Practical Statistics

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Practical Statistics

• Chi-Square Statistics

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• There are six statistics that will
• answer 90 of all questions!
• Descriptive
• Chi-square
• Z-tests
• Comparison of Means
• Correlation
• Regression

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Chi-square Chi-square is a simple test for
counts..
Which means nominal data and if some cases
Ordinal data
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• Chi-square
• There are three types
• Test for population variance
• Test of goodness-of-fit
• Contingency table analysis

Which is essentially a measure of association!
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• Chi-square
• There are three types
• Test for population variance

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• Chi-square
• There are three types
• Test for population variance
• Test of goodness-of-fit

Where o frequency of actual observation, and
e frequency you expected to find
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Coin thrown 100 times Expect (e) heads 50,
tails 50 Observed (o) heads 40,
tails 60
Is this a fair coin?
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According to marketing research, the clientele of
a Monkey Shine Restaurant is made up of 30
Western businessmen, 30 women who stop in while
shopping, 30 Chinese businessmen, and 10
tourists. A random sample of 600 customers at
the Kowloon Monkey Shine found 150 Western
businessmen, 190 Chinese businessmen, 100
tourists, and 65 women who were shopping.
Is the clientele at this establishment different
than the norm for this company?
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Type Percent Expected 600 Observed 600
Western Business 30 180 150
Chinese Business 30 180 190
Women Shoppers 30 180 160
Tourist 10 60 100
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5.00 0.56 2.22 26.67
34.45 With (4-1) degrees of
freedom
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The chi-square distribution is highly skewed and
dependent upon how many degrees of freedom (df) a
problems has.
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The chi-square for the restaurant problem
was Chi-square 34.45, df 3 By looking in a
table, the critical value of Chi-square with df
3 is 7.82. The probability that the researched
frequency equals the frequency found in the MR
project was p lt .001.
http//www.fourmilab.ch/rpkp/experiments/analysis/
chiCalc.html
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By looking at the analysis, it is obvious
that the largest contribution to chi-square came
from the tourists.
5.00 0.56 2.22 26.67 34.45 df 3
Hence, the Kowloon property is attracting
more tourist than what would be expected at the
Monkey Shine.
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• Chi-square
• There are three types
• Test for population variance
• Test of goodness-of-fit
• Contingency table analysis

Where o frequency of actual observation, and
e frequency you expected to find
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A contingency table is a table with numbers
grouped by frequency.
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A contingency table is a table with numbers
grouped by frequency.
Consider a study There are three groups brand
loyal customers, regular buyers, and occasional
buyers. Each is asked if they like the taste of
new product over the old. They answer with a
yes or a no.
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A contingency table would look like this
YES NO Totals
Loyal 50 40 90
Regular 60 40 100
Occasional 40 40 80
Total 150 120 270
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A contingency table is a table with numbers
grouped by frequency. All the numbers in the
table are observed frequencies (o). So, what
are the expected values?
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The expected values (e) would be a
random distribution of frequencies.
YES NO Totals
Loyal 50 40 90
Regular 60 40 100
Occasional 40 40 80
Total 150 120 270
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The expected values (e) would be a
random distribution of frequencies. These can be
calculated by multiplying the row frequency by
the column frequency and dividing by the total
number of observations.
YES NO Totals
Loyal 50 40 90
Regular 60 40 100
Occasional 40 40 80
Total 150 120 270
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For example, the expected values (e) of
loyal and yes would be (150 X 90)/270 50
YES NO Totals
Loyal 50 40 90
Regular 60 40 100
Occasional 40 40 80
Total 150 120 270
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For example, the expected values (e) of
regular And no would be (120 X 100)/270
44.4
YES NO Totals
Loyal 50 40 90
Regular 60 40 100
Occasional 40 40 80
Total 150 120 270
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The expected values (e) for the entire
table would be
YES NO Totals
Loyal 50.0 40.0 90
Regular 55.6 44.4 100
Occasional 44.4 35.6 80
Total 150 120 270
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The chi-square value is calculated for every
cell, and then summed over all the cells.
YES NO Totals
Loyal 50.0 40.0 90
Regular 55.6 44.4 100
Occasional 44.4 35.6 80
Total 150 120 270
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The chi-square value is calculated for every
cell For Cell A (50-50)2/50 0 For Cell D
(40-44.4)2/44.4 0.44
YES NO Totals
Loyal A 50.0 40.0 90
Regular 55.6 D 44.4 100
Occasional 44.4 35.6 80
Total 150 120 270
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The chi-square value is calculated for every
cell
YES NO Totals
Loyal 0 0
Regular .36 .44
Occasional .44 .55
Total
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The chi-square value is calculated for every
cell Chi-square 0 0 .35 .44 .44 .54
1.77 The df (r-1)(c-1) 1 X 2 2
YES NO Totals
Loyal 0 0
Regular .35 .44
Occasional .44 .54
Total
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A chi-square with a df 2 has a critical
value of 5.99, this chi-square 1.77, so the
results are nonsignificant.
http//www.fourmilab.ch/rpkp/experiments/analysis/
chiCalc.html
The probability 0.4127. This means that the
distribution is random, and there is no
association between customer type and taste
preference.
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A chi-square with a df 2 has a critical
value of 5.99, this chi-square 1.77, so the
results are nonsignificant. This means that the
distribution is random, and there is no
association between customer type and taste
preference.
Note This type of chi-square is a test
of association using nothing but counts
(frequency) VERY useful in business research.
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Service Encounter and Personality
Normally, 60 of our shoppers are women. Is our
sample correct? 0.6 X 271 163 women .4 X 271
109 men
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Service Encounter and Personality
Do men and women shop at different times?
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Service Encounter and Personality
Do men and women shop at different times?