Descriptive and Inferential Statistics Descriptive statistics The science of describing distributions of samples or populations Inferential statistics The science of using SAMPLE statistics to make INFERENCES or DECISIONS about population parameters Inferential Statistics Examples Quantitative (Confidence Intervals) Using sample mean X to estimate population mean Using sample stdev S to estimate population stdev Qualitative (Hypothesis Testing) Make Conclusions about behavior in population Most widely used inferential statistic Are these people homeless? Possible Cause #1 Have homes and lazy owners Comes from distribution of dogs with homes Possible Cause #2 Homeless Comes from distributions of dogs without homes Why are these people so scruffy? Less Scruffy More Scruffy People with homes People without homes These people Distribution of Scores Why are these people so scruffy? People with homes People without homes Distribution of Scores Less Scruffy More Scruffy People with homes People without homes These dogs Distribution of Means (N=25) Cause of Differences Null hypothesis (H 0 ) Alternate hypothesis (H 1 ) Goal is to REJECT NULL HYPOTHESIS Show probability of null hypothesis true as low Hypothesis Testing When do we reject Null Hypothesis? When we get an event which is unlikely? How big is the red area (rejection region)? Hypothesis Testing When do we reject Null Hypothesis? Rejection Region =.05 (5%) Why? Why Not? What if.50? What if ? Hypothesis Testing By using different types of distributions! Single sample Z (easy but uncommon) T (harder but more common) F distributions (ANOVA) Chi-square Distributions (Nominal data) How do we calculate probabilities of rejection regions? Hypothesis Testing: Single sample z test How do we reject the null hypothesis 1) Creating a null hypothesis Example: The Mean IQ of UCLA students is 100 H 0 : =100 2) Creating a distribution of outcomes for H 0 : =100 Example: A mean distribution ( X =10,,N=25) Hypothesis Testing: Single sample z test 3) Determine outcomes that we consider Unlikely Example: 4) Evaluate if our experimental result is one of those unlikely outcomes Example: (X = 105) 5) Two possible outcomes Reject H 0 Fail to Reject H 0 X = 105 X = 102 Inferential Statistics: Hypothesis Testing If we reject H 0, we have show evidence that it is LIKELY to be untrue. But we might be wrong. How likely is it that we are wrong? Answer: The size of the rejection region = Alpha () Inferential Statistics: Hypothesis Testing If H 0 is true in reality Probability of an error Probability of no error is But what if H 0 is not true? Null hypothesis can wrong in many ways Inferential Statistics: Hypothesis Testing If null hypothesis is not true, then Error if Fail to reject =Beta () Correct if reject = 1- Much harder to calculate than because depends on how distributions overlap which is affected by Effect Size Sample Size (N) Standard Deviation ( X ) Alpha () Tails of Test Hypothesis Testing Hypothesis can be two tail one tail (right) one-tail (left) (non-directional) (directional) (directional) No prior evidence Prior (>a) Prior (=a H 1 :