1. Introductory Data Analysis & Interpretation

5. Parametric and Nonparametric Counterparts Function Para Nonpara Efficiency of Nonpar to Normal Test for one sample t or z-test Sign test 0.63 Difff bet 2 dependent samples t - or z-test Wilcoxon signed-ranks 0.95 Difff bet 2 independent samples t or z-test Man-Whitney U/ Wilcoxon Rank-s Test 0.95 More than 2 independent samples 1-ANOVA 2-ANOVA Kruskal-Wallis Friedman’s 0.95 Relationship bet 2 variables Linear (Pearson) Rank Corr (Spearrman) 0.91

11. Types of Statistical Errors

14. Reject H 0 Do not reject H 0 Sampling Distribution Maximum probability of committing a Type I error =  Establishing the Decision Rule

15. Rejection region  = 0.05 0 From the standard normal table Then 0.5 0.4 Establishing the Critical Value as a z -Value

17. Rejection region  = 0.05 0 0.5 0.4 Test Statistic in the Rejection Region

19. Rejection region  = 0.05 0 0.5 0.4 Relationship Between the p-Value and the Rejection Region p-value = 0.0036

23. 0 Two-Tailed Hypothesis Tests

24. Choosing the Correct Statistical Test Number of dependent variables Number of independent Variables Type of Dependent Variable(s) Type of Independent Variable(s) Measure Test(s) 1 0 (1 population) continuous normal not applicable (none) mean one-sample t-test continuous non-normal median one-sample median categorical proportions Chi Square goodness-of-fit, binomial test 1 1 (2 independent populations) normal 2 categories mean 2 independent sample t-test non-normal medians Mann Whitney, Wilcoxon rank sum test categorical proportions Chi square test Fisher’s Exact test

25. Choosing the Correct Statistical Test Number of dependent variables Number of Independent** Variables Type of Dependent Variable(s) Type of Independent Variable(s) Measure Test(s) 1 0 (1 population measured twice) or 1 (2 matched populations) normal not applicable/ categorical means paired t-test non-normal medians Wilcoxon signed ranks test categorical proportions McNemar, Chi-square test 1 1 (3 or more populations) normal categorical means one-way ANOVA non-normal medians Kruskal Wallis categorical proportions Chi square test

26. Choosing the Correct Statistical Test Number of dependent variables Number of independent Variables Type of Dependent Variable(s) Type of Independent Variable(s) Measure Test(s) 1 2 or more (e.g., 2-way ANOVA) normal categorical means Factorial ANOVA non-normal medians Friedman test categorical proportions log-linear, logistic regression 1 0 (1 population measured 3 or more times) normal not applicable means Repeated measures ANOVA

27. Choosing the Correct Statistical Test Number of dependent Variables Number of independent variables Type of Dependent Variable(s) Type of Independent Variable(s)/ Measure Test(s) 1 1 normal continuous correlation simple linear regression non-normal non-parametric correlation categorical categorical or continuous logistic regression continuous discriminant analysis 1 2 or more normal continuous multiple linear regression non-normal categorical logistic regression normal mixed categorical and continuous Analysis of Covariance General Linear Models (regression) non-normal categorical logistic regression

28. Choosing the Correct Statistical Test Number of dependent Variables Number of independent Variables Type of Dependent Variable(s) Type of Independent Variable(s)/ Measure Test(s) 2 2 or more normal categorical MANOVA 2 or more 2 or more normal continuous multivariate multiple linear regression 2 sets of 2 or more 0 normal not applicable canonical correlation 2 or more 0 normal not applicable factor analysis

30. Some statistical tests The mean of the variable write for this particular sample of students is 52.775, which is statistically significantly different from the test value of 50. We would conclude that this group of students has a significantly higher mean on the writing test than 50.

32. Chi-square goodness of fit These results show that racial composition in our sample does not differ significantly from the hypothesized values that we supplied (chi-square with three degrees of freedom = 5.029, p = .170).

36. Chi-square test These results indicate that there is no statistically significant relationship between the type of school attended and gender (chi-square with one degree of freedom = 0.047, p = 0.828).

38. One-way ANOVA From this we can see that the students in the academic program have the highest mean writing score, while students in the vocational program have the lowest

41. Simple linear regression We see that the relationship between write and read is positive (.552) and based on the t-value (10.47) and p-value (0.000), we would conclude this relationship is statistically significant. Hence, we would say there is a statistically significant positive linear relationship between reading and writing

43. THANK YOU ! Have a statistically significant day!