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 = .051 / 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 = .051 / 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 / TotalMales / 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 / NX22 -- Satisfaction / 4.65 / .955 / 400
X24 -- Likely to Recommend / 3.46 / .930 / 400
Correlations
X22 -- Satisfaction / X24 -- Likely to RecommendX22 -- 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 QualitySpearman'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______
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