This article provides a detailed analysis of SPSS with solved examples of correlation, chi-square and two-way ANOVA. It includes the hypothesis, interpretation and conclusion of each test. The subject matter is suitable for students of statistics and data analysis.
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Running Head: SPSS ANALYSIS Assignment 2 - SPSS Analysis Name of the student: Name of the university: Course ID:
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2SPSS ANALYSIS Table of Contents Part A: Pearson’s Correlation Analysis:..........................................................................................2 A. a) Hypothesis of Correlation test:...........................................................................................2 A. b) Interpretation and Conclusion of Correlation test:.............................................................3 Part B: Chi-square testing:...............................................................................................................4 B. a) Hypothesis of Chi-square test:............................................................................................4 B. b) Interpretation and Conclusion of Chi-square test:..............................................................5 Part C. Two-way ANOVA testing:..................................................................................................6 C. a) Hypothesis of Two-way ANOVA test:...............................................................................6 C. b) Interpretation and Conclusion of Two-way ANOVA test:.................................................7 Summary of the Analysis:...............................................................................................................8 Table of Tables Table 1: Pearson Correlation co-efficient matrix............................................................................3 Table 2: Cross tabulation.................................................................................................................5 Table 3: Chi-square test to find association or significance............................................................5 Table 4: Descriptive statistics of Two-way ANOVA test...............................................................7 Table 5: Tests of between-subjects effect of Two-way ANOVA test.............................................7
3SPSS ANALYSIS Part A: Pearson’s Correlation Analysis: Table1: Pearson Correlation co-efficient matrix A. a)Hypothesis of Correlation test: The correlation matrix considers ‘customer satisfaction index’ as dependent variable and ‘Age-group’ as well as ‘Gender type’ the independent variables. The correlation coefficients find the link between independent and dependent variables. The hypotheses are- Null hypothesis (H01):There exists no significant correlation between Age and Customer Satisfaction Index in brand X. Alternativehypothesis(HA1):ThereexistsasignificantcorrelationbetweenAgeand Customer Satisfaction Index in brand X.
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4SPSS ANALYSIS Null hypothesis (H02):There exists no significant correlation between Gender and Customer Satisfaction Index in brand X. Alternative hypothesis (HA2):There exists a significant correlation between Gender and Customer Satisfaction Index in brand X. A. b) Interpretation and Conclusionof Correlation test: The Pearson’s correlation coefficient finds the link or correlation between two numerical variables. Its values have a range of (-1) to 1. (-1) indicates absolute negative correlation and 1 indicates the absolute positive correlation between two factors. The value of correlation coefficient (-1) to 0 indicates the negative link and 0 to 1 indicates the positive link of two variables. The value of correlation coefficient (0 to±0.3) denotes the week correlation, (±0.3 to±0.5) denotes the moderately strong correlation and (±0.5 to±1) denotes the strong correlation between two variables. The level of significance of this hypothesis test is assumed to be 1%. The outcome table refers that- The Pearson’s correlation coefficient between Age and Customer Satisfaction Index (0.555) has p-value (0.0) that is lesser than 1%. Hence, the null hypothesis of insignificant correlation between these two factors can be rejected at 5% level of significance. Hence, Age and Customer Satisfaction Index are highly correlated to each other. The link of these two factors is moderate and positive. Hence, for higher age of any sample, the customer satisfaction also increases. Similarly, for lower age of any sample, the customer satisfaction also decreases. The Pearson’s correlation coefficient between Customer Satisfaction Index and Gender (0.322) has p-value (0.0) that is less than 1%. Therefore, the null hypothesis of insignificant correlation between these two factors can be rejected at 5% level of significance. Hence, Gender and Customer Satisfaction Index are moderately but significantly correlated to each other. It indicates that males (=1) are more satisfied as per greater satisfaction index rather than females (=0).
5SPSS ANALYSIS Part B: Chi-square testing: Table2: Cross tabulationof Age-group and Brand choice Table3: Chi-square test to find association or significance
6SPSS ANALYSIS B. a) Hypothesisof Chi-square test: The hypothesis is- Null hypothesis (H01):The two categorical variables ‘Age-group’ and ‘Brand choice’ are independent to each other. Alternative hypothesis (HA1):The two categorical variables ‘Age-group’ and ‘Brand choice’ have significant relationship to each other. B. b)Interpretation and Conclusion of Chi-square test: Chi-square test is a well-known non-parametric test of hypothesis. The Chi-square test is applicable to find the association between two categorical variables. Here, the Chi-square test considers two categorical variables that are ‘Age-group’ (three levels: less than 30 years, 31-50 years and >50 years) and ‘Brand choice’ (1 = Not buy and 2= Buy). The independent variable is ‘Brand choice’ and the dependent variable is ‘Age-group’. The level of significance of this hypothesis test is assumed to be 5%. The calculated Chi-square statistic (χ2(2)) = 30.102 with p-value = 0.0. Therefore, the null hypothesis of independence of two factors could be rejected with 95% confidence. It could be interpreted that different age-groups and various brand-choices are related to each other. These two factors are not at all independent to each other. It further concludes that there exists significant difference between observed and expected frequencies of the cross-tabulation table. Part C. Two-way ANOVA testing: Table4: Descriptive statistics of Two-way ANOVA test
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7SPSS ANALYSIS Table5: Tests of between-subjects effect of Two-way ANOVA test C. a) Hypothesisof Two-way ANOVA test: The hypothesis for the test-
8SPSS ANALYSIS Null hypothesis (H01):Different levels of independent variable ‘income’ has no significant effect on dependent variable ‘Customer Satisfaction Index for Brand X’. Alternative hypothesis (HA1):Different levels of independent variable ‘income’ has significant effect on dependent variable ‘Customer Satisfaction Index for Brand X’. Null hypothesis (H02):Different levels of independent variable ‘Age-group’ has no significant effect on dependent variable ‘Customer Satisfaction Index for Brand X’. Alternativehypothesis(HA2):Differentlevelsofindependentvariable‘Age-group’has significant effect on dependent variable ‘Customer Satisfaction Index for Brand X’. Null hypothesis (H03):For different levels of independent variable ‘Age-group’ with respect to various ‘income’ levels, the values of dependent variable ‘Customer Satisfaction Index for Brand X’ do not vary. Alternative hypothesis (HA3):For different levels of independent variable ‘Age-group’ with respect to various ‘income’ levels, the values of dependent variable ‘Customer Satisfaction Index for Brand X’ vary. C. b)Interpretation and Conclusion of Two-way ANOVA test: Thetwo-wayANOVAtestisappliedtotestthehypotheses.Theaveragecustomer satisfaction index is investigated with respect to income groups and age groups. The test investigates the equality and variability of customer satisfaction index with respect to the independent variables and their interaction effects. The dependent variable for this test is assumed to be ‘Customer Satisfaction Index for Brand X’ and the independent variables for this test is assumed to be ‘Income’ and ‘Age-group’. The ‘Two-way ANOVA test’ includes the results of ‘descriptives’ and ‘between-subjects effects’. The outcome tables help to interpret that-
9SPSS ANALYSIS The F-statistic of main effect ‘Income’ is 3.333 (d.f = 1) with p-value 0.7. The p-values is greater than 0.05. The null hypothesis could not be rejected with 95% confidence. Hence, no difference of customer satisfaction index is observed for different income levels (<$50,000 and ≥$50,000) when the effect of ‘Age-group’ is absent. The F-statistic of main effect ‘Age-group’ is 40.589 (d.f. = 2) with p-value 0.0. The p- value is less than 0.05. The null hypothesis could be rejected with 95% confidence. Therefore, difference of customer satisfaction index is observed for various age-groups (less than 30 years, 31-50 years and more than 50 years) while the effect of ‘Income’ is absent. The F-statistic of interaction effect of two main effects ‘Income’ and ‘Age-group’ is 0.023 (d.f. = 2) with p-value 0.977. The null hypothesis of insignificant effect of ‘Income’ and ‘Age-group’ could not be rejected with 95% probability. Hence, there exists significant differences of customer satisfaction indexes between various levels of ‘Age-group’ with respect to different levels of ‘Income’. Note that, the effects of both the independent variables are simultaneously present in this context. Summary of the Analysis: The SPSS dataanalysissummarizesthatage and customersatisfactionindex are positively and significantly correlated to each other. Similarly, gender type and customer satisfaction index are positively and significantly correlated. Also, it was found that brand choice (buying or not buying) is dependent upon the age-group of the samples. In the next stage it was discovered that variation in age-groups is a cause of variation in customer satisfaction index for brand X. However, the variation in income levels is not a cause of variation in customer satisfaction index for brand X. Further, the joint effect of age-groups and income groups is not a significant cause of customer satisfaction index for brand X. Overall it is found that age-groups are the significant predictors of customer satisfaction index in brand X; however, gender and income categories cannot truly predict the variability of customer satisfaction index.