Inferential Statistics

1. 15 Inferential Statistics

2. Learning Objectives • Recall The Two Purposes Of Inferential Statistics • Discuss The Sampling Distribution Of The Mean • Define Terms Used In Inferential Statistics • Distinguish Between A One-tailed And A Two-Tailed Test

3. Learning Objectives Describe Type I And Type II Errors Differentiate Between Parametric And Nonparametric Statistical Tests Discuss The Power Of A Statistical Test List Criteria For Selecting A Statistical Test Identify Statistical Tests Commonly Reported In Nursing Studies

4. Learning Objectives Critique The Inferential Statistics Section Of Research Reports

5. Learning Objective OneRecall The Two Purposes Of Inferential Statistics

6. Broad Purposes of Inferential Statistics • Estimating population parameters from sample data (after data collection) • Testing hypotheses (before data collection)

7. Learning Objective TwoDiscuss The Sampling Distribution Of The Mean

8. Sampling Distribution of the Mean • Approximates the normal curve • Larger samples are more adequate.

9. Standard Error of the Mean • Standard deviation of the sampling distribution of the mean • Symbolized ˆ • Smaller ˆ value means it is more likely the sample is an accurate reflection of the population mean. x x

10. Learning Objective ThreeDefine Terms Used In Inferential Statistics

11. Inferential Statistics • Central limit theorem • Tendency of sample values to be normally distributed around population value • Sampling distribution • Theoretical frequency distribution based on infinite samples

12. Confidence Interval • CI • Range thought to contain the population value • Includes lower and upper limit, with specified degree of probability

13. Hypotheses • Directional research hypothesis • Predicts results of study • Null hypothesis • No difference exists between populations or no correlation exists between variables in the population. • (H0) • Subjected to statistical analysis

14. Hypotheses (cont’d) • Null • Rejected or retained • Research • Supported or not supported

15. Level of Significance • Probability level of rejecting a null hypothesis when it is true • Symbolized by letter p and Greek letter alpha (α) • The most common probability level in nursing research is p = .05.

16. Inferential Statistics • Critical value • Value in a theoretical distribution at which all obtained sample values that are equal to or beyond that point in the distribution are said to be statistically significant • Critical region or region of rejection—all values beyond the critical value

17. Degrees of Freedom • Symbolized (df) • Concerns the number of values that are free to vary • Interpretation of statistical tests dependent on the degrees of freedom

18. Learning Objective FourDistinguish Between A One-tailed And A Two-Tailed Test

19. One-Tailed VersusTwo-Tailed Tests • One-tailed tests • Appropriate for directional research hypotheses • Degree of difference or type of correlation predicted • Easier to reject the null hypothesis

20. One-Tailed VersusTwo-Tailed Tests • Two-tailed tests • Appropriate for nondirectional research hypotheses • Difference or correlation predicted, but the degree is not indicated • More difficult to reject the null hypothesis

21. Learning Objective FiveDescribe Type I And Type II Errors

22. Errors • Type I error • Null hypothesis is actually true, but is rejected. • Type II error • Null hypothesis is actually false and it is retained.

23. Learning Objective SixDifferentiate Between Parametric And Nonparametric Statistical Tests

24. Parametric Tests • Population parameters

25. Parametric Tests • Make assumptions about the population from which a sample was drawn • The level of measurement of the data is interval or ratio. • Data taken from populations that are normally distributed on the variable that is being measured • Data taken from populations that have equal variances on the variable that is being measured

26. Nonparametric Tests • Distribution-free statistics • Makes no assumptions about the distribution of the population • May be used with nominal and ordinal data • Sample sizes may be small.

27. Learning Objective SevenDiscuss The Power Of A Statistical Test

28. Power of a Statistical Test • Ability of the test to reject a null hypothesis when it is false • Dependent on the sample size and the level of significance that is chosen • The larger the sample size chosen, the more power the statistical test has. • The higher the level of significance selected, the more power the statistical test has.

29. Power of a Statistical Test (cont’d) • A one-tailed test is more powerful than a two-tailed test. • If the assumptions of parametric tests are met they are more powerful than nonparametric tests.

30. Learning Objective EightList Criteria For Selecting A Statistical Test

31. The T Test • Parametric test assumptions • Compares the difference between mean values of some variable in two groups • Particularly useful for small sample sizes • Interval or ratio data required

32. Analysis of Variance (ANOVA) • Parametric statistical test • Compares differences among more than two means at one time • Based on assumptions that data • Are interval or ratio level • Have been selected from populations that are normally distributed • Have equal variances on the variable that is being measured

33. Chi-Square (χ2) • Nonparametric inferential technique • Used for comparing nominal sets of data

34. Learning Objective NineIdentify Statistical Tests Commonly Reported In Nursing Studies

35. t Tests • Parametric test that examines differences between the means of two groups of values • Independent t test or unrelated samples t test • Test for samples with no association or connection

36. t Tests (cont’d) Dependent t test or paired t test Used when scores or values are associated or have some connection

37. Analysis of Variance (ANOVA) • Examines the two types of variances in data obtained • “Mean square between” (MSB) groups explore variation between the means of the groups. • “Mean square within” (MSW) groups examine variation of individual scores within each of the groups.

38. Chi-Square (χ2) • Observed frequencies are compared to expected frequencies. • Null hypothesis is rejected if the observed frequencies are quite different from the expected frequencies at a specified level of significance.

39. Advanced Statistical Tests • Multiple regression • Analysis of covariance (ANCOVA) • Canonical correlation • Multivariate analysis of variance (MANOVA) • Meta-analysis • Metasynthesis

40. Learning Objective TenCritique The Inferential Statistics Section Of Research Reports

41. Critique of Research Reports • Minimal understanding of inferential statistics is sufficient.

42. Critique of Research Reports (cont’d) • Reader should • Search the report for any inferential statistics that were used in data analysis • Determine if there is enough information to make a decision about the appropriateness of each test that was used

43. Critique of Research Reports (cont’d) Reader should Be provided with the value of the statistical test that was obtained, the degrees of freedom, and the significance level that was reached when each hypothesis was tested Be able to determine if each of the researcher’s hypotheses was supported or not

44. Critique of Research Reports (cont’d) Every research report should clearly present the results of hypothesis testing in both the text of the report and in the tables.