Practical Statistics Chi-Square Statistics

There are six statistics that will answer 90% of all questions! 1. Descriptive 2. Chi-square 3. Z-tests 4. Comparison of Means 5. Correlation 6. Regression

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

Chi-square: Chi-square is a simple test for counts….. Which means: nominal data and… if some cases… Ordinal data

Chi-square: There are three types: 1. Test for population variance

Chi-square: There are three types: 1. Test for population variance 2. Test of “goodness-of-fit”

Chi-square: There are three types: 1. Test for population variance 2. Test of “goodness-of-fit” 3. Contingency table analysis

Chi-square: There are three types: 1. Test for population variance

Chi-square: There are three types: 1. Test for population variance 2. Test of “goodness-of-fit” Where o = frequency of actual observation, and e = frequency you expected to find

Coin thrown 100 times: Expect (e): heads = 50, tails = 50 Observed (o): heads = 40, tails = 60 Is this a “fair” coin?

HeadsTails Observed4060 Expected

HeadsTails Observed4060 Expected 5050

HeadsTails Observed4060 Expected 5050 = = 4

Chi-Sq = 4.0, df = 1, p = ? P = But this is the probability of what?

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 of the this company?

TypePercentExpected 600 Observed 600 Western Business 30% Chinese Business 30% Women Shoppers 30% Tourist10%

= = With (4-1) degrees of freedom

The chi-square distribution is highly skewed and dependent upon how many degrees of freedom (df) a problems has.

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 The probability that the researched frequency equals the frequency found in the MR project was p <

= = df = 3 By looking at the analysis, it is obvious that the largest contribution to chi-square came from the tourists. Hence, the Kowloon property is attracting more tourists than what would be expected at the Monkey Shine.

Chi-square: There are three types: 1. Test for population variance 2. Test of “goodness-of-fit” 3. Contingency table analysis Where o = frequency of actual observation, and e = frequency you expected to find

A contingency table is a table with numbers grouped by frequency.

A contingency table (cross-tabs) 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.”

A contingency table would look like this: YES NO Totals Loyal Regular Occasional Total

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?

YES NO Totals Loyal Regular Occasional Total The expected values (e) would be a random distribution of frequencies.

YES NO Totals Loyal Regular Occasional Total 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 Regular Occasional Total For example, the expected values (e) of “loyal” and “yes” would be (150 X 90)/270 = 50

YES NO Totals Loyal Regular Occasional Total For example, the expected values (e) of “regular” And “no” would be (120 X 100)/270 = 44.4

The expected values (e) for the entire table would be: YES NO Totals Loyal Regular Occasional Total

The chi-square value is calculated for every cell, and then summed over all the cells. YES NO Totals Loyal Regular Occasional Total

The chi-square value is calculated for every cell: For Cell A: (50-50)^2/50 = 0 For Cell D: ( )^2/44.4 = 0.44 YES NO Totals Loyal A Regular 55.6 D Occasional Total

The chi-square value is calculated for every cell: YES NO Totals Loyal 0 0 Regular Occasional Total

The chi-square value is calculated for every cell: Chi-square = = 1.77 The df = (r-1)(c-1) = 1 X 2 = 2 YES NO Totals Loyal 0 0 Regular Occasional Total

A chi-square with a df = 2 has a critical value of 5.99, this chi-square = 1.77, so the results are nonsignificant. The probability = This means that the distribution is random, and there is no association between customer type and taste preference.

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); It is VERY useful in business research.

Example: Suppose that a study of service providers and personality had two questions (among many): Your favorite shopping time: Day Evening.. Sex: M F

Your favorite shopping time: Results: Day: 19271% Evening: 7929% Total271 Sex: Results: Male:12245% Female14955% Total271

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

Service Encounter and Personality Do men and women shop at different times?

Service Encounter and Personality Do men and women shop at different times?