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Practical Statistics. Chi-Square Statistics. There are six statistics that will answer 90\% of all questions! Descriptive Chi-square Z-tests Comparison of Means Correlation Regression. Chi-square: Chi-square is a simple test for counts….. . Chi-square:

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practical statistics

Practical Statistics

Chi-Square Statistics

slide2
There are six statistics that will
  • answer90% of all questions!
  • Descriptive
  • Chi-square
  • Z-tests
  • Comparison of Means
  • Correlation
  • Regression
slide3
Chi-square:

Chi-square is a simple test for counts…..

slide4
Chi-square:

Chi-square is a simple test for counts…..

Which means: nominal data

and… if some cases…

Ordinal data

slide5
Chi-square:
  • There are three types:
  • Test for population variance
  • Test of “goodness-of-fit”
  • Contingency table analysis
slide6
Chi-square:
  • There are three types:
  • Test for population variance
slide7
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

slide8
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 business men,

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 of the this company?

slide10
= 5.00 + 0.56 + 2.22 + 26.67 = 34.45

With (4-1) degrees of freedom

slide11
The chi-square distribution is highly skewed

and dependent upon how many degrees of

freedom (df) a problems has.

slide12
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 < .001.

http://www.fourmilab.ch/rpkp/experiments/analysis/chiCalc.html

slide13
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.

slide14
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

slide15
A contingency table

is a table with numbers grouped by frequency.

slide16
A contingency table

is a table with numbers grouped by frequency.

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.”

slide18
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?

slide19
The expected values (e) would be a random

distribution of frequencies.

slide20
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.

slide21
For example, the expected values (e) of “loyal”

And “yes” would be (150 X 90)/270 = 50

slide22
For example, the expected values (e) of “regular”

And “no” would be (120 X 100)/270 = 44.4

slide24
The chi-square value is calculated for every cell,

and then summed over all the cells.

slide25
The chi-square value is calculated for every cell:

For Cell A: (50-50)^2/50 = 0

For Cell D: (40-44.4)^/44.4 = 0.44

slide27
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

slide28
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.

slide29
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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