Slide Number 1Slide Number 2Slide Number 3Research Slide Number 5Slide Number 6Slide Number 7Slide Number 8Slide Number 9Slide Number 10Slide Number 11Slide Number 12Slide Number 13Slide Number 14Slide Number 15Slide Number 16Slide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21Slide Number 22Slide Number 23Slide Number 24Slide Number 25Slide Number 26Slide Number 27Slide Number 28Slide Number 29Slide Number 30Slide Number 31Slide Number 32Slide Number 33Slide Number 34Slide Number 35Slide Number 36Slide Number 37Slide Number 38Slide Number 39Slide Number 40Slide Number 41Slide Number 42Slide Number 43Slide Number 44Slide Number 45Slide Number 46Slide Number 47Slide Number 48Slide Number 49Slide Number 50Slide Number 51Slide Number 52Slide Number 53Slide Number 54Slide Number 55Slide Number 56Slide Number 57Slide Number 58Slide Number 59Slide Number 60Health Behavior Statistical Methods HP 340L Lecture 9 Introduction to Statistical Hypothesis Testing: z-test and t-tests Chapter 8 We covered material in Kiess & Green Chapter 7  Point estimation:  Mean: as a point estimator for µ  SD: s as a point estimator for σ  Sampling distribution of the mean  Mean and a standard error of the sampling distribution of the mean  Approximate normality of the sampling distribution of the mean (Central Limit Theorem)  Estimating the standard error of the mean  Interval estimation  Constructing a CI for the population mean Last Lecture x We will cover material in Kiess & Green Chapter 8  Hypothesis testing  Null and alternative hypotheses  One- and two-sided hypotheses  Statistical tests  z-test  t-test (t-tables) Today’s LectureHP-340: Fall 2016 4 Research Research question Reach an inference Population/sample Analyze the data Define variables Describe the data Design the study Collect data Organize, describe and summarize data  Descriptive Statistics  Estimate a population parameter  Inferential Statistics  Test hypotheses: Rules for making decisions about a research hypothesis  Arguably one of the most widely used statistical tools in scientific research Some Key Uses of StatisticsHP-340: Fall 2016 6 • The process of making conclusions regarding a population using measurements made on a sample from the population is called statistical inference. • The basic steps in statistical inference are: – Form hypothesis to be tested. – Take your data and compute a test statistic based on your hypothesis. – Use the test statistic to compute a p-value derived from a distribution based on the null hypothesis and the type of data you have. – Draw your conclusion. Statistical Inference Two types of statistical hypothesis tests  Parametric Test: Parametric tests assume the scores in the population have certain characteristics (or distributions)  Non-parametric Test: No assumptions about the distribution of scores in the population  Commonly known as distribution-free tests (Chapter 15) Statistical Hypothesis TestsFLOW CHART # 1: Statistical decision tree Dependent Variable Categorical/Qualitative Numeric/Quantitative Independent var. categorical Independent var. categorical Independent var. numeric Independent var. numeric Dependent var. not normally distributed Flow-Chart # 2 Flow-Chart # 4 Flow-Chart # 5 Flow-Chart # 6 Dependent var. normally distributed Flow-Chart # 3 Time to event Flow-Chart # 7FLOW CHART # 2: Tests for normally distributed numeric dependent variable & categorical independent variable (*These are also known as “parametric tests”) 1 sample (Compared to a population mean) Test for MEANS 2 samples (paired/matched) 2 samples (Independent) population variance known population variance unknown z-test t-test Variances unequal Variances equal Paired t-test Student’s t-test Welch t-test >2 non- independent samples (Repeated measures/crossover design) >2 independent samples (Completely randomized design) Repeated measures ANOVA One-way ANOVA >2 variables of interest ANCOVA Start with a research question  Translate it into a statistical hypothesis  The statistical hypothesis is a statement about a population parameter  A testable statement  The statement may or may not be true Statistical Hypothesis Tests Statistical technique to answer yes/no research questions  Examples:  Does the MMR vaccine increase the risk of autism? NO!  Is sugar-sweetened beverage consumption associated with obesity?  Does the choice of online dating user name improve chances of securing a date?  Do micro credits reduce poverty? Statistical Hypothesis Tests Example: Are USC students less or more intelligent on average than the average US college student?  Population of US college students have a mean IQ of 120  Specifically, is the mean IQ of USC students, µ, different from 120?  Research investigation:  We measure IQ on a random sample of 65 USC students  Estimate a mean IQ for our sample:  Assume population standard deviation is known: 127x = = 21σStatistical Hypothesis Tests n = 65;  A 95% CI for the mean IQ of USC students is:  With 95% confidence the CI contains the true value of the average USC students IQ  So, with 95% confidence the average USC students IQ is between 121.9 and 132.1  But not certain, it could be lower in truth and we just happened to sample an ‘unusual’ sample 127; = 21x = σStatistical Hypothesis Tests ( )21127 1 96 = 121 9 132.165. .,± Option A: Another way to look at this (null explanation):  What if µ really was 120?  How usual/unusual would be to observe an in a sample of n = 65?  If µ = 120, then would be 2.69 SD units away from the mean of the sampling distribution of the mean  Therefore less than 0.4% of the samples of size 65 would yield a that far away in the tails! x =1272165127 120 = = = 2.69nXzσ−µ −Statistical Hypothesis Tests x =127x Option B: An ‘alternative’ explanation for would be that µ > 120  What if µ = 125 then would not be at all unusual!  22% of samples of size n = 65 would have as large or larger  would not be unusual at all if µ = 125! Statistical Hypothesis Tests x =1272165127 125 = = = 0.77nXzσ−µ −x =127x Which explanation/hypothesis do you believe?  Option A: µ