Evaluating Hypotheses Chapter 9

Descriptive vs. Inferential Statistics n Descriptive l quantitative descriptions of characteristics

Inferential Statistics n Making conclusions (inferences) about parameters e.g.,   X confidence intervals: infer  lies within interval l also quantitative ~

Hypothesis Testing n Most widely used inferential statistics n Hypothesis l testable assumption or inference about a parameter or distribution l should conclusion (inference) be accepted l final result a decision: YES or NO l qualitative not quantitative ~

Hypothesis Testing n Example: IQ scores  = 100,  = 15 l Take random sample of students n = 10 n Hypothesis: sample is consistent with population with above parameters l sample is the same as population ~

Evaluating Hypotheses n Test statement about population l using a statistic X l for a sample: add values & divide by n l impossible or difficult for population l need rules based on properties of samples ~

Evaluating Hypotheses

Proving / Disproving Hypotheses n Logic of science built on disproving l easier than proving l but ultimately want to prove n State 2 mutually exclusive hypotheses l if one is true, other cannot be true ~

Steps in Hypothesis Evaluation 1. State null & alternative hypotheses H 0 and H 1 2. Set criterion for rejecting H 0 level of significance:  3. collect sample; compute sample statistic & test statistic 4. Interpret results is outcome statistically significant? ~

Hypothesis Evaluation n 1. Null Hypothesis: H 0 l there is no difference between groups n 2. Alternative Hypothesis: H 1 l there is a difference between groups ~

Hypothesis Evaluation n Example: IQ and electric fields l question: Does living near power lines affect IQ of children? n H 0 : there is no difference l Living near power lines does not alter IQ.  = 100 n H 1 : Living near power lines does alter IQ.   100 ~

Hypothesis Evaluation n Outcome of study l reject or “accept” null hypothesis n Reject H o l accept as H 1 true n “Accepting” null hypothesis l difficult or impossible to “prove” H o l actually: fail to reject H o do not have enough evidence to reject ~

Evaluating H o and H 1 n Hypotheses about population parameters n Test statistic l especially designed to test H o n Procedure depends on… l particular test statistic used l directionality of hypotheses l level of significance ~

Directionality & Hypotheses n Directionality effects critical values used n Nondirectional l two-tailed test H o :  = 100; H 1 :   100 l change could be either direction l Do not know what effect will be may increase or decrease values ~

Directionality & Hypotheses n Directional l one tailed l Have prior evidence that suggests direction of effect predict that effect will be larger or smaller, but only 1 H o :  < 100 H 1 :  > 100 ~

Errors n “Accept” or reject H o l only probability we made correct decision l also probability made wrong decision n Type I error l rejecting H o when it is really true l e.g., may think a new antidepressant is effective, when it is NOT ~

Errors n Type II error l “accepting” H o when it is really false l e.g., may think a new antidepressant is not effective, when it really is n Do not know if we make error l because we do not know true population parameters ~

Actual state of nature H 0 is true H 0 is false Decision Accept H 0 Reject H 0 Correct Type I Error Type II Error Errors

Level of Significance (  ) n Probability of making Type I error l complement of level of confidence l = 1  =.05 l conduct experiment 100 times l 5 times will make Type I error rejected H 0 when it should be accepted n Want probability of Type I error small ~

Statistical Significance n If reject H 0 n Outcome is “statistically significant” l difference between groups is... greater than expected by chance alone l due to sampling, etc. n Does NOT say it is meaningful ~

Statistical Power n Power l probability of correctly rejecting H 0  = probability of type II error l complement of power ~

Practical Significance n Degree to which result is important l result can be statistically significant l but not important in real world l no practical implications l no universal method for reporting n Effect size l measure of magnitude of result l difference between means of 2 groups l e.g., IQ: 1 point small effect, 15 large ~

Procedure for Evaluating Hypotheses n Experiment l Draw random sample l compute statistic l determine if reasonably comes from population If no reject H 0 n Use test statistic to make decision n 3 important distributions variable, sample statistic, test statistic~

Test Statistic n distribution of test statistic l has known probabilities n General form test statistic = sample statistic - population parameter standard error of sample statistic l difference actually obtained X -  l divided by difference by chance alone ~

Steps in Hypothesis Evaluation 1. State null & alternative hypotheses H 0 and H 1 2. Set criterion for rejecting H 0 level of significance:  3. collect sample; compute sample statistic & test statistic 4. Interpret results is outcome statistically significant? ~