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Descriptive, Correlation and Chi-Square Tests

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Description of basic statistics including descriptives, correlations and chi square techniques

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Basic Statistics

Descriptive Statistics
Descriptive statistics are ways of summarising numerical data to make them more easily interpretable. Descriptive statistics include the mean, standard deviation, variance, minimum, maximum, range, standard error of the mean, kurtosis and skewness of a set of scores. Correlations between variables are also descriptive statistics, however in practice these are usually treated separately.

Descriptive statistics are very useful and can clearly display data in a form that people can easily understand. They can add colour and interest to a project or presentation.

Correlation
The ...

Solution Summary

Descriptive statistics are ways of summarising numerical data to make them more easily interpretable. Descriptive statistics include the mean, standard deviation, variance, minimum, maximum, range, standard error of the mean, kurtosis and skewness of a set of scores.

The correlation between two variables is the degree of (usually) linear relationship between them. The concept of correlation was first introduced by Sir Francis Galton in 1877.

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SPSS Input

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.

Variable Position Label Measurement Level
id 1 ID Scale Participant ID number
delivery 2 Delivery Reliability Scale On a scale of 1 to 10, how would you rate the reliability of delivery of your orders?
Prodsat 3 Product Satisfaction Scale On a scale of 1 to 10, how would you rate your satisfaction with the quality of your most recently purchased products?
Techsat 4 Technical Support Scale On a scale of 1 to 10, how would you rate your satisfaction with the technical support?
Salesat 5 Salesforce Scale On a scale of 1 to 10, how would you rate your satisfaction with the sales support?
Size 6 Firm Size Ordinal 0 = small (less than 100 emp.) 1 = large (100 or more)
Usage 7 Usage Level Scale What percent of your purchases are from our company?
Satjan 8 Overall Satisfaction in January Scale On a scale of 1 to 7, rate your overall satisfaction with your most recent purchasing experience.
Satjun 8 Overall Satisfaction in June Scale On a scale of 1 to 7, rate your overall satisfaction with your most recent purchasing experience.
Structure 10 Structure of Procurement Nominal How your purchasing is structured?
0 = Decentralized; 1 = Centralized
OwnType 11 Type of Ownership Nominal 0 = Publicly Traded; 1 Privately owned
PurType 12 Type of Purchasing Nominal 1 = 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.
2. Create a scatterplot for the following pairs: (1) delivery reliability-overall satisfaction in June; (2) product satisfaction-overall satisfaction in June; and delivery reliability-product satisfaction.
3. Report the descriptive statistics, assumptions tests, as well as tests of statistical significance identify of positive and negative relationships.

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.
2. Report the descriptive statistics, assumptions tests (scatter plots), as well as tests of statistical significance.

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.
2. Report the descriptive statistics, assumptions tests (scatter plots), as well as tests of statistical significance.

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?

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?

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.
2. Report the observed and expected values and the tests of statistical significance.

Question 3: Is there a relationship between the company size and type of procurement?
1. Run chi-square independence test (crosstabs) using company size and type of procurement.
2. Use the chi square and the phi coefficient to evaluate the relationship and statistical significance.
3. Report the observed and expected values and the tests of statistical significance.

Id delivery Prodsat Techsat Salesat Size Usage Satjan Satjun Structure OwnType PurType
4 6 7 3 3 0 54 6 6 1 0 3
5 4 5 3 2 0 49 7 5 0 0 3
6 4 5 4 3 0 38 5 4 1 1 2
7 7 6 3 4 0 54 3 6 0 1 3
8 4 3 1 2 0 35 3 3 1 0 1
9 6 5 3 3 0 49 2 5 1 0 2
10 6 6 3 3 0 49 5 6 1 1 3
17 7 8 3 5 0 58 4 7 0 1 3
18 6 5 3 3 0 48 2 5 1 0 2
20 6 5 4 1 0 54 4 6 0 0 3
22 7 5 3 2 0 57 4 5 0 1 3
23 5 6 2 3 0 41 3 5 1 0 2
26 5 3 2 2 0 39 3 4 0 0 1
27 7 6 4 3 0 65 7 6 0 0 3
28 6 6 4 2 0 60 5 6 1 0 3
29 5 6 3 3 0 47 4 5 0 1 3
30 4 5 3 3 0 36 3 4 1 1 2
31 5 6 3 4 0 59 5 6 0 0 3
32 7 4 4 2 0 58 3 4 1 0 3
35 5 5 3 3 0 49 3 5 1 1 2
36 5 6 2 3 0 42 4 5 0 0 2
37 4 3 3 2 0 47 5 5 0 1 3
38 6 5 3 2 0 56 3 5 0 0 3
39 4 8 4 4 0 47 4 6 1 1 2
44 4 7 3 4 0 49 3 4 1 1 2
45 6 4 3 1 0 39 4 6 0 0 2
47 5 5 2 2 0 31 4 4 0 1 1
1 4 6 4 3 1 48 3 5 0 1 2
2 1 5 3 2 1 45 3 4 1 1 2
3 4 4 2 1 1 39 1 4 0 0 1
11 5 6 4 3 1 46 5 5 1 0 2
12 3 3 2 1 1 35 2 4 0 0 1
13 1 5 3 2 1 39 3 4 1 1 1
14 5 6 4 3 1 44 4 5 0 1 2
15 1 5 1 3 1 29 4 4 1 1 1
16 3 5 2 2 1 28 1 3 0 1 1
19 3 4 2 2 1 38 3 3 1 1 1
21 4 6 4 2 1 43 4 5 0 1 2
24 3 5 4 3 1 53 2 5 1 1 2
25 4 5 3 3 1 32 4 4 0 1 1
33 5 6 5 3 1 50 5 5 1 1 2
34 4 7 2 3 1 41 2 4 0 0 1
40 2 6 2 4 1 41 5 4 1 0 1
41 3 4 3 2 1 43 3 4 0 1 1
42 3 6 3 3 1 51 4 6 1 0 2
43 4 6 2 3 1 34 2 4 0 1 1
46 1 5 2 3 1 36 5 4 1 0 1
48 1 5 1 2 1 25 3 3 0 1 1
49 3 5 2 3 1 38 2 4 1 0 1
50 4 7 3 3 1 42 1 4 0 0 1

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