KIN 4310 1nd Edition Lecture 12Outline of Last Lecture I. WorkshopII. ProbabilityIII. Probability ExampleIV. ProbabilityV. Probability and StatisticsVI. Introduction to ProbabilityVII. Probability LimitsVIII. Rare Event RuleIX. Challenger DisasterX. Formal HypothesesXI. Formal HypothesesXII. Formal HypothesesOutline of Current Lecture I. Positive ResultII. Positive vs. NegativeIII. Workshop #1IV. Workshop #2V. Important ConceptsThese 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 StatisticVII. Research HypothesisVIII. Null HypothesisIX. Scientific MethodX. Scientific Method ExampleXI. Scientific Method XII. Test StatisticXIII. Significance LevelXIV. Critical Region, Critical Value, Test Statistic XV. Critical ValueXVI. Conclusions in Hypothesis TestingXVII. Decision CriterionXVIII. p-valueXIX. Decision Criterion: p-value methodXX. Decision Criterion: another optionCurrent LectureI. Positive Resulta. We assume that HO is true when we analyze our datab. We reject HO if it is very unlikely to result in what we observedc. In research, we are very conservative and skeptical. We do not reject HO unless we really have toII. Positive vs. Negativea. Rejecting HO is a positive resultb. Not rejecting HO is a negative resultc. Note: Rejecting null hypothesis is positive – it means you’ve proved somethingIII. Workshop #1a. Claim: i. Men are taller than womenb. Research Hypothesisi.c. Null Hypothesisi.d. This calls for a right-tailed test b/c the research hypothesis is righte. Note: a research hypothesis always refers to samples and a null hypothesis IV. Workshop #2a. Claim:i. Hand span is correlated with grip strengthb. Research Hypothesisi.c. Null Hypothesisi.d. Note: this is a non directional hypothesis so it is two-tailede. Note: the null hypothesis Greek letter is “row” and is the linear coefficient of the populationV. Important Conceptsa. Test Statistic i. Can appear in research hypothesis and null hypothesisb. Research Hypothesis, H1c. Null Hypothesis, HOd. Critical Valuee. p-valuei. The results of a hypothesis testii. p stands for probabilityVI. Test Statistica. A test statistic is a value that comes from your sample datab. It is used to test the null hypothesisi. E.g., z-scoreii. Linear correlation coefficient, riii. Proportion of successful trails, Piv. Difference of means,VII. Research Hypothesisa. The research hypothesis is a formal statement of the claim; its an assertion, a positive statementb. 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 Hypothesisa. A null hypothesis is the negation of the research hypothesisb. 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 Methoda. Assume that HO is trueb. Select an appropriate samplec. Perform experiment (or make observationsd. Collect datae. 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 HOii. NO: Reject HO: The evidence is conclusive and you have proof that research hypothesis is goodX. Scientific Method Examplea. Sketchers claims that its Shape-Ups shoes:i. Improve postureii. Tone musclesiii. 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 shoesi.c. HO: The amount of calories burned while walking in Shape-Ups is the same as walking in regular athletic shoesi.XI. Scientific Methoda. Assume that HO is trueb. Select an appropriate samplec. Perform testd. Collect datae. Given that HO is true, is it likely that you would end up with the data that you got?XII. Test Statistica. A test statistic is a value that is calculated from your sample datab. It describes how extreme is your datac. In the shape up example, t = 0.386 which means that this is quite likely to happenby random chanced. If HO is true, the test statistic is a random variable from a known solutione.XIII. Significance Levela. The significance level (denoted by alpha) Is the probability representing how rareor unusual (or extreme) must a test statistic be in order to reject the null hypothesisb. Common choices for alpha are 0.05, 0.01, and 0.001i. 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 Statistica.b. Note:i. The blue is the area where you cannot reject the null hypothesis1. It is 95% of most frequently occurring valuesii. The red is the area that is the rejection zoneiii. The height of the hill is how likely each value isiv. The area under the curve is 100%v. Every test statistic has a different curveXV. Critical Valuea. A critical value is a value of the test statistic that is used to determine the result of the hypothesis testb. If the test statistic has a smaller probability than the critical value, the null hypothesis will be rejectedXVI. Conclusions in Hypothesis Testinga. We always test the null hypothesis. The initial conclusion will always be one of the following:i. 1. Reject the null hypothesisii. 2. Fail to reject the null hypothesisXVII. Decision Criteriona. Reject HO is the test statistic falls within the critical regionb. Fail to reject HO if the test statistic does not fall within the critical regionXVIII. p-valuea. 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 trueb. If the p-value is less than the level of significance, we reject the null hypothesisc. Note: i. A small p-value – strong evidence so its unlikely to happen by random chanceii. A big value – weak evidence so its not strong enough to rejectXIX. Decision Criterion: p-value methoda. Reject HO if the p-value < or equal to alpha (where alpha is the significance level, such as 0.05)i. Red zoneb. Fail to reject HO if the p-value is > alphai. Blue zoneXX. Decision Criterion: another optiona. Instead of using significance level such as 0.05, simply identify the p-value and leave the decision to the