Lab assignment 2
Part 1: Correlation Analysis

1. Explain when we run a correlation analysis? (1 Mark)

Answer:
We run a correlation to see if there are any significant associations between variables and/or before we do a regression analysis.

2. Interpret the correlations. Which variables are correlated? (hint: as p/sig values are provided use a cut-off of 0.05 to determine significance). Explain the nature of each relationship (8 Marks)

Answer: a) Inquiry and Memory variables are significantly correlated as suggested by their Sig value of .000 (p < .001) which is less than 0.05. The Pearson Correlation of .718 indicates a strong positive correlation. b) Satisfaction with rates and Memory variables are significantly correlated as suggest by their Sig value of 0.010 (p < .05) which is below 0.05. The Pearson Correlation of -.563 indicates a moderate negative correlation. c) Satisfaction with service and Service perception variables are significantly correlated as suggest by their Sig value of 0.000 (p < .001) which is well below 0.05. The Pearson Correlation of .710 indicates a strong positive correlation. d) Memory and Rates perception variables are significantly correlated as suggest by their Sig value of 0.010 (p < .05) which is below 0.05.The Pearson Correlation of .560 indicates a moderate positive correlation. 3. What are your recommendations to the manager (refer back to the decision problem) (3 Marks)

Answer:
Sun Insurance should not continue to run the advertisement because they cannot satisfy both of the boss’s two conditions. First, it was supposed to emphasise low rates in the hopes that those dissatisfied with their current rates would ring in and Sun would have a chance to sell callers. Second, the advert was to make the free phone number particularly memorable so that people could remember it and ring after the show they were watching was over. (Only the second condition has been met): a) The first point is not supported by the correlation analysis as there is no significant correlation found between satisfactions with rates and likely to ring; Sig value is .400 (p = .400), over the cut-off of 0.05 to determine significance. The Pearson Correlation of -.199 shows a weak negative correlation. b) The second point is supported by the correlation analysis as there is a significant correlation between the Memory and Likely to ring (inquiry) variables; Sig value is .000 (p < .001), which is under the cut-off of 0.05 to determine significance. Meaning that the free phone number is particularly memorable and people do ring Sun Insurance. The Pearson Correlations of .718 also shows a strong positive correlation between the two variables.

Part 2: Cross Tab/ Chi Square

1. Why has a cross-tab, Chi Square analysis been used? [1 Mark]

Answer:
A cross-tab has been used to determine an association between two nominal (categorical) variables. However, cross-tabs are observation tools only; a Chi-square analysis is a necessary statistical test to determine the significance of the association.

2. Interpret the Cross-tab for memory/inquiry, is there a relationship and why? [1 Marks]

Answer:
The cross tab analysis suggests there is a relationship between MEMORY and INQUIRY since there appears to be a clear pattern along the as the highlighted diagonal line (80%, 83.3%, 66.7%). This pattern indicates that when MEMORY is low, INQUIRY is low, when MEMORY is medium, INQUIRY is medium, and when MEMORY is high, INQUIRY is high.

3. Interpret the Chi-Square result for memory/inquiry, is there a relationship and why? [1 Marks]

Answer:
There is a significant relationship between the two variables, MEMORY and INQUIRY, since the Sig value is .002 (p = .002) which is less than 0.05 which is our cut-off for significance.

4. Interpret the Cross-tab for satrate/ inquiry, is there a relationship and why? [1 Mark]

Answer:
The cross tab analysis does not suggest there is a relationship between SATRATE and INQUIRY since there is no clear pattern (association) between the two variables. For example, when SATRATE is low, INQUIRY is medium, and when SATRATE is medium, INQUIRY is medium.

5. Interpret the Chi-Square result for satrate/inquiry, is there a relationship and why? [1 Marks]

Answer:
There is no significant relationship between the two variables, SATRATE and INQUIRY, since the Sig value is .202 (p = .202) which is greater than 0.05 which is our cut-off for significance.

6. What does the chi-square tell you that the cross-tab doesn’t? [1 Marks]

Answer:
The cross-tab by itself is an observational tool and can only suggest a relationship between variables. The Chi-square is the statistical test which calculates the Pearson’s Chi-square significance value to test whether there is a statistically significant relationship between the two variables in the cross tab. If the Pearson’s Chi-square significance value is less than 0.05 then a statistically significant relationship exist between two variables.

7. Make a recommendation to the manager [2 Marks]

Answer:
There is not enough evidence to satisfy the two criteria to continue to run the advertisements. The first criteria was supposed to emphasise low rates in the hopes that those dissatisfied with their current rates would ring in and Sun would have a chance to sell callers. However, after completing correlation, cross-tab and chi-square analysis, we are unable to find any significant relationship between these two variables. The three tests do suggest there is a significant relationship between memory and inquiry which satisfies the second criteria. The boss stated that he will only run the adverts if both conditions were satisfied, only one condition is true, therefore the advertisements should not continue to run.