KIN 4310 1st Edition Lecture 13 Outline of Last Lecture I Positive Result II Positive vs Negative III Workshop 1 IV Workshop 2 V Important Concepts VI Test Statistic VII Research Hypothesis VIII Null Hypothesis IX Scientific Method X Scientific Method Example XI Scientific Method XII Test Statistic XIII Significance Level XIV Critical Region Critical Value Test Statistic XV Critical Value XVI Conclusions in Hypothesis Testing XVII Decision Criterion XVIII p value 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 XIX Decision Criterion p value method XX Decision Criterion another option Outline of Current Lecture I Decision Criterion another option II Non Directional or Two tailed Test III Directional Right tailed Test IV Directional Left tailed Test V Type 1 Error VI Type 2 Error VII Type 1 and Type 2 Errors VIII Controlling Type 1 and Type 2 Errors IX Fish Oil Study X Hypotheses XI Hypothesis Tests XII One sample Z Test XIII One sample Z Test Example XIV One sample Z Test cont XV Example Current Lecture I Decision Criterion another option a Instead of using a significance level such as 0 05 simply identify the p value and leave the decision to the reader b This is another option but its more common to just report p value II Non Directional or Two tailed Test a b Note for this type of test you use the non equal sign and you have 2 rejection zones III Directional Right tailed Test a b Note Just 1 rejection zone IV Directional Left tailed Test a V Type 1 Error a A Type 1 error is the mistake of rejecting the null hypothesis when it is true b The symbol alpha is used to represent the probability of a type 1 error i Alpha is usually 5 c AKA False Positives d Note Ex is that you do a clinical trial on a drug and it says that it works but it appeared to work by random chance Its when the data tells you to reject the null but the data occurred randomly VI Type 2 Error a Type 2 Error is the mistake of failing to reject the null hypothesis when it is false b The symbol beta is used to represent the probability of a type 2 error c AKA False Negative d Note when you have a hypothesis the null is wrong but you fail to reject the null hypothesis So basically you fail to reject the null hypothesis when you should have Type 1 and Type 2 Errors TQ VII a b Table 9 1 VIII IX Controlling Type 1 and Type 2 Errors a For any fixed alpha an increase in the sample size n will cause a decrease in beta b 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 c To decrease both alpha and beta increase the sample size d Note use a large n if you do no want errors Fish Oil Study a b Null hypothesis fish oil diet has no effect on blood pressure c Are these data likely to result when the null hypothesis is true d What is our test statistic i e What level of significance should we use i Alpha 0 05 f Traditional method i The test statistic was in the rejection zone ii Therefore we reject the null hypothesis g p value method i p 0 0088 0 05 ii Therefore we reject the null hypothesis X Hypotheses a Determine a test statistic b Use an appropriate statistical method to test the hypothesis c Two possible outcomes i Reject null hypothesis ii Fail to reject null hypothesis XI Hypothesis Tests a Critical value method i Based on a statistical model find a value that partitions 95 of the usual values from 5 of the unusual values b p value method i The probability of getting your test statistic or one more extreme if the null hypothesis is true ii A low p value means strong data c Type 1 Errors i False positive ii When you reject a null hypothesis that is true iii Level of significance alpha d Type 2 Errors i False negative ii When you fail to reject a null hypothesis that is false iii Beta iv Note here the skeptic is wrong but you failed to prove him wrong XII One sample Z Test a A special hypothesis test for comparing a sample to a population b c Requires a priori knowledge of the population mean e g census data d Useful for questions like i Do left handed people have higher IQs than the general population ii Do UH students consume more energy drinks than other college students iii Do teenage drivers get into more traffic collisions than all drivers e Random sample of a population i ii Note here the x bar values are a little bit different from mu The question that we are asking is is that difference significant XIII One sample Z Test Example a Assume the null hypothesis The sample was randomly selected from the population in question b Therefore any difference between x bar and mu is due to random effects Sampling error c What is the probability of getting a difference equal to or more extreme than our data i AKA what is the p value XIV One sample Z Test cont a Test Statistic i b where i ii SEM stands for standard error measure and it is the population s d sample size c If the null hypothesis is true z has a normal distribution d So use Table B1 XV Example a In the U S the mercury concentration in blood is normally distributed with a mean of 2 55 microg L and standard deviation of 0 43 microg L b 15 residents of Grand Isle LA were tested Their mean blood mercury concentration was 2 79 microg L c Are the residents of Grand Isle significantly different than the general population i significantly different than is a non directional phrase d e Critical values i Use Table B1 f Area under the curve between the mean and z 1 96 is 47 50 g Critical values z 1 96 and z 1 96 h i j From the data i SEM 0 111 ii z 2 16 iii Since z is greater than both critical values we reject HO