha an increase in the sample size n will cause a decrease in beta for any fixed sample size n a decrease in alpha will cause an increase in beta Conversely an increase in alpha will cause a decrease in beta To decrease both alpha and beta increase the sample size These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute