ITEC6310 Research Methods in Information Technology Instructor: Prof. Z. Yang Course Website: c6310.htm Office: Tel 3049

22 T test The t-test procedure performs t-tests for one sample, two independent samples and two paired (dependent) samples. –The single-sample t-test compares the mean of the sample to a given number (which you supply). –Two independent samples t-test compares the difference in the means from the two groups to a given value (usually 0). In other words, it tests whether the difference in the means is 0. –The dependent-sample or paired t-test compares the difference in the means from the two variables measured on the same set of subjects to a given number (usually 0), while taking into account the fact that the scores are not independent.

3 One-sample t test example The police claims cars traveling past the speed limit sign average 55 km/h, but you think they are actually traveling much faster or much slower. You use a police radar gun and record the speed of the next nine cars that pass the sign: 45,60,65,55,65,60,50,70,60.

4 Two independent samples t test We have 200 observations from a sample of high school students with demographic information about the students, such as their gender (1=female 0=male), socio-economic status (ses, 1=low 2=middle 3=high), ethnic background race, 1=hispanic 2=asian 3=african-amer 4=white), type of school (schtyp, 1=public 2=private) and type of program (prog, 1=general 2=academic 3=vocational). It also contains a number of scores on standardized tests, including tests of reading (read), writing (write), mathematics (math) and social studies (socst). See hsb2.sav for more details. We compare the mean writing score between the group of female students and the group of male students.

5 Paired t test A paired (or ”dependent”) t-test is used when the observations are not independent of one another. In the example below, the same students took both the writing and the reading test. Hence, you would expect a relationship between the scores provided by each student. The paired t-test accounts for this. For each student, we are essentially looking at the differences in the values of the two variables and testing if the mean of these differences is equal to zero.

6 The chi-square test A chi-square test is used when you want to see if there is a relationship between two categorical variables. Remember that the chi-square test assumes that the expected value for each cell is five or higher. Using the data in hsb2.sav, let’s see if there is a relationship between the type of school attended (schtyp) and students’ gender (female).

7 Mann-Whitney U test The Mann-Whitney U test is a non-parametric analog to the independent samples t-test and can be used when you do not assume that the dependent variable is a normally distributed variable (you only assume that the variable is at least ordinal). We will use the same data variables hsb2.sav. We will not assume that write, our dependent variable, is normally distributed. Test the difference between the write scores of males and the write scores of females.

8 Wilcoxon signed rank sum test The Wilcoxon signed rank sum test is the non- parametric version of a paired samples t-test. You use the Wilcoxon signed rank sum test when you do not wish to make normal distribution assumption. We will use the same example as above, but we will not assume that read and write is normally distributed. Test the difference between read and write.

9 One-Way ANOVA (between subjects) This section shows how ANOVA can be used to analyze a one factor between-subjects design. If the null hypothesis (all population means are equal) is rejected, then it can be concluded that at least one of the population means is different from at least one other population means. It is important to consider the assumptions made by ANOVA: –The populations have the same variance. This assumption is called the assumption of homogeneity of variance. –The populations are normally distributed. –Each value is sampled independently from each other value.

10 One-Way ANOVA (between subjects) (Cont’d) We are interested in knowing whether one course is easier (lower score) than another.

11 Two-Way ANOVA (between subjects) Do courses have different effects in males and females? Data:

12 One-Way Repeated Measures ANOVA (within-subject) Did the scores of the three students differ? Data: one independent variable, e.g. score after study:

13 Correlation A correlation is useful when you want to see the relationship between two (or more) normally distributed interval variables assumed in Pearson Product-Moment Correlation analysis. For example, using hsb2.sav we can run a correlation between two continuous variables, read and write.

14 Point-Biserial Correlation The point biserial correlation is simply a special case of the Pearson product moment correlation applied to dichotomous and continuous variables. We run a correlation between a dichotomous variable, female, and a continuous variable, writing.

15 Spearman rank order correlation coefficient The Spearman Rank Order Correlation coefficient is a non-parametric measure of the strength and direction of association that exists between two variables measured on at least an ordinal scale. The test is used for either ordinal variables or for interval and ratio data that has failed the assumptions necessary for conducting the Pearson’s product-moment correlation such as variables are normally distributed. We can run a correlation between two continuous variables, read and write.

16 Phi Coefficient The phi coefficient is the equivalent of the correlation between nominal variables. we can run a correlation between two nominal variables, female and ses.

17 SPSS in-class exercise The researcher wants to address the environmental factors that affect the efficiency rating of the bank branches. The potential factors are the follows: –Region –Preferred language –Branch age –Average employment income in the branch area –Percentage of all families with employment income The data can be downloaded from the course web site. Identify H 0 and H a for the analysis and use SPSS to analyze the data.