tailieunhanh - 100 STATISTICAL TESTS phần 3

Tham khảo tài liệu '100 statistical tests phần 3', ngoại ngữ, ngữ pháp tiếng anh phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 42 100 STATISTICAL TESTS Test 14 Z-test for two correlation coefficients Object To investigate the significance of the difference between the correlation coefficients for a pair of variables occurring from two different samples and the difference between two specified values P1 and P2. Limitations 1. The x and y values originate from normal distributions. 2. The variance in the y values is independent of the x values. 3. The relationships are linear. Method Using the notation of the Z-test of a correlation coefficient we form for the first sample Zi 1loge ị T ị T- 2 1 71 1 71 which has mean IXZ1 2loge 1 P1 1 P1 and variance ƠZ1 1 Zn1 3 where n1 is the size of the first sample Z2 is determined in a similar manner. The test statistic is now Z Z1 Z2 Z1 lJZ2 Ơ where ơ ơị ơZ2 2. Z is normally distributed with mean 0 and with variance 1. Example A market research company is keen to categorize a variety of brands of potato crisp based on the correlation coefficients of consumer preferences. The market research company has found that if consumers preferences for brands are similar then marketing programmes can be merged. Two brands of potato crisp are compared for two advertising regions. Panels are selected of sizes 28 and 35 for the two regions and correlation coefficients for brand preferences are and respectively. Are the two associations statistically different or can marketing programmes be merged The calculated Z value is and the acceptance region for the null hypothesis is Z . So we accept the null hypothesis and conclude that we can go ahead and merge the marketing programmes. This of course assumes that the correlation coefficient is a good measure to use for grouping market research programmes. Numerical calculation ni 28 n2 35 T1 T2 a Zi log10 7 Table 4 1 t1 THE TESTS 43 1 72 Z log10 I 44-i Table4 1 r2 1 1 1 Ơ I --------- I H 3 n2 3 J Z 05493 - . -5 The .