1. ITEC6310 Research Methods in Information Technology Instructor: Prof. Z. Yang Course Website: http://people.math.yorku.ca/~zyang/ite c6310.htm Office: Tel 3049

2. 2 Nonparametric Statistics Used if data violate assumptions of parametric statistics or if you have ordinal or nominal data Chi-square –Used when your dependent variable is a dichotomous decision (e.g., yes or no) –Chi-square for contingency tables is used when you have more than one variable to analyze Mann-Whitney U-Test –Used when data scaled on at least an ordinal scale –Good nonparametric alternative to the t-test when assumptions are violated The Wilcoxon Signed Ranks Test –Used for a single-factor design with correlated samples

3. 3 Example I have recently conducted a study in which I ranked my participants on height and weight. I am interested in whether there are any differences in height and weight depending on whether the participant is an athlete (defined as being a member of a sports team) or not an athlete. Which statistic would you recommend using to analyze these data? If the actual height ad weight data were available, what statistic would be appropriate.

4. 4 Example How do the χ2 tests differ in use from a t test? Why is the χ2 test of independence a nonparametric test and what does it mean?

5. 5 Nonparametric Statistics for the Multiple-Group Experiment Nonparametric equivalents to the ANOVA. Kruskal-Wallis test Friedman rank test

6. 6 Special Topics Power of a statistical test –Power refers to a statistic’s ability to detect differences between groups –Power is affected by The alpha level chosen Sample size Whether a one-tailed or two-tailed test is used Effect size –Power can be determined statistically

7. 7 Example How is effect size different from significance level? In other words, how is it possible to have a significant result yet a small effect size? How does increasing the sample size affect a t test? Why does it affect a t test in this manner?

8. 8 Statistical vs. Practical Significance –A statistically significant effect is not likely due to chance –Statistical significance does not mean that a difference is important –A finding may have practical significance if the finding has practical applications Special Topics

9. 9 The meaning of statistical significance –The alpha level adopted (e.g., p <.05) tells you the likelihood of making a type I error –A finding found to be significant at p <.01 is NOT more significant than one at p <.05 Special Topics

10. 10 Data Transformations –Data may need to be transformed with a data transformation Adding or subtracting a constant from each datum does not change the shape of the original frequency distribution –The mean changes and standard deviation does not change Multiplying by a constant does change the distribution and the mean and standard deviation –This is a linear transformation –You may need to transform data if the data do not meet assumptions of statistical tests Data must be rechecked for other problems Special Topics

11. 11 Alternatives to Inferential Statistics –Some research designs preclude using inferential statistics (e.g., single-subject design) Reliability of data may be checked using replication –You should be able to repeat (replicate) a reliable finding –Replication need not be limited to single-subject designs Special Topics

12. 12 Parametric Statistics vs. Nonparametric Statistics Parametric Statistics –t test –z test –ANOVA Nonparametric Statistics –Chi-square Used when your dependent variable is a dichotomous decision (e.g., yes or no) Chi-square for contingency tables is used when you have more than one variable to analyze –Mann-Whitney U-Test Used when data scaled on at least an ordinal scale Good nonparametric alternative to the t-test when assumptions are violated –The Wilcoxon Signed Ranks Test Used for a single-factor design with correlated samples

13. 13 Examples Identify the statistical procedure that should be used to analyze the data from each of the following studies: 1. A study investigates whether men or women (age 16-20) spend more money on clothing. Assume the amount of money spent is normally distributed. 2. The same study as 1, however, it has since been determined that amount of money spent really is not normally distributed 3. A study that investigates the frequency of drug use in suburban versus urban high schools. 4. A study investigates whether students perform better in a class that uses group learning exercises versus in a class that uses the traditional lecture method. Two classes that learn the same information are selected. Performance on a 50-item final exam at the end of the semester is measured.

14. 14 Examples (cont’d) A study investigates whether there is a difference between male and female students in the amount of time they spend studying each week. The information is gathered from a random sample of male and female students on campus. The amount of time spent studying are normally distributed. A study investigates whether participating in sports positively influence self-esteem in young kids. A group of young kids is identified who have not played sports before but are now planning to begin participating in organized sports. A 50-item self-esteem inventory is given before they begin playing sports and administers the same test again after 6 months of playing sports. The self-esteem inventory is measured on an interval scale. In addition, scores on the inventory are normally distributed. A researcher is interested in comparing the GPA of students who volunteer the community service versus those who do not. The researcher assumes that those who perform community service will have higher GPA. GPA scores tend to be skewed.

15. 15 Factor Analysis Used to reduce a large number of variables to smaller sets comprising related variables A factor is a set of related variables representing a common underlying dimension The strength of the relationship between a variable and a factor is indicted by the factor loading –Factor loadings below.3 are usually not interpreted Factor rotation is used to make factors more distinct and easier to interpret

16. 16 Two types of factor analysis –Principle components analysis is used to reduce a large set of variables and to obtain an empirical summary of the data –Principle factors analysis is used when your research is driven by theoretical or empirical predictions Exploratory factor analysis is used to describe a large set of variables in simpler terms and you have no a priori ideas about variable clustering Confrimatory factor analysis is used when you specify how variables should cluster Factor Analysis