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Table 5.8 Chi-Square Calculation for Counties and Channels Example

COUNTY

EXPECTED TM

OTHER

DEVIATION TM

OTHER

CHI-SQUARE TM DM

OTHER

BRONX

1,850.2

523.1

4,187.7

1,362

-110

-1,252

1,002.3

23.2

374.1

KINGS

6,257.9

1,769.4

14,163.7

3,515

-376

-3,139

1,974.5

80.1

695.6

NASSAU

4,251.1

1,202.0

9,621.8

-1,116

293.0

114.5

57.7

NEW YORK

11,005.3

3,111.7

24,908.9

-3,811

-245

4,056

1,319.9

19.2

660.5

QUEENS

5,245.2

1,483.1

11,871.7

1,021

-103

-918

198.7

70.9

RICHMOND

798.9

225.9

1,808.2

11.6

SUFFOLK

3,133.6

886.0

7,092.4

-223

15.8

27.5

WESTCHESTER

3,443.8

973.7

7,794.5

-733

155.9

67.4

29.1



Table 5.9 Chi-Square Calculation for Bronx and TM

EXPECTED

DEVIATION

CHI-SQUARE

COUNTY

TM NOT TM

TM NOT TM

TM NOT TM

BRONX

1,850.2 4,710.8

1,361.8 -1,361.8

1,002.3 393.7

NOT BRONX

34,135.8 86,913.2

-1,361.8 1,361.8

54.3 21.3

The result is a set of chi-square values for the Bronx-TM combination, in a table with 1 degree of freedom. The Bronx-TM score by itself is a good approximation of the overall chi-square value for the 2 x 2 table (this assumes that the original cells are roughly the same size). The calculation for the chi-square value uses this value (1002.3) with 1 degree of freedom. Conveniently, the chi-square calculation for this cell is the same as the chi-square for the cell in the original calculation, although the other values do not match anything. This makes it unnecessary to do additional calculations.

This means that an estimate of the effect of each combination of variables can be obtained using the chi-square value in the cell with a degree of freedom of 1. The result is a table that has a set of p-values that a given square is caused by chance, as shown in Table 5.10.

However, there is a second correction that needs to be made because there are many comparisons taking place at the same time. Bonferronis adjustment takes care of this by multiplying each p-value by the number of comparisons- which is the number of cells in the table. For final presentation purposes, convert the p-values to their opposite, the confidence and multiply by the sign of the deviation to get a signed confidence. Figure 5.10 illustrates the result.

Table 5.10 Estimated P-Value for Each Combination of County and Channel, without Correcting for Number of Comparisons

COUNTY

OTHER

BRONX

0.00%

0.00%

0.00%

KINGS

0.00%

0.00%

0.00%

NASSAU

0.00%

0.00%

0.00%

NEW YORK

0.00%

0.00%

0.00%

QUEENS

0.00%

0.74%

0.00%

RICHMOND

59.79%

0.07%

39.45%

SUFFOLK

0.01%

0.00%

42.91%

WESTCHESTER

0.00%

0.00%

0.00%




Figure 5.10 This chart shows the signed confidence values for each county and region combination; the preponderance of values near 100% and -100% indicate that observed differences are statistically significant.

The result is interesting. First, almost all the values are near 100 percent or -100 percent, meaning that there are statistically significant differences among the counties. In fact, telemarketing (the diamond) and direct mail (the square) are always at opposite ends. There is a direct inverse relationship between the two. Direct mail is high and telemarketing low in three counties-Manhattan, Nassau, and Suffolk. There are many wealthy areas in these counties, suggesting that wealthy customers are more likely to respond to direct mail than telemarketing. Of course, this could also mean that direct mail campaigns are directed to these areas, and telemarketing to other areas, so the geography was determined by the business operations. To determine which of these possibilities is correct, we would need to know who was contacted as well as who responded.

Data Mining and Statistics

Many of the data mining techniques discussed in the next eight chapters were invented by statisticians or have now been integrated into statistical software; they are extensions of standard statistics. Although data miners and



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