MODULE 6_7 Application Assignments

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 interviewed and were asked to rate overall satisfaction again.

Variable id delivery

Position Label 1 ID 2

Delivery Reliability

3

Product Satisfaction

4

Technical Support

Prodsat

Techsat

Salesat 5 Salesforce Size Usage

6 Firm Size 7 Usage Level

Satjan 8 Satjun 8 Structure OwnType PurType

10 11 12

Overall Satisfaction in January Overall Satisfaction in June Structure of Procurement Type of Ownership Type of Purchasing

Variables in the working file

Measurement Level Scale Participant ID number On a scale of 1 to 10, how would you Scale rate the reliability of delivery of your orders? On a scale of 1 to 10, how would you rate your satisfaction with the quality Scale of your most recently purchased products? On a scale of 1 to 10, how would you Scale rate your satisfaction with the technical support? On a scale of 1 to 10, how would you Scale rate your satisfaction with the sales support? 0 = small (less than 100 emp.) 1 = Ordinal large (100 or more) What percent of your purchases are Scale from our company? On a scale of 1 to 7, rate your overall Scale satisfaction with your most recent purchasing experience. On a scale of 1 to 7, rate your overall Scale satisfaction with your most recent purchasing experience. How your purchasing is structured? Nominal 0 = Decentralized; 1 = Centralized 0 = Publicly Traded; 1 Privately Nominal owned 1 = Private Label; 2 = Company C ompany Nominal Brand; 3 = Both

, describe in your Microsoft Word document the application F or each r esearch questi on 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

Product

Reliability Satisfaction Delivery Reliability

Pearson Correlation

1

Satisfaction

Support

force

January

in June

**

.206

.628

.180

.002

.439

.152

.000

50

50

50

50

50

50

Pearson Correlation

.193

1

.317

.726

Sig. (2-tailed)

.180

.025

50

*

50 **

*

.000

.174

.000

50

50

50

50

1

.133

.340

.555

.356

.016

.000

50

50

50

50

1

.173

.326

.229

.021

50

50

50

1

.317

Sig. (2-tailed)

.002

.025

50

50

Pearson Correlation

.112

.726

.133

Sig. (2-tailed)

.439

.000

.356

50

50

50

N Overall Satisfaction in

Pearson Correlation

.206

.195

.340

*

.173

January

Sig. (2-tailed)

.152

.174

.016

.229

50

50

50

50

N

**

**

**

*

.479

50 *

50 **

.628

.484

.555

.326

.479

Sig. (2-tailed)

.000

.000

.000

.021

.000

50

50

50

50

50

**. Correlation is significant at the 0.01 level (2-tailed). *. Correlation is significant at the 0 .05 level (2-tailed).

**

*

**

.000

Pearson Correlation

N

**

.484

.436

**

**

.195

Pearson Correlation

N

Overall Satisfaction in June

**

.112

N

Salesforce

Satisfaction in

Technical Sales

.436

N

Technical Suppor

Overall

.193

Sig. (2-tailed)


Overall

1

50

2. Create a scatter plot for the following pairs: (1) delivery reliability — overall satisfaction in June; (2) product satisfaction — overall satisfaction in June; and delivery reliability — product satisfaction.

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 Mean

Std. Deviation

N


4.34

1.673

50


5.34

1.154

50

Technical Support

2.88

.895

50

Sales force

2.66

.848

50

Overall Satisfaction in January

3.58

1.372

50


4.70

.953

50

Student‘s t test is adopted to check whether there is any significant positive correlation between the variables. H0: Correlation coefficient =0 H1: Correlation coefficient >0 (One sided hypothesis) Test Statistic used is t test

r t

n2



1



2

r

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

Product

Reliability Satisfaction Delivery Reliability

Pearson Correlation

1

Sig. (1-tailed) Product Satisfaction Pearson Correlation

Technical Support

Sales force

.193

Technical

Sales

Satisfaction in

Satisfaction

Support

force

January

in June

**

.436

.112

.206

0.090

.001

0.219

0.075

*

1

**

.317 .726

0.090

Pearson Correlation

.436

.317

Sig. (1-tailed)

.001

0.0125

Pearson Correlation

.112

.726

Sig. (1-tailed)

*

**

1

.133

.340

0.178

.016

.000

1

.173

.326

0.1145

0.015

.133

.206

.195

.340

.173

0.087

.016

0.114 5

in January

Sig. (1-tailed)

0.075

Overall Satisfaction

Pearson Correlation

.628

.484

in June

Sig. (1-tailed)

.000

.000

**

**

.484

0.087

0.178

Pearson Correlation

.000

.000

.000

Overall Satisfaction

.195

**

.628

0.0125

0.219

**

Overall

.193

Sig. (1-tailed)

**

Overall

*

**

*

.555 .326 .000

.0.015

*

.000 **

.555

*

**

1

.479

.000 **

.479

.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 satisfactionDelivery reliability, Over all satisfaction – Product satisfaction ,Sales force – Technical support, Overall satisfaction in January – Technical support are insignificant.

1

Question 2: Does delivery reliability impact overall satisfaction in June? 1. Run a simple regression using delivery reliability as the independent v ariable and overall satisfaction in June as the dependent variable. a

Coefficients Unstandardized

Standardized

Coefficients

Coefficients

Std. Model 1

B

Error

(Constant)

3.147

.297


.358

.064

Beta

.628

t

Sig.

10.595

.000

5.596

.000

a. Dependent Variable: Overall Satisfaction in June

The estimated regression model is Overall Satisfaction in June = 3.147 +0.358 * Delivery Reliability

b

Model Summary

Model 1

R a

.628

Adjusted R

Std. Error of the

R Square

Square

Estimate

.395

.382

.749

a. Predictors: (Constant), Delivery Reliability b. Dependent Variable: Overall Satisfaction in June

2

The model adequacy measure R 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 Mean

Std. Deviation

N


4.70

.953

50


4.34

1.673

50

Correlations

Pearson Correlation Sig. (1-tailed)




1.000

.628


.628

1.000

.

.000

.000

.


50

50


50

50

Overall Satisfaction in June Delivery Reliability

N

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 units’

The significance of this regression coefficient is tested using the t test H0: Regression coefficient =0 H1: Regression coefficient > 0 Significance level =0.05 Decision rule: Reject the null hypothesis if the p value is less than the significance level. Details T statistic =5.596 P value =0.000 Conclusion: 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. a

Coefficients

Standardized Unstandardized Coefficients Model 1

B

Std. Error

(Constant)

1.662

.479


.316

.058


.312

.084

Coefficients Beta

t

Sig.

3.467

.001

.556

5.464

.000

.377

3.712

.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 b

Model Summary

Model 1

R a

.729

Adjusted R

Std. Error of the

R Square

Square

Estimate

.532

.512

.666

a. Predictors: (Constant), Product Satisfaction, Delivery Reliability b. Dependent Variable: Overall Satisfaction in June 2

The model adequacy measure R 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 Mean

Std. Deviation

N


4.70

.953

50


4.34

1.673

50


5.34

1.154

50

Correlations

Pearson Correlation

Sig. (1-tailed)

N





1.000

.628

.484


.628

1.000

.193


.484

.193

1.000

.

.000

.000


.000

.

.090


.000

.090

.


50

50

50


50

50

50


50

50

50


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 test H0: Regression coefficient =0 H1: Regression coefficient > 0 Significance level =0.05 Decision rule: Reject the null hypothesis if the p value is less than the significance level. Details Delivery Reliability Product Satisfaction T statistic 5.464 3.712 P value 0.000 0.001

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 Satisfaction Satisfaction 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 N

Expected N

Residual

Private label

18

16.7

1.3

Company Brand

18

16.7

1.3

Both

14

16.7

-2.7

Total

50

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 =0.05 Decision rule: Reject the null hypothesis if the p value is less than the significance level. Details

Test Statistics

Type of Purchasing Chi-Square df Asymp. Sig.

a

.640 2

.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 N

Expected N

Residual

Private label

18

12.0

6.0

Company Brand

18

26.0

-8.0

Both

14

12.0

2.0

Total

50

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 =0.05 Decision rule: Reject the null hypothesis if the p value is less than the significance level. Details Test Statistics Type of Purchasing Chi-Square df

a

5.795 2

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 =0.05 Decision 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 Procurement

Firm Size

Decentralized

Centralized

Total

Small

14

13

27

Large

12

11

23

26

24

50

Total

Firm Size * Structure of Procurement Crosstabulation Expected Count Structure of Procurement

Firm Size Total

Decentralized

Centralized

Total

Small

14.0

13.0

27.0

Large

12.0

11.0

23.0

26.0

24.0

50.0

Value

df

Asymp. Sig. (2sided)

Pearson Chi-Square

.001

a

1

.982

Continuity Correction

.000

1

1.000

Likelihood Ratio

.001

1

.982

.001

1

.982

Fisher's Exact Test Linear-by-Linear Association N of Valid Cases

50

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

Nominal by Nominal

N of Valid Cases

Value

Approx. Sig.

Phi

-.003

.982

Cramer's V

.003

.982

50

MODULE 6_7 Application Assignments

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