Marketing research - Statistics Project Example

Research Analysis Response: A Marketing Research Simulation Question Using the independent samples t-test in SPSS, I first sought to establish whether there are significant statistical differences between the performances of domestic and international students regarding item 5 of the survey data. The test is carried out at the 5% level of significance. In the survey, 48 domestic (mean = 5.7708, standard deviation = 2.2993) and 169 international students (mean = 4.6923, standard deviation = 2.6748) responded to item five of the survey.

This indicates that the international students’ response was a little lower than that of the fewer domestic students. To evaluate the significance of the test, I formulated the hypotheses:H0: There is no significant difference between the average scores of the domestic and international students regarding their responses to item 5 of the survey.H1: There is significant difference between the average scores of the domestic and international students regarding their responses to item 5 of the survey.

In order to decide which t-value to adopt, I checked over the results of the Levene’s test for equality of variances (Allingham & Rayner, 2011; Wuensch, 2014). The significance level (p-value = 0.002) of the F-statistic (9.847) is less than the 0.05 level of significance adopted for the entire test. Therefore, taking a default hypothesis that the variances are equal, these results confirm that this hypothesis should be rejected (Lee, 2013). Consequently, the variances are not equal. This advises my option to adopt the t-value -2.

762 which has a p-value 0.007. Since 0.007 is less than the default p-value (0.05) adopted for the test, I reject the null hypothesis. There is significant difference between the scores of domestic and international students.Question 2 The one-way analysis of variance (ANOVA) was carried out to establish whether there exists significant statistical difference between the students’ responses to item 5 of the survey based on their year of admission. All students in the survey were admitted into courses in the years 2003, 2004, 2005 and 2007.

The hypotheses:H0: There are no significant differences between performances/ responses of students based on the year that they were admitted into the university.H1: There are significant differences between performances/ responses of students based on the year they were admitted into the university.The significance level (p< 0.001) of the F-statistic is less than the significance level (p = 0.05) of the test. Therefore, I opt to reject the null hypothesis. There exists significant statistical difference for the performances of students admitted across different years.

According to the post-hoc results for multiple comparisons, significant differences exist for students admitted between the following pairs of years: 2003 and 2005, 2003 and 2007, 2004 and 2005, 2004 and 2007, and 2005 and 2007. For all these pairings, the significance levels of the mean differences were less than 0.001. In fact, the only non-significant differences were observed for the pair of years 2003 and 2004. Question 3 Correlation analysis was carried out to determine whether any of the units 1 – 19 are related to item number 20.

Based on the results, significant relationships are established to exist between item 20 and: item 1 (ρ = 0.258, p < 0.001), item 2 (ρ = 0.300, p < 0.001), item 4 (ρ = 0.175, p = 0.009), item 7 (ρ = 0.547, p < 0.001), item 8 (ρ = 0.255, p < 0.001), item 9 (ρ = 0.380, p < 0.001), item 10 (ρ = 0.193, p = 0.004), item 11 (ρ = 0.394, p < 0.001), item 12 (ρ = 0.388, p < 0.001), item 13 (ρ = 0.625, p < 0.001), item 14 (ρ = 0.667, p < 0.001), item 15 (ρ = 0.620, p < 0.001), item 16 (ρ = 0.

703, p < 0.001), item 17 (ρ = 0.621, p < 0.001), item 18 (ρ = 0.303, p < 0.001), and item 19 (ρ = 0.709, p < 0.001).ReferencesAllingham, D. & Rayner, J. (2011). Two-sample testing for equality of variances: Proceedings of the fourth annual ASEARC Conference, 17th – 18th February, 2011. University of Western Sydney, Paramatta, Australia.Lee, P. A. (2013). Independent samples t test and dependent samples t test. San Jose State University.Wuensch, K. L. (2014). Binary logistic regression with SPSS.

East Carolina University. Retrieved from core.ecu.edu/psyc/wuenschk/MV/Multreg/Logistic-SPSS.PDF. (Accessed 29th May, 2014).