quantitative data analysis using spss
- 1. QUANTITATIVE DATA ANALYSIS USING SPSS Lecture by Viraiyan Teeroovengadum Department of Management, Faculty of Law and Management, University of Mauritius Hypothesis Testing (Testing for Differences)
- 2. 3.0 3.1 One-Sample T Test (Parametric) 3.2 Independent-Samples T Test (Parametric) 3.3 Paired-Samples T Test (Parametric) 3.4 One-Way ANOVA (Parametric) 3.5 One-Sample Median Test (Non-Parametric) 3.6 Mann-Whitney U Test (Non-Parametric) 3.7 Wilcoxon Sign Rank Test (Non-Parametric) 3.8 Kruskal-Wallis Test (Non-Parametric) 3.9 Chi-Square Test (Non-Parametric) Lecture by Viraiyan Teeroovengadum Department of Management, Faculty of Law and Management, University of Mauritius Introduction
- 3. 3.1 One-Sample T Test Testing for differences between test value (hypothesised population value) and obtained value Lecture by Viraiyan Teeroovengadum Department of Management, Faculty of Law and Management, University of Mauritius
- 4. When to Use the Test?3.2 Lecture by Viraiyan Teeroovengadum Department of Management, Faculty of Law and Management, University of Mauritius The One-Sample T-Test can be used when: • We want to compare a sample result to a population test value • The variable is measured at scale level • Variable follows a normal distribution
- 5. 3.2 Independent-Samples T Test Testing for differences between two independent samples / groups Lecture by Viraiyan Teeroovengadum Department of Management, Faculty of Law and Management, University of Mauritius
- 6. When to Use the Test?3.2 Lecture by Viraiyan Teeroovengadum Department of Management, Faculty of Law and Management, University of Mauritius The Independent-Samples T Test can be used when: • The independent variable consists of two categories (considered as two samples) • The two samples/ groups are independent (the two means are from different cases) • The dependent variable is measured at scale level • The dependent variable follows a normal distribution for the two groups • The variances are homogeneous
- 7. Performing the test using SPSS3.2 Lecture by Viraiyan Teeroovengadum Department of Management, Faculty of Law and Management, University of Mauritius Preliminary Steps Analyse Compare Means Independent-Samples T Test
- 8. Performing the test using SPSS3.2 Lecture by Viraiyan Teeroovengadum Department of Management, Faculty of Law and Management, University of Mauritius Further Steps: 1. Transfer the dependent variable to the test variable list. 2. Transfer the grouping (categorical) variable 3. Define the grouping variable
- 9. Interpreting the results3.2 Lecture by Viraiyan Teeroovengadum Department of Management, Faculty of Law and Management, University of Mauritius As a general guideline the following should be reported when interpreting the results of an independent-samples t test: 1. The descriptive statistics (Mean and Standard Deviation) for both samples. Including a couple of statements. 2. Explain that an independent-samples t test shall be used to test for statistically significant differences between the two means 3. Hypotheses can be re stated 4. Report the results for assumptions of normality and equality of variances 5. Interpret the results of the t test, comparing the obtained p-value (significance value) to the significance level set. 6. Statement to describe the meaning of the result 7. Report the effect size
- 10. Interpreting the results (Example)3.2 Lecture by Viraiyan Teeroovengadum Department of Management, Faculty of Law and Management, University of Mauritius Research Question: Is there a difference between the perception of undergraduate and postgraduate students with respect to the quality of infrastructure at the University of Mauritius? Hypothesis: H0: There is no significant difference between the perception of undergraduate and postgraduate students with respect to the quality of infrastructure at the University of Mauritius (µundergraduate = µpostgraduate) H1: There is a significant difference between the perception of undergraduate and postgraduate students with respect to the quality of infrastructure at the University of Mauritius (µundergraduate ≠ µpostgraduate)
- 11. Interpreting the results (Example)3.2 Lecture by Viraiyan Teeroovengadum Department of Management, Faculty of Law and Management, University of Mauritius
- 12. Interpreting the results3.2 Lecture by Viraiyan Teeroovengadum Department of Management, Faculty of Law and Management, University of Mauritius Interpretation of the results: The undergraduate students group (N=97) had a score of M=2.99 with regards to their perception of infrastructure quality at UoM. By comparison, the mean score for postgraduate students was lower (M=2.86). To test the hypothesis that undergraduate students and postgraduate students had statistically significantly different mean perception of infrastructure quality, an independent- samples t test was performed. The undergraduate and postgraduate distributions were sufficiently normal for the purposes of conducting a t test. Moreover, the assumption of homogeneity of variances was tested and satisfied via Levene’s F Test, F(205) = 0.04, p= 0.947. The independent-samples t test was associated with a statistically significant effect, t(205) = -2.08, p = 0.038. Thus, the mean score for postgraduate students was statistically significantly lower than the mean score for undergraduate students. In other words, the quality of infrastructure at UoM is perceived to be lower by postgraduate students as compared to undergraduate students.
- 13. 3.3 Paired-Samples T Test Testing for differences between two dependent samples / groups Lecture by Viraiyan Teeroovengadum Department of Management, Faculty of Law and Management, University of Mauritius
- 14. When to Use the Test?3.3 Lecture by Viraiyan Teeroovengadum Department of Management, Faculty of Law and Management, University of Mauritius The Paired-Samples T Test can be used when: • The independent variable consists of two categories (considered as two samples) • The two samples/groups are related/dependent (the two means are from the same cases but correspond to scores measured at different points in time) • The dependent variable is measured at scale level • The difference score follows a normal distribution
- 15. Performing the test using SPSS3.3 Lecture by Viraiyan Teeroovengadum Department of Management, Faculty of Law and Management, University of Mauritius Preliminary Steps Analyse Compare Means Paired-Samples T Test
- 16. Performing the test using SPSS3.3 Lecture by Viraiyan Teeroovengadum Department of Management, Faculty of Law and Management, University of Mauritius Further Steps: 1. Transfer the first variable (time period 1) to variable 1 2. Transfer the second variable (time period 2) to variable 2
- 17. Interpreting the results3.3 Lecture by Viraiyan Teeroovengadum Department of Management, Faculty of Law and Management, University of Mauritius As a general guideline the following should be reported when interpreting the results of a paired- samples t test: 1. The descriptive statistics (Mean and Standard Deviation) for both samples (time periods). 2. Explain that a paired-samples t test shall be used to test for statistically significant differences between the two means 3. Hypotheses can be re stated 4. Report the results for assumptions of normality of score differences 5. Interpret the results of the t test, comparing the obtained p-value (significance value) to the significance level set. 6. Statement to describe the meaning of the result 7. Report the effect size
- 18. Interpreting the results (Example)3.3 Lecture by Viraiyan Teeroovengadum Department of Management, Faculty of Law and Management, University of Mauritius Research Question: Has there been an improvement in the academic performance of students in 2012 as compared to 2013? Hypothesis: H0: There is no significant improvement in the academic performance of students in 2012 as compared to their academic performance in 2013 (µ2013 = µ2012) H1: There is a significant improvement in the academic performance of students in 2012 as compared to their academic performance in 2013 (µ2013 > µ2012)
- 19. Interpreting the results (Example)3.3 Lecture by Viraiyan Teeroovengadum Department of Management, Faculty of Law and Management, University of Mauritius Paired Samples Statistics Mean N Std. Deviation Std. Error Mean Pair 1 Academic Performance_Average Marks in 2012 51.28 106 20.533 1.994 Academic Performance _ Average Marks in 2013 57.15 106 18.777 1.824 Paired Samples Test Paired Differences t df Sig. (2- tailed)Mean Std. Deviation Std. Error Mean 95% Confidence Interval of the Difference Lower Upper Pair 1 Academic Performance_Aver age Marks in 2012 - Academic Performance _ Average Marks in 2013 -5.868 12.521 1.216 -8.279 -3.456 -4.825 105 .000
- 20. Interpreting the results3.3 Lecture by Viraiyan Teeroovengadum Department of Management, Faculty of Law and Management, University of Mauritius Interpretation of the results: To test the hypothesis that the academic performance of students in 2012 (M= 51.28, SD = 20.53) had improved significantly in 2013 (M= 57.15, SD = 18.78), a paired-samples t test was performed. Prior to conducting the analysis, the assumption of normally distributed difference scores was examined. The assumption was considered satisfied, as the skewness and kurtosis were estimated at 0.10 and -1.12, respectively, which is less than the maximum allowable values for a t-test (i.e, skewness │2.0 │ and kurtosis │9.0 │; Posten, 1984). The null hypothesis of equal academic performance means was rejected, t = - 4.83, p < 0.05. Thus the mean of academic performance of students in 2013 was statistically significantly higher than the mean of academic performance in 2012. In other words, students performed better in 2013 than in 2012.
- 21. 3.4 One-Way ANOVA Testing for differences between more than 2 independent samples / groups Lecture by Viraiyan Teeroovengadum Department of Management, Faculty of Law and Management, University of Mauritius
- 22. When to Use the Test?3.4 Lecture by Viraiyan Teeroovengadum Department of Management, Faculty of Law and Management, University of Mauritius The One-Way ANOVA can be used when: • The independent variable consists of more than two categories (considered as more than two samples) • The k samples/ groups are independent (the k means are from different cases) • The dependent variable is measured at scale level • The dependent variable follows a normal distribution for each sample • Variances are homogeoneous
- 23. Performing the test using SPSS3.4 Lecture by Viraiyan Teeroovengadum Department of Management, Faculty of Law and Management, University of Mauritius Preliminary Steps Analyse Compare Means One-Way ANOVA
- 24. Performing the test using SPSS3.4 Lecture by Viraiyan Teeroovengadum Department of Management, Faculty of Law and Management, University of Mauritius Further Steps: 1. Transfer the dependent variable to the dependent list. 2. Transfer the grouping (categorical) variable to factor list 3. Click on Post Hoc and select Tukey
- 25. Interpreting the results3.4 Lecture by Viraiyan Teeroovengadum Department of Management, Faculty of Law and Management, University of Mauritius As a general guideline the following should be reported when interpreting the results of a One-Way ANOVA: 1. The descriptive statistics (Mean and Standard Deviation) for each samples. Including a couple of statements. 2. Explain that a one-way ANOVA test shall be used to test for statistically significant differences between the multiple means 3. Hypotheses can be re stated 4. Report the results for assumptions of normality and equality of variances 5. Interpret the results of the F test, comparing the obtained p-value (significance value) to the significance level set. 6. Statement to describe the meaning of the result 7. Report the effect size
- 26. Interpreting the results (Example)3.4 Lecture by Viraiyan Teeroovengadum Department of Management, Faculty of Law and Management, University of Mauritius Research Question: Is there a difference between the four ISO certified schools with regards to perceived ISO Benefits? Hypothesis: H0: There is no significant difference between the four ISO certified schools with regards to perceived ISO Benefits H1: There is a significant difference between the four different ISO certified schools with regards to perceived ISO Benefits
- 27. Interpreting the results (Example)3.4 Lecture by Viraiyan Teeroovengadum Department of Management, Faculty of Law and Management, University of Mauritius ANOVA Benef Sum of Squares df Mean Square F Sig. Between Groups 28.081 3 9.360 27.782 .000 Within Groups 37.398 111 .337 Total 65.479 114 Descriptives Benef N Mean Std. Deviation Std. Error 95% Confidence Interval for Mean Minimu m Maxim umLower Bound Upper Bound Hindu Girls College 38 3.6661 .54801 .08890 3.4860 3.8462 2.38 5.00 Prof Basdeo Bissoondoyal Secondary School 47 4.3191 .46227 .06743 4.1834 4.4549 3.50 5.00 Mauritius College 17 3.2537 .86390 .20953 2.8095 3.6979 1.50 4.75 SSS Sodnac 13 2.9375 .61343 .17014 2.5668 3.3082 2.00 4.00 Total 115 3.7897 .75788 .07067 3.6497 3.9297 1.50 5.00
- 28. Interpreting the results (Example)3.4 Lecture by Viraiyan Teeroovengadum Department of Management, Faculty of Law and Management, University of Mauritius Multiple Comparisons Dependent Variable: Benef Tukey HSD (I) Name of School/Department (J) Name of School/Department Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval Lower Bound Upper Bound Hindu Girls College Prof Basdeo Bissoondoyal Secondary School -.65303* .12663 .000 -.9833 -.3227 Mauritius College .41244 .16937 .076 -.0293 .8542 SSS Sodnac .72862* .18650 .001 .2421 1.2151 Prof Basdeo Bissoondoyal Secondary School Hindu Girls College .65303* .12663 .000 .3227 .9833 Mauritius College 1.06547* .16428 .000 .6370 1.4940 SSS Sodnac 1.38165* .18189 .000 .9072 1.8561 Mauritius College Hindu Girls College -.41244 .16937 .076 -.8542 .0293 Prof Basdeo Bissoondoyal Secondary School -1.06547* .16428 .000 -1.4940 -.6370 SSS Sodnac .31618 .21386 .454 -.2417 .8740 SSS Sodnac Hindu Girls College -.72862* .18650 .001 -1.2151 -.2421 Prof Basdeo Bissoondoyal Secondary School -1.38165* .18189 .000 -1.8561 -.9072 Mauritius College -.31618 .21386 .454 -.8740 .2417 *. The mean difference is significant at the 0.05 level.
- 29. Interpreting the results3.4 Lecture by Viraiyan Teeroovengadum Department of Management, Faculty of Law and Management, University of Mauritius Interpretation of the results: The descriptive statistics associated with perceived benefits of ISO certification across the four schools are reported in table x. It can be seen that the SSS Sodnac school was associated with the numerically smallest mean level of perceived ISO benefits (M=2.94) and the Prof Basdeo Bissoondoyal Secondary School was associated with numerically the highest mean level of perceived ISO benefits (M=4.32). In order to test the hypothesis that school difference had an effect on perceived ISO benefits, a one-way between-groups ANOVA was performed. Prior to conducting the ANOVA, the assumption of normality was evaluated and determined to be satisfied as the three groups’ distributions were associated with skewness and kurtosis less that │2.0 │ and │9.0 │, respectively (Schmider et al., 2010). The assumption of homogeneity of variances was tested and was not satisfied, based on Levene’s F Test, F(3, 111) = 3.43, p = 0.019 < 0.05. The Welch Test was therefore used to account for that.
- 30. Interpreting the results3.4 Lecture by Viraiyan Teeroovengadum Department of Management, Faculty of Law and Management, University of Mauritius Interpretation of the results: The independent between-groups ANOVA yielded a statistically significant effect, F(3, 35.07) = 27.79, p < 0.05, = 0.429. Thus the null hypothesis of no differences between the means was rejected, and 42.9% of the variance in perceived ISO benefits was accounted for by the school difference. To evaluate the nature of the differences between the four means further, the statistically significant ANOVA was followed up with a multiple comparison test. 2