Download presentation

Presentation is loading. Please wait.

1
Evaluating Hypotheses Chapter 9 Homework: 1-9

2
Descriptive vs. Inferential Statistics n Descriptive l quantitative descriptions of characteristics ~

3
Inferential Statistics n Making conclusions (inferences) about parameters e.g., X confidence intervals: infer lies within interval l also quantitative ~

4
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 ~

5
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 ~

6
Evaluating Hypotheses

7
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 ~

8
Hypothesis Evaluation n Null Hypothesis: H 0 l there is no difference between groups n Alternative Hypothesis: H 1 also called “experimental” hypothesis l there is a difference between groups ~

9
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? ~

10
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 ~

11
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 l i.e., data are inconclusive ~

12
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 ~

13
Directionality & Hypotheses n Directionality affects 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 IQ ~

14
Directionality & Hypotheses n Directional l one tailed test l Have prior evidence that suggests direction of effect l predict that effect will be larger or smaller, but only 1 H o: < 100 H 1 : > 100 ~

15
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 incorrectly rejecting H o l e.g., may think a new antidepressant is effective, when it is NOT ~

16
Errors n Type II error l incorrectly “accepting” H o 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 ~

17
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

18
Level of Significance ( ) n Probability of making Type I error l complement of level of confidence.95 +.05 = 1 =.05 l conduct experiment 100 times l 5 times will make Type I error n Want probability of Type I error small ~

19
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 ~

20
Statistical Power n Power l probability of correctly rejecting H 0 = probability of Type II error l complement of power *power = 1 - ~

21
Practical Significance n Degree to which result is important l result can be statistically significant l but not important in real world 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 ~

22
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~

23
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 difference actually obtained: X - l divided by difference by chance alone ~

24
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 u is outcome statistically significant? u *If so, is it practically significant? ~

Similar presentations

© 2020 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google