module 6_7 application assignments
DESCRIPTION
StatisticsTRANSCRIPT
Example Data
Example Data
A Survey of 50 Companies
In January 08, fifty customers of a lumber manufacturer were surveyed regarding their satisfaction with products and service. These customers buy from the supplier and sell to retail chains like Home Depot and Lowes. Shortly after, the manufacturing company was sold. In June 08, the customers were telephoned and interviewed and were asked to rate overall satisfaction again.
VariablePositionLabelMeasurement Level
id1IDScaleParticipant ID number
delivery2Delivery ReliabilityScaleOn a scale of 1 to 10, how would you rate the reliability of delivery of your orders?
Prodsat3Product SatisfactionScaleOn a scale of 1 to 10, how would you rate your satisfaction with the quality of your most recently purchased products?
Techsat4Technical SupportScaleOn a scale of 1 to 10, how would you rate your satisfaction with the technical support?
Salesat5Salesforce ScaleOn a scale of 1 to 10, how would you rate your satisfaction with the sales support?
Size6Firm SizeOrdinal0 = small (less than 100 emp.) 1 = large (100 or more)
Usage7Usage LevelScaleWhat percent of your purchases are from our company?
Satjan8Overall Satisfaction in JanuaryScaleOn a scale of 1 to 7, rate your overall satisfaction with your most recent purchasing experience.
Satjun8Overall Satisfaction in JuneScaleOn a scale of 1 to 7, rate your overall satisfaction with your most recent purchasing experience.
Structure10Structure of ProcurementNominalHow your purchasing is structured?0 = Decentralized; 1 = Centralized
OwnType11Type of OwnershipNominal0 = Publicly Traded; 1 Privately owned
PurType12Type of PurchasingNominal1 = Private Label; 2 = Company Brand; 3 = Both
Variables in the working file
For each research question, describe in your Microsoft Word document the application of the seven steps of the hypothesis testing model.
Step 1: State the hypothesis (null and alternate).Step 2: State your alpha (unless requested otherwise, this is always set to alpha = .05).Step 3: Collect the data (use one of the data sets).Step 4: Calculate your statistic and p-value. (This is where you run spss and examine your output files.) Step 5: Accept or reject the null hypothesis. (This is where you report the results of your analyses t (df) = t-value, p = sig. level.) Step 6: Assess the Risk of Type I and Type II Error. (Did the data meet the assumptions of the statistic, effect size, and sample size?)Step 7: State your results in APA style and format.
Example 7
Question 1: Is there a relationship among the variables measuring different aspects of customer satisfaction?1. Run a Pearson correlation matrix using delivery reliability, product satisfaction, technical support, sales satisfaction, overall satisfaction in January and overall satisfaction in June.
Correlations
Delivery ReliabilityProduct SatisfactionTechnical SupportSalesforceOverall Satisfaction in JanuaryOverall Satisfaction in June
Delivery ReliabilityPearson Correlation1.193.436**.112.206.628**
Sig. (2-tailed).180.002.439.152.000
N505050505050
Product SatisfactionPearson Correlation.1931.317*.726**.195.484**
Sig. (2-tailed).180.025.000.174.000
N505050505050
Technical SupporPearson Correlation.436**.317*1.133.340*.555**
Sig. (2-tailed).002.025.356.016.000
N505050505050
SalesforcePearson Correlation.112.726**.1331.173.326*
Sig. (2-tailed).439.000.356.229.021
N505050505050
Overall Satisfaction in JanuaryPearson Correlation.206.195.340*.1731.479**
Sig. (2-tailed).152.174.016.229.000
N505050505050
Overall Satisfaction in JunePearson Correlation.628**.484**.555**.326*.479**1
Sig. (2-tailed).000.000.000.021.000
N505050505050
**. Correlation is significant at the 0.01 level (2-tailed).
*. Correlation is significant at the 0.05 level (2-tailed).
2. Create a scatter plot for the following pairs: (1) delivery reliabilityoverall satisfaction in June; (2) product satisfactionoverall satisfaction in June; and delivery reliabilityproduct satisfaction.
The scatter diagram suggest that there is a weak positive correlation between the two variables.
The scatter diagram suggest that there is a weak positive correlation between the two variables.
The scatter diagram suggest that there is a weak positive correlation between the two variables.
3. Report the descriptive statistics, assumptions tests, as well as tests of statistical significance identify of positive and negative relationships.
Descriptive Statistics
MeanStd. DeviationN
Delivery Reliability4.341.67350
Product Satisfaction5.341.15450
Technical Support2.88.89550
Sales force2.66.84850
Overall Satisfaction in January3.581.37250
Overall Satisfaction in June4.70.95350
Students t test is adopted to check whether there is any significant positive correlation between the variables.
H0: Correlation coefficient =0H1: Correlation coefficient >0 (One sided hypothesis)
Test Statistic used is t test Significance level =0.05 Decision rule : Reject the null hypothesis if the p value is less than the significance level.
The Correlation coefficient with p value of the one tailed test is given below. Correlations
Delivery ReliabilityProduct SatisfactionTechnical SupportSalesforceOverall Satisfaction in JanuaryOverall Satisfaction in June
Delivery ReliabilityPearson Correlation1.193.436**.112.206.628**
Sig. (1-tailed)0.090.0010.2190.075.000
Product SatisfactionPearson Correlation.1931.317*.726**.195.484**
Sig. (1-tailed)0.0900.0125.0000.087.000
Technical SupportPearson Correlation.436**.317*1.133.340*.555**
Sig. (1-tailed).0010.01250.178.016.000
Sales forcePearson Correlation.112.726**.1331.173.326*
Sig. (1-tailed)0.219.0000.1780.11450.015
Overall Satisfaction in JanuaryPearson Correlation.206.195.340*.1731.479**
Sig. (1-tailed)0.0750.087.0160.1145.000
Overall Satisfaction in JunePearson Correlation.628**.484**.555**.326*.479**1
Sig. (1-tailed).000.000.000.0.015.000
**. Correlation is significant at the 0.01 level (2-tailed).
*. Correlation is significant at the 0.05 level (2-tailed).
Conclusion The t test for the significant correlation indicates that the correlation between Product satisfaction- Delivery reliability, Sales force- Delivery reliability, Overall satisfaction- Delivery reliability, Over all satisfaction Product satisfaction ,Sales force Technical support, Overall satisfaction in January Technical support are insignificant.
Question 2: Does delivery reliability impact overall satisfaction in June?1. Run a simple regression using delivery reliability as the independent variable and overall satisfaction in June as the dependent variable.
Coefficientsa
ModelUnstandardized CoefficientsStandardized CoefficientstSig.
BStd. ErrorBeta
1(Constant)3.147.29710.595.000
Delivery Reliability.358.064.6285.596.000
a. Dependent Variable: Overall Satisfaction in June
The estimated regression model is Overall Satisfaction in June = 3.147 +0.358 * Delivery Reliability
Model Summaryb
ModelRR SquareAdjusted R SquareStd. Error of the Estimate
1.628a.395.382.749
a. Predictors: (Constant), Delivery Reliability
b. Dependent Variable: Overall Satisfaction in June
The model adequacy measure R2 suggests that 39.5% variability in Overall Satisfaction in June can be explained by the regression model.
2. Report the descriptive statistics, assumptions tests (scatter plots), as well as tests of statistical significance.
Descriptive Statistics
MeanStd. DeviationN
Overall Satisfaction in June4.70.95350
Delivery Reliability4.341.67350
Correlations
Overall Satisfaction in JuneDelivery Reliability
Pearson CorrelationOverall Satisfaction in June1.000.628
Delivery Reliability.6281.000
Sig. (1-tailed)Overall Satisfaction in June..000
Delivery Reliability.000.
NOverall Satisfaction in June5050
Delivery Reliability5050
The Correlation coefficient between Overall Satisfaction in June and delivery reliability is positive with 0.628. The regression coefficient of Delivery Reliability on Overall Satisfaction in June can be interpreted as For a unit increase in Delivery Reliability, the Overall Satisfaction in June increase by 0.358 unitsThe significance of this regression coefficient is tested using the t testH0: Regression coefficient =0H1: Regression coefficient > 0
Significance level =0.05Decision rule: Reject the null hypothesis if the p value is less than the significance level.Details T statistic =5.596P value =0.000Conclusion: Reject the null hypothesis. The sample provides enough evidence to support the claim that Delivery Reliability has a significant effect on Overall Satisfaction in June.
The assumption for the validity of regression analysis is checked using the residual analysis. The histogram and normal probability plots suggest that the residuals are normally distributed. The homogeneity of variance assumption is valid as the plots of residuals against the predicted values are random.
Question 3: Does delivery reliability and product satisfaction impact overall satisfaction in June?1. Run a multiple regression using delivery reliability as the independent variable and overall satisfaction in June as the dependent variable.
Coefficientsa
ModelUnstandardized CoefficientsStandardized CoefficientstSig.
BStd. ErrorBeta
1(Constant)1.662.4793.467.001
Delivery Reliability.316.058.5565.464.000
Product Satisfaction.312.084.3773.712.001
a. Dependent Variable: Overall Satisfaction in June
The estimated regression model is
Overall Satisfaction in June =1.662+ 0.316 * Delivery Reliability+0.312* Product Satisfaction
Model Summaryb
ModelRR SquareAdjusted R SquareStd. Error of the Estimate
1.729a.532.512.666
a. Predictors: (Constant), Product Satisfaction, Delivery Reliability
b. Dependent Variable: Overall Satisfaction in June
The model adequacy measure R2 suggests that 53.2 % variability in Overall Satisfaction in June can be explained by the regression model.
2. Report the descriptive statistics, assumptions tests (scatter plots), as well as tests of statistical significance.
Descriptive Statistics
MeanStd. DeviationN
Overall Satisfaction in June4.70.95350
Delivery Reliability4.341.67350
Product Satisfaction5.341.15450
Correlations
Overall Satisfaction in JuneDelivery ReliabilityProduct Satisfaction
Pearson CorrelationOverall Satisfaction in June1.000.628.484
Delivery Reliability.6281.000.193
Product Satisfaction.484.1931.000
Sig. (1-tailed)Overall Satisfaction in June..000.000
Delivery Reliability.000..090
Product Satisfaction.000.090.
NOverall Satisfaction in June505050
Delivery Reliability505050
Product Satisfaction505050
The Correlation coefficient between Overall Satisfaction in June and delivery reliability is positive with 0.628 and Overall Satisfaction in June and Product satisfaction is 0.484 . The regression coefficient of Delivery Reliability on Overall Satisfaction in June can be interpreted as For a unit increase in Delivery Reliability, the Overall Satisfaction in June increase by 0.358 units,. For a unit increase in product satisfaction, the Overall Satisfaction in June increase by 0.312 units,.
The significance of this regression coefficient is tested using the t testH0: Regression coefficient =0H1: Regression coefficient > 0
Significance level =0.05Decision rule: Reject the null hypothesis if the p value is less than the significance level.Details Delivery ReliabilityProduct SatisfactionT statistic5.4643.712P value 0.0000.001
Conclusion: Reject the null hypothesis. The sample provides enough evidence to support the claim that Delivery Reliability and product satisfaction has a significant effect on Overall Satisfaction in June.
The assumption for the validity of regression analysis is checked using the residual analysis. The histogram and normal probability plots suggest that the residuals are normally distributed. The homogeneity of variance assumption is valid as the plots of residuals against the predicted values are random.
Write a brief conclusion statement summarizing your results. What can you tell this manufacturing company about the relationship among satisfaction variables? Are there any areas they need to improve? Does adding a second variable to the regression equation increase prediction of customer satisfaction?
The regression analysis indicates that both Delivery Reliability and Product SatisfactionSatisfaction variables have a significant effect on overall satisfaction in June. The multiple regression models is able to explain 52.3% variability in overall satisfaction in June. We may add more explanatory variables to improve the model adequacy to a higher level.It can be noted that the model adequacy increase from 39.5% to 52.3% due to the addition of Product Satisfaction as the second explanatory variable .
Example 8
Question 1: Before the change of ownership, the company was encouraging its customers to reduce private labeling as a way to reduce cost of goods sold. Explore the distribution of customers by purchase type. Does the distribution of customers (private label, brand label, or both) differ from what one would expect by chance? Does if differ they expect more brand labeling?
Type of Purchasing
Observed NExpected NResidual
Private label1816.71.3
Company Brand1816.71.3
Both1416.7-2.7
Total50
H0: There is no significant difference in the number of customers in the three categories.H1: There is significant difference in the number of customers in the three categories.Test Statistic used is Chi square test for goodness of fit.Significance level =0.05Decision rule: Reject the null hypothesis if the p value is less than the significance level.Details
Test Statistics
Type of Purchasing
Chi-Square.640a
df2
Asymp. Sig..726
a. 0 cells (.0%) have expected frequencies less than 5. The minimum expected cell frequency is 16.7.
Conclusion: Fails to reject the null hypothesis. The sample does not provides enough evidence to support the claim that there is significant difference in the number of customers in the three categories.
Question 2: Run a chi square goodness of fit using purchase type as the variable with all categories equal for the expected value.1. Run a chi square goodness of fit using purchase type as the variable with all categories unequal with 12, 26, and 12 as the expected values.
Type of Purchasing
Observed NExpected NResidual
Private label1812.06.0
Company Brand1826.0-8.0
Both1412.02.0
Total50
2. Report the observed and expected values and the tests of statistical significance.
H0: The number of customers in the three categories are (12,26,12).H0: The number of customers in the three categories are different from (12,26,12).
Significance level =0.05Decision rule: Reject the null hypothesis if the p value is less than the significance level.Details Test Statistics
Type of Purchasing
Chi-Square5.795a
df2
Asymp. Sig..055
a. 0 cells (.0%) have expected frequencies less than 5. The minimum expected cell frequency is 12.0.
Conclusion: Fails to reject the null hypothesis. The sample does not provides enough evidence to support the claim that there is significant difference in the number of customers in the three categories are different from (12,26,12).
Question 3: Is there a relationship between the company size and type of procurement?Run chi-square independence test (crosstabs) using company size and type of procurement. Use the chi square and the phi coefficient to evaluate the relationship and statistical significance. Report the observed and expected values and the tests of statistical significance.
H0: There is no association between company size and type of procurement.H1: There is association between company size and type of procurement.
Test Statistic used is Chi square test for independence Significance level =0.05Decision rule: Reject the null hypothesis if the p value is less than the significance level.Details
Firm Size * Structure of Procurement Crosstabulation
Count
Structure of ProcurementTotal
DecentralizedCentralized
Firm SizeSmall141327
Large121123
Total262450
Firm Size * Structure of Procurement Crosstabulation
Expected Count
Structure of ProcurementTotal
DecentralizedCentralized
Firm SizeSmall14.013.027.0
Large12.011.023.0
Total26.024.050.0
ValuedfAsymp. Sig. (2-sided)
Pearson Chi-Square.001a1.982
Continuity Correctionb.00011.000
Likelihood Ratio.0011.982
Fisher's Exact Test
Linear-by-Linear Association.0011.982
N of Valid Cases50
Conclusion: Fails to reject the null hypothesis. The sample does not provide enough evidence to support the claim that there is association between company size and type of procurement. The phi and chi square coefficients indicate jointly the strength and the significance of a relationship. The value of Phi is very small indicating that there is no relationship between company size and type of procurement.
Symmetric Measures
ValueApprox. Sig.
Nominal by NominalPhi-.003.982
Cramer's V.003.982
N of Valid Cases50