MKF5912 Sample Examples of Analysis of Statistical Outputs
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MKF5912
Sample Examples of Analysis of Statistical Outputs
Note: These are the sample examples of how to interpret SPSS outputs for
various tests. The examples are taken from the lecture notes. The proposed steps are the suggestions only and not fixed rules.
Cross-Tabulation
Question: Is there an association between Age and Soft drink preference?
Brand Preference * Age Group Crosstabulation
Count
|
|
|
Age Group |
Total |
|
|
Less than 40 |
40 and more |
|||
|
|
Pepsi |
45 |
28 |
73 |
|
Coca-Cola |
53 98 |
64 92 |
117 190 |
|
Step 1: Formulate null and alternative hypotheses
Step 2: Test null hypothesis
|
|
Value |
df |
Asymp. Sig. (2- sided) |
Exact Sig. (2- sided) |
Exact Sig. (1- sided) |
|
Continuity Correctionb Likelihood Ratio Fisher's Exact Test Linear-by-Linear Association N of Valid Cases |
4.808a 4.176 4.842
4.783 190 |
1 1 1
1 |
.029 |
.037 |
.020 |
a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 35.35.
and compare the significance (p-value) of Chi-Square statistic with α=0.05. In our case: 0.028<0.05 => Reject null hypothesis about absence of association and accept alternative hypothesis.
Conclusion: age and brand preference are associated with each other.
Note: If significance of Chi-Square statistic would be higher than α=0.05 (for instance, 0.3>0.05), then the null hypothesis would not be rejected and the
conclusion would be: age and brand preference are not associated. If we do not reject null hypothesis the analysis stops.
Step 3: Determine the strength of association
Symmetric Measures
|
|
|
Value |
Approx. Sig. |
|
Nominal by Nominal |
|
|
.028 |
|
N of Valid Cases |
Cramer's V |
.159 |
.028 |
|
Contingency Coefficient |
.157 190 |
.028 |
The Phi coefficient is 0.159 which indicates poor associated between variables. Recall that this coefficient varies from 0 (no association) to 1 (perfect association).
Step 4: Interpret the pattern of the relationship between variables
Brand Preference * Age Group Crosstabulation
|
|
|
|
Age Group |
Total |
|
|
Less than 40 |
40 and more |
||||
|
Brand Preference |
Pepsi |
Count |
45 |
28 |
73 |
|
% within Age Group |
45.9% |
30.4% |
38.4% |
||
|
Coca-Cola |
Count |
53 |
64 |
117 |
|
|
% within Age Group |
54.1% |
69.6% |
61.6% |
||
|
Total |
|
Count |
98 |
92 |
190 |
|
% within Age Group |
100.0% |
100.0% |
100.0% |
||
Interpretation. Both younger and older customers prefer Coke to Pepsi (54.1% and 69.9% respectively). However, this preference is stronger for older customers (69.6% Coke vs 30.4% Pepsi) than for younger ones (54.1% Coke vs 45.9% Pepsi).
2022-05-09