1. Inference1 Data Analysis Inferential Statistics Research Methods Gail Johnson

2. Inference2 Inferential Statistics Enables you to estimate population mean based on sample results Enables you to estimate sampling error Enables you to test for statistical significance

3. Inference3 Confidence Intervals Estimate the population mean based on the sample survey We want to be 95% certain that our population estimate is correct within a narrow range. If I take a random sample of people in a community and ask them who much they earned in 2005, I could then calculate the mean, median and mode of the respondents.

4. Inference4 Confidence Intervals The specific estimate would be the “Point estimate” Based on my excellent random sample data, I estimate that the average salary of the community is $35,715.

5. Inference5 Confidence Intervals I would also construct confidence intervals that would calculate where the the true mean of the population resides. Trusting my computer’s calculations, I would then provide the lower and upper estimates (confidence intervals), saying I am 95% certain that the true average salary of the community is between $34,357 and $37,072.

6. Inference6 In the News Estimating Iraqi deaths since the war Johns Hopkins Study May—July 2006, national cross-sectional cluster sample survey 1,849 households Point Estimate: 601,027 due to violence Confidence Interval: 426,369—793,5663

7. Inference7 Sampling Error Polling data: working with nominal data: Typically results are within +/- 5 % That means that if we had surveyed everyone, the results would be within +/- 5% of the results from the survey.

8. Inference8 Sampling Error Most recent survey shows: –Gush has 43% –Bore has 46% The report a +/-5% sampling error. So if surveyed everyone, we might find that 48% of the population favors Gush and 41% surveys Bore Conclusion: race is too close to call.

9. Inference9 Sampling Error Most recent survey shows: –Gush has 43% –Bore has 46% The report a +/-1% sampling error. So if surveyed everyone, we high have found that 44% of the population favors Gush and 45% surveys Bore Conclusion?

10. Inference10 Statistical Significance Statisticians have provided us with the tools to estimate how likely are sample results are based on chance or how likely are results are in error. These are called tests of statistical significance.

11. Inference11 101 Tests for Statistical Significance Most Common Chi Square: nominal and ordinal data T-tests: dependent variable is ratio/interval data Anova: dependent variable is ratio/interval, and independent variable is nominal or ordinal with more than 2 categories F-tests: interval data

12. Inference12 Statistical Significance I Believe, I Believe

13. Inference13 Statistical Significance They allow you to estimate how likely it is that you have gotten the results you see in your analysis of sample data as a result of chance.

14. Inference14 Statistical Significance Typically, we use a standard for determining how likely we would be to get these results by chance alone. The convention is to set an alpha level or p value of.05 or less.

15. Inference15 Statistical Significance This means there is only a 5% chance or less that you would have obtained these results if there really was no difference in the larger population. Another way to say it: your results are statistically significant at the.05 level.

16. Inference16 Statistical Significance With only a 5% chance of being incorrect, I am willing to take a risk that my sample results fairly accurately captures the true population

17. Inference17 How much risk? It All Depends!

18. Inference18 The Logic of Hypothesis Testing Research Hypothesis –Women and men earn different salaries. Null Hypothesis: –There is no difference between women and men’s salaries.

19. Inference19 Hypothesis The research hypothesis is your best guess as to the relationship between variables or what you predict will be impact of one variable on another. The null hypothesis is always a statement that "there is no difference" or "no impact" between our independent variable and the dependent variable.

20. Inference20 The Logic of Hypothesis Testing Analysis Steps: –collect data from a random sample of men and women across the U.S. –analyze the data. there is indeed a $5,000 difference But, is the difference statistically significant? i.e. not due to chance?

21. Inference21 Testing for statistical significance: What is the probability of getting a$5,000 difference when we assume that in the population from which this sample was drawn if there really is $0 difference? If the probability is “small” for getting the $5,000 difference, then I can reject the null hypothesis.

22. Inference22 Remember: A significance test is nothing more than a determination of the probability of getting the results you got by chance. While the formulas differ, they all get interpreted the same way. The social science standard is an p value or an alpha value of.05 or less

23. Inference23 Chi Square Based on what you would expect if the there was no difference in the frequency distribution. Use with nominal or ordinal data.

24. Inference24 Interval/Ratio T-Tests Single Mean: –Interval/ration data where you are comparing to a known population mean Paired Means: – before and after design Independent Means: –comparing 2 means For t-tests: you must have interval or ratio data.

25. Inference25 Testing a Hypothesis about a Single Mean: Research hypothesis: There is a difference in average hours worked as compared to “40.” Null: not different from 40

26. Inference26 Testing a Hypothesis about a Single Mean: Results: Average number of hours =42. T-test: =.000 Interpretation?

27. Inference27 Interpretation It is very unlikely you would have gotten these results. You reject the null hypothesis: You are 95% certain that the average number of hours worked by is slightly more than the assumed 40 hours.

28. Inference28 Comparing 2 Means: Gender and Income Is there a difference in men’s and women’s income? The research hypothesis is that there is a difference. The null hypothesis: The two population means are equal or the groups are independent or there is no difference in the population means for these 2 groups.

29. Inference29

30. Inference30 Analysis of Variance ANOVA test What happens when you have more than 2 groups you want to compare? Religion? Marital status (single, married, divorced) Education (HS, College, Graduate Degree)

31. Inference31 Statistical Significance? Is there a difference in income based on whether one has a High School degree or less, some college or completed a bachelor’s degree, or has a graduate degree Your Research Hypothesis is? Your Null Hypothesis is?

32. Inference32 Education and Income HS or less:$29,225 College$46,764 Graduate$62,275 But are these results statistically significant? F-test =.001

33. Inference33 Potential Errors Type I Error: – This occurs when you reject the null hypothesis even though there is a possibility that the null hypothesis is true. Type II Error: – This occurs when you fail to reject the null hypothesis, even though there is a possibility that, in reality, it is false.

34. Inference34 Type I and Type II Generally, social scientists feel that it is worse to make a Type I error than a Type II error. As a program manager, you may feel that it is worse to make a Type II error. Why?

35. Inference35 One and Two-Tailed Tests ONE-Tailed Test: is used whenever the hypothesis specifies a direction. We are concerned with only one tail of the normal curve. TWO-tailed test: when the research question does not specify a direction.

36. Inference36 Statistical Significance = Meaningful Significance? They surveyed 3000 people, selected randomly across the U.S. 87% with a private physician reported being satisfied 85% of those with an HMO physician reported being satisfied. These results were statistically significant. Are they meaningfully different?

37. Inference37 Naff: Glass Ceiling Look at the data she presented Why does she show some statistical significance on some tables but not others? Let’s look at some of the tables with statistical significance: what do they mean?

38. Inference38 Statistical Significance Does Not Mean Your results are meaningful or important. The relationship is strong or weak. That design errors have been eliminated. Your study has no value if your results are not statistically significant. A p value of.001 is not more important than a p value of.01 or.05

39. Inference39 “Unfortunately, researchers often place undue emphasis on significance tests….Perhaps it is because they have spent so much time in courses learning to use significance tests, that many researchers give the tests an undue emphasis in their research.” {Shively, p. 172}