Chi Square Tests noteshells

# Chi Square Tests noteshells - Chi-Square Tests Chapter...

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1 Chi-Square Tests 1 Chi-Square Tests Chapter 12.1-12.3 and elsewhere Chi-Square Tests 2 Categorical Data h When analyzing continuous data, underlying theory is from normal dist. h If the data represent attributes, theory is from the binomial. h If there are multiple categories, there is a multinomial generalization. h We will look at these, but first revisit some categorical data analysis we’ve already done.

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2 Chi-Square Tests 3 10.3: Comparing two proportions h Two (large) samples of size n 1 and n 2 h Let X 1 denote the number in sample 1 that have some characteristic, X 2 the same in sample 2. h Compute sample proportions p 1 = X 1 /n 1 and p 2 = X 2 /n 2 h Use these to test the hypothesis about population proportions H 0 : π 1 π 2 = 0 Chi-Square Tests 4 Example Do people use credit cards more frequently during sales? From an upscale store's data base, we sampled a number of transactions over two weekends. 416 300 Transactions sampled 312 201 Paid by credit card During annual Mega Sale Merchandise at Regular Price Weekend Sampled
3 Chi-Square Tests 5 Is there a difference? 201 312 p = ------ = .67 p = ------ = .75 1 300 2 416 How much is significant? The SE (page 355) is .03414 Chi-Square Tests 6 PHStat results h Critical values ± 1.96 h Z CALC = -2.34 h There is more CC usage during sales.

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4 Chi-Square Tests 7 12.1: An alternate test h It is difficult to generalize this Z-test to a problem with more than two populations; for example, weekdays and weekends during both sales and regular-priced days (four samples). h It would be even more difficult to accommodate multiple categories like payment by cash, check, credit card, debit card and gift card. h We will look at a test that can handle all these. But first, let’s apply it to the current example. Chi-Square Tests 8 Contingency tables h These are tables cross-tabulating count data by two factors (here, these are time period and type of payment). h In general, we are going to see if the rows differ by the columns, on a proportionate basis. h We thus have the time period on the columns and type of \$ on the rows.
5 Chi-Square Tests 9 Our example again Time Period 716 300 416 Total 203 99 104 Cash 513 201 312 Credit Card Total At Regular Prices During Mega Sale Type Of Payment This is a 2-by-2 table, so there are four “cells” Chi-Square Tests 10 Methodology h Method: compute an expected frequency for each “cell” and compare it to what we actually observed. h In each cell, compute the difference between what was observed and expected. h If the payment methods were used at about the same frequency in both time periods, the differences would be small.

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6 Chi-Square Tests 11 Overall credit card usage 201 + 312 513 p = -------------- = ----- = .71648 Credit 300 + 416 716 Expected during sales = During regular = Cash usage expected = Chi-Square Tests 12 Observed and expected 716 300 416 Total 203 99 85.1 104 117.9 Cash 513 201 214.9 312 298.1 Credit Card Total At Regular Prices During Sales Type Of Payment
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## This note was uploaded on 02/14/2011 for the course QMB 3250 taught by Professor Thompson during the Spring '08 term at University of Florida.

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Chi Square Tests noteshells - Chi-Square Tests Chapter...

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