Data Analysis Using SPSS EDU5950 SEM1 2014-15 Test of Differences Between Means

1. Data Analysis Using SPSSEDU5950SEM1 2014-15Test of Differences Between Means Assoc. Prof. Dr. Rohani Ahmad Tarmizi Institute for Mathematical Research/ Faculty of Educational Studies UPM

2. Overview First objective – learn what is important in choosing analyses, and information about some of the more common statistical analyses Second objective – will get a data set and walk through how to conduct some analyses of differences between means

3. Statistical Tools For Inferential Statistics • PARAMETRIC TESTS: • Test of hypothesis of differences between means - Z-test, t-test, F-test, MANOVA • Test of hypothesis of relationship – Pearson r, Point-biserial, Regression • NON-PARAMETRIC TESTS: • Chi-square, • Mann-Whitney, • Kruskal Wallis, • Spearman rho, • Cramer’s V, Lambda, dll.

4. In most research projects, it is likely that you will use quite a variety of different types of statistics, depending on the question you are addressing and the nature (level of measurement) of the data that you have. • It is therefore important that you have a basic understanding of the different statistical tools, the type of objectives/research questions/hypotheses to address and the underlying assumptions and requirements.

5. Summary of Statistical Tools For Descriptive Analyses • Frequency/percentage table, • Pie or bar Charts, • Histogram • Frequency Polygon, • Cross-tabulation • Scatter diagram • Mean, Median, Mode, Maximum, Minimum • Range, Variance, Standard Deviation, Coefficient of variation, Standard Scores

6. ACTIVITY 1- COMPARISON OF MEANS OF TWO GROUPS

7. EXPLORING DIFFERENCES BETWEEN TWO GROUPS • t-test • t-tests are used when you have two groups (e.g. males and females) or two sets of data (before and after), and you wish to compare the mean score on some continuous variable. • There are two main types of t-tests. • Paired sample t-tests (also called repeated measures) are used when you are interested in changes in scores for subject tested at Time 1, and then at Time 2 (often after some intervention or event). The samples are ‘related’ because they are the same people tested each time. • Independent sample t-tests are used when you have two different (independent) groups of people (males and females), and you are interested in comparing their scores. In this case, you collect information on only one occasion, but from two different sets of people.

8. TO MAKE COMPARISONS BETWEEN GROUPS ON ANY MEASURED VARIABLES AT INTERVAL AND RATIO LEVEL • CLICK ANALYZE =>COMPARE MEANS • You will get the following Sub-menus • MEANS • ONE-SAMPLE T-TEST • INDEPENDENT SAMPLES T-TEST • PAIRED SAMPLES T-TEST • ONE-WAY ANOVA

10. To Compare Means of Two Groups • Click: Analyze>Compare means>Independent T-test • You will get a Independent T-test dialog box • Select your variables – Test variables & Group variables • Click OK

11. DECISION MATRIX

12. DECISION MATRIX

15. To Compare Means of Two Dependent Groups • Click: Analyze>Compare means>Paired Sample T-test • You will get a Paired Sample T-test dialog box • Select your variables – Paired variables • Click OK

16. DECISION MATRIX

17. ACTIVITY 2 ANOVA

18. EXPLORING DIFFERENCES BETWEEN GROUPS One-way analysis variance • One-way analysis variance is similar to a t-test, but is used when you have two or more groups and you wish to compare their mean scores on a continuous variable. • It is called one-way because you are looking at the impact of only one independent variable on your dependent variable. • A one-way analysis of variance (ANOVA) will let you know whether your groups differ, but it won’t tell you where the significant difference is (gp1/gp2, gp3/gp4 etc). • You can conduct post-hoc comparisons to find out which groups are significantly different from one another. • You could also choose to test differences between specific groups, rather than comparing all the groups by using planned comparisons. Similar to t-tests, there are two types of one-way ANOVAs: repeated measures ANOVA (same people on more than two occasions), and between-groups (or independent samples) ANOVA, where you are comparing the mean scores of two or more different groups of people.

20. To Compare Means of Three or More Groups • Click: Analyze>Compare means>One-Way ANOVA • You will get a One-Way ANOVA dialog box • Select your variables – Dependent variables & Factor or Group variables • Click: Options • Click OK

21. DECISION MATRIX

22. Two-way analysis of variance • Two-way analysis of variance allows you to test the impact of two independent variables on one dependent variable. • The advantage of using the two-way ANOVA is that it allows you to test for an interaction effect – that is, when the effect of one independent variable is influenced by another; for example, when you suspect that optimism increases with age, but only for males. • It also tests for ‘main effects’ – that is, the overall effect of each independent variable (e.g. sex, age). • There are two different two-way ANOVAs: between - groups ANOVA (when the groups are different) and repeated measures ANOVA (when the same peoples are tested on more than one occasion). • Some research designs combine both between-group and repeated measures in the one study. These are referred to as ‘Mixed Between-Within Designs’, or ‘Split Plot’.

24. Click Analyze => General Linear Model => Univariate… 2. At the Univariate dialog box, enter Y into Dependent variable box, and X1 and X2 into Fixed Factors box.

25. 3. Click the option button and select the followings

31. Presenting the results of Factorial ANOVA • A factorial ANOVA was conducted to explore the impact of gender and leadership style of principals on their teachers’ job stress level. Three leadership style was explored viz-a-viz autocratic, democratic and laisserfaire style. There was a statistically significant main effect for both gender and leadership style on teachers’ job stress level. Therefore gender of principals has an impact on teachers’ job stress level significantly, F (1,60) = 12.22, p = .001. In addition, there is also significant impact of principals’ leadership style on job stress of teachers significantly, F (2,60) = 10.61, p = .000. However the interaction effect between gender and leadership style was not statistically significant F ((2, 60) = 1.42, p = .25.

32. Post-hoc comparison using Tukey HSD test indicated that the mean job stress score for the female (M=78.63, SD=8.98) is significantly higher than the male teachers (M=71.93, SD=8.22). The mean job stress scores between the three groups of leadership style indicated that the autocratic style impacted significantly higher stress level compared to democratic and laisserfaire. However there is no significant difference in stress level between the democratic and lasserfaire leadership style.

33. REPEATED MEASURES ANOVA FOLLOW THE PROCEDURES ON THE NEXT SLIDE

38. A repeated measures ANOVA was carried out. Assumptions of normality, homogeneity of variance and sphericity were met. Results showed that differences between conditions were significant, F (2,35) = 41.424, p=.001. An overall effect size of .588 (partial eta-squared) showed that 60% of the variation in fear of statistics scores can be accounted by differing time.