STATISTICS
Choosing among statistics:
– 1. number of independent variables
– 2. level of measurement (nominal to ratio)
– 3. number of dependent variables
– 4. level of measurement (nominal to ratio)
– 5. other considerations (normality)
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Example:
Male
Female
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Bought [Did not]
70%
[30%]
40%
[60%]
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Statistical analysis
Cross-tabulation
• 1 Independent variable (categorical)
• 1 Dependent variable (categorical)
• Example: percentages by group
– 70 % of men
– 50% of women
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Crosstabs
Covariation
one categorical independent variable
• e.g., male or female
one categorical dependent variable
• e.g., blonde, not blonde
– 10% of males are blonde, 40% of females
– significant covariation?
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Two approaches:
How do you measure the covariation?
• 1. “inter-ocular” test
– does it “hit you between the eyes?”
– does it look big?
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Crosstabs
2. Statistics (exact probability)
calculate the difference between:
– observed rates
– expected rates (chance)
• if observed is different than chance,
• non-independence between variables
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Crosstabs
OBSERVED
Blonde
Not |
Male
10
90
|
100
Female
40
60
|
100
TOTAL
50
150 |
200
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TOTAL
7
Chi-square Test statistic
Calculate Chi-square:
Sum of (Observed-Expected) 2
Expected
[do this for each cell]
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Chi-square Calculation
Male
Female
TOTAL
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Blonde
10
25
[9]
40
25
[9]
50
Not
90
75
[3]
60
75
[3]
150
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| TOTAL
| 100
12
| 100
12
| 200
24
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Chi-square Test statistic
2. Interpret result:
– to X2 w/ (k-1)*(n-1) “degrees of freedom”
(Table X2 1 d.f. p < .05 = 3.84)
– Because X2 obs = 24 > 3.84,
• REJECT Ho
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SPSS Output
Crosstabulation
Count
SEX
Total
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male
female
DIANAFUN
yes
no
83
94
239
95
322
189
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maybe
67
83
150
Total
244
417
661
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SPSS Output
Crosstab
% within SEX
SEX
Total
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male
female
DIANAFUN
yes
no
34.0%
38.5%
57.3%
22.8%
48.7%
28.6%
Marketing Research
maybe
27.5%
19.9%
22.7%
Total
100.0%
100.0%
100.0%
12
SPSS Output
Chi-Square Tests
Pearson Chi-Square
N of Valid Cases
Value
34.365a
661
df
2
Asymp. Sig.
(2-sided)
.000
a. 0 cells (.0%) have expected count less than 5. The
minimum expected count is 55.37.
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SPSS Output
Crosstabulation
Count
SEX
Total
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male
female
DIFUN1
none
yes
94
83
95
239
189
322
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Total
177
334
511
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SPSS Output
Crosstabulation
% within SEX
SEX
Total
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male
female
DIFUN1
none
yes
53.1%
46.9%
28.4%
71.6%
37.0%
63.0%
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Total
100.0%
100.0%
100.0%
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SPSS Output
Chi-Square Tests
Pearson Chi-Square
N of Valid Cases
Value
30.197b
511
df
1
Asymp. Sig.
(2-sided)
.000
a. Computed only for a 2x2 table
b. 0 cells (.0%) have expected count less than 5. The
minimum expected count is 65.47.
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The End
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