SPSS LAB # 5

ANOVA, Chi-square Analysis, Correlation Analysis

Open the file Remingtonsag.sav

What are the major factors customers have when selecting a restaurant?

A-DS-F

Variables select X1-X6

Stats box select mean

OK

What are your conclusions?___Food quality and Speed of Service are the most important factors for customers selecting a restaurant followed by Prices

Next try to understand the perceptions of the three competitors?

Conduct an ANOVA analysis

A-CM-One way

Dependent variables X1-X6

Factor box X22

Options select descriptive

OK

Page 526

Draw a performance chart for Remingtons (Perceptual map) The two dimensions are: Variables and Rating

How does Remington’s compare on the Variables? Better or worse?

X1______slightly better______

X2______better______

X3______better______

X4______average______

X5______worse______

X6______better______

What areas should Remington’s improve and why? Service because it is important ______

Run a follow up test using the Scheffe approach

A-CM-One way

Dependent variables X1-X6

Factor box X22

Post Hoc select Scheffe

Options select descriptive

OK

Examine X1

What is the mean value for X1 for each of the competitors?_____ X1 -- Large Portions

Scheffe

X22 -- Competitor Most Familiar With / N / Subset for alpha = .05
1 / 2
Longhorn / 65 / 4.48
Remington's / 49 / 5.02
Outback / 86 / 5.27
Sig. / 1.000 / .218

Means for groups in homogeneous subsets are displayed.

a Uses Harmonic Mean Sample Size = 63.264.

b The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error levels are not guaranteed.

______

is there any significant differences between the competitors? ___yes______

If so explain between who?______outback and longhorn and remingtons and longhorn __Scheffe test significant at .05______

What is the mean value of X2 for each of the competitors?_ X2 -- Competent Employees

Scheffe

X22 -- Competitor Most Familiar With / N / Subset for alpha = .05
1 / 2 / 3
Outback / 86 / 1.85
Longhorn / 65 / 3.75
Remington's / 49 / 4.51
Sig. / 1.000 / 1.000 / 1.000

Means for groups in homogeneous subsets are displayed.

a Uses Harmonic Mean Sample Size = 63.264.

b The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error levels are not guaranteed.

______

Is there any significant differences between the competitors?____yes ______

Explain______the are all significantly different_from each other______

Page 551 Chi-square (X2) analysis allows us to test for significance between the frequency distributions for two or more nominally scaled variables in a cross-tabulation to determine if there is any associations

Chi-square analysis assumes that no association exists between the nominal-scaled variables being examined

Warning: The Chi-square results will be distorted if more than 20% of the cells have and expected count of less than 5, or if any cell has an expected count of less than 1.

Open the file Santafegrill2ag

Do male customers travel farther than females to get to the Santa Fe Restaurant

What is the null Hypothesis? ______

What is the alternative Hypothesis? ______

A-DS-C

Select x30 for the row variable

Select X32 for the column variable

Statistics button select chi-square box

Cells button select expected frequencies under counts

OK

x30 -- Distance Driven * X32 -- Gender Crosstabulation

X32 -- Gender / Total
Males / Females
x30 -- Distance Driven / Less than 1 mile / Count / 88 / 95 / 183
Expected Count / 108.0 / 75.0 / 183.0
1 -- 3 miles / Count / 58 / 40 / 98
Expected Count / 57.8 / 40.2 / 98.0
More than 3 miles / Count / 90 / 29 / 119
Expected Count / 70.2 / 48.8 / 119.0
Total / Count / 236 / 164 / 400
Expected Count / 236.0 / 164.0 / 400.0

Compare the observed to the expected frequencies

Chi-Square Tests

Value / df / Asymp. Sig. (2-sided)
Pearson Chi-Square / 22.616(a) / 2 / .000
Likelihood Ratio / 23.368 / 2 / .000
Linear-by-Linear Association / 22.343 / 1 / .000
N of Valid Cases / 400

a 0 cells (.0%) have expected count less than 5. The minimum expected count is 40.18.

What is the Pearson Chi-Square value?______22.61______

Is it significant?______yes______

Should we reject the null hypothesis based on a criteria of .05 ?______yes______

Male customers drive farther than female to get to the Santa Fe Grill

Page 553

Relationships between variables can be described in several ways:

1.  presence

2.  Direction

3.  Strength

4.  Type

Correlation Analysis

Pearson correlation coefficient measures degree of linear association between two variables

It varies between -1.00 and 1.00 0 means there is no association

Several assumptions are made about the data you are analyzing:

1.  two variables have been measured using interval or ratio scaled measures

2.  the relationship is linear

3.  variables come from bivariate normally distributed population

Determine if the relationship between satisfaction and likelihood to recommend the restaurant is significant and positive.

A-Correlate-B

Transfer x22 and x24 into the variables box

Options select Means & Standard Deviations

OK

Descriptive Statistics

Mean / Std. Deviation / N
X22 -- Satisfaction / 4.65 / .955 / 400
X24 -- Likely to Recommend / 3.46 / .930 / 400

Correlations

X22 -- Satisfaction / X24 -- Likely to Recommend
X22 -- Satisfaction / Pearson Correlation / 1 / .672(**)
Sig. (2-tailed) / .000
N / 400 / 400
X24 -- Likely to Recommend / Pearson Correlation / .672(**) / 1
Sig. (2-tailed) / .000
N / 400 / 400

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

Is there a relationship between the variables? ____yes______

Is it positive or negative?___positive______

Is it significant?______yes_at .01 level__

What is the Pearson Correlation coefficient?_____.672______

Satisfaction is positively related to likely to recommend

When the correlation is weak there are two possibilities:

1.  there simply is no systematic relationship between the two variables

2.  the association exists but it is not linear

When you square the correlation coefficient you get the coefficient of determination r2

For the example above r2 = .672^2 =.452 meaning that approximately 45.2 percent of the variation in likelihood to recommend is associated with satisfaction.

What if the correlation coefficient was .3 and What is the coefficient of determination?____

Would this be a meaningful result?______

Spearman rank order correlation coefficient can be used when the variables are measured using ordinal scales or Nominal Scales.

Management would like to determine if food quality is significantly more important selection factor than service X26 and X29

Since this data is ordinal data use the Spearmen correlation statistic

A-C-B

Select the Spearman statistic

Correlations

X29 -- Service / X27 -- Food Quality
Spearman's rho / X29 -- Service / Correlation Coefficient / 1.000 / -.130(**)
Sig. (2-tailed) / . / .009
N / 400 / 400
X27 -- Food Quality / Correlation Coefficient / -.130(**) / 1.000
Sig. (2-tailed) / .009 / .
N / 400 / 400

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

Is there is a relationship? ___yes___Customers who rank food quality as important tend to rank service significantly lower______Is it significant?______yes_but very small______

1