KIN 4310 1nd Edition Lecture 12 Outline of Last Lecture I Workshop II Probability III Probability Example IV Probability V Probability and Statistics VI Introduction to Probability VII Probability Limits VIII Rare Event Rule IX Challenger Disaster X Formal Hypotheses XI Formal Hypotheses XII Formal Hypotheses Outline of Current Lecture I Positive Result II Positive vs Negative III Workshop 1 IV Workshop 2 V Important Concepts 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 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 XIX Decision Criterion p value method XX Decision Criterion another option Current Lecture I Positive Result a We assume that HO is true when we analyze our data b We reject HO if it is very unlikely to result in what we observed c In research we are very conservative and skeptical We do not reject HO unless we really have to II Positive vs Negative a Rejecting HO is a positive result b Not rejecting HO is a negative result c Note Rejecting null hypothesis is positive it means you ve proved something III Workshop 1 a Claim i Men are taller than women b Research Hypothesis i c Null Hypothesis i d This calls for a right tailed test b c the research hypothesis is right e Note a research hypothesis always refers to samples and a null hypothesis IV Workshop 2 a Claim i Hand span is correlated with grip strength b Research Hypothesis i c Null Hypothesis i d Note this is a non directional hypothesis so it is two tailed e Note the null hypothesis Greek letter is row and is the linear coefficient of the population V Important Concepts a Test Statistic i Can appear in research hypothesis and null hypothesis b Research Hypothesis H1 c Null Hypothesis HO d Critical Value e p value i The results of a hypothesis test ii p stands for probability VI Test Statistic a A test statistic is a value that comes from your sample data b It is used to test the null hypothesis i E g z score ii Linear correlation coefficient r iii Proportion of successful trails P iv Difference of means VII Research Hypothesis a The research hypothesis is a formal statement of the claim its an assertion a positive statement b H1 says i Yes A has an effect on B ii There is a relationship between A and B iii There is a difference between A and B iv A reduces B v A is greater than B vi A increases as B decreases VIII Null Hypothesis a A null hypothesis is the negation of the research hypothesis b HO says i No there is no effect ii There is no relationship between A and B iii There is no difference between A and B IX Scientific Method a Assume that HO is true b Select an appropriate sample c Perform experiment or make observations d Collect data e Given that HO is true is it likely that you would end up with the data that you got AKA what are the odd of this happening by random chance i Yes Fail to reject HO ii NO Reject HO The evidence is conclusive and you have proof that research hypothesis is good X Scientific Method Example a Sketchers claims that its Shape Ups shoes i Improve posture ii Tone muscles iii Increase the amount of calories that you burn while walking b H1 The amount of calories burned while walking in Shape Ups is greater than walking in regular athletic shoes i c HO The amount of calories burned while walking in Shape Ups is the same as walking in regular athletic shoes i XI Scientific Method a Assume that HO is true b Select an appropriate sample c Perform test d Collect data e Given that HO is true is it likely that you would end up with the data that you got XII Test Statistic a A test statistic is a value that is calculated from your sample data b It describes how extreme is your data c In the shape up example t 0 386 which means that this is quite likely to happen by random chance d If HO is true the test statistic is a random variable from a known solution e XIII Significance Level a 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 b Common choices for alpha are 0 05 0 01 and 0 001 i In health science alpha is normally 0 05 ii In this class alpha will always be 0 05 or 5 c Note alpha how rare is rare XIV Critical Region Critical Value Test Statistic a b Note i The blue is the area where you cannot reject the null hypothesis 1 It is 95 of most frequently occurring values ii The red is the area that is the rejection zone iii The height of the hill is how likely each value is iv The area under the curve is 100 v Every test statistic has a different curve XV Critical Value a A critical value is a value of the test statistic that is used to determine the result of the hypothesis test b If the test statistic has a smaller probability than the critical value the null hypothesis will be rejected XVI Conclusions in Hypothesis Testing a We always test the null hypothesis The initial conclusion will always be one of the following i 1 Reject the null hypothesis ii 2 Fail to reject the null hypothesis XVII Decision Criterion a Reject HO is the test statistic falls within the critical region b Fail to reject HO if the test statistic does not fall within the critical region XVIII p value a The p value is the probability of getting a value more extreme than the test statistic by random change assuming that the null hypothesis is actually true b If the p value is less than the level of significance we reject the null hypothesis c Note i A small p value strong evidence so its unlikely to happen by random chance ii A big value weak evidence so its not strong enough to reject XIX Decision Criterion p value method a Reject HO if the p value or equal to alpha where alpha is the significance level such as 0 05 i Red zone b Fail to reject HO if the p value is alpha i Blue zone XX Decision Criterion another option a Instead of using significance level such as 0 05 simply identify the p value and leave the decision to the reader