Below is R output for a 2´2 bivariate table that cross-tabulates subjective social class (that is, the social class to which the respondent believes they belong) and how fundamentalist the respondent is in terms of their religion. Note that the relationship is statistically significant (X^2 = 38.99; p < .001). The  (lambda) statistic is reported below the table. What is its interpretation? How is the interpretation of lambda different or unique from phi and Cramér’s ?

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Below is R output for a 2´2 bivariate table that cross-tabulates subjective social class (that is, the social class to which the respondent believes they belong) and how fundamentalist the respondent is in terms of their religion. Note that the relationship is statistically significant (X^2 = 38.99; p < .001). The  (lambda) statistic is reported below the table. What is its interpretation? How is the interpretation of lambda different or unique from phi and Cramér’s ?

Cell Contents
Count
Chi-square contribution
Row Percent
Column Percent
Total Percent
Total Observations in Table:
2408
gss$fund
fundamentalist |
gss$class
moderate
liberal |
Row Total
lower class
64
1.517
69
90
223
4.173
0.202
30.9428
40.3598
28.7008
9.2618
11.8358
8.8328
7.940%
2.865%
3.7388
2.6588
working class
295
477
328
1100
3.088
0.285
4.387
26.818%
43.3648
29.818%
45.6818
50.600%
46.811%
40.695%
12.2518
19.8098
13.621%
middle class
214
431
380
1025
4.703
20.878%
0.017
3.972
42.0498
37.0738
42.5668
36.707%
42.296%
47.146%
8.8878
17.8998
15.7818
upper class
5
21
34
60
6.248
0.759
9.644
8.3338
35.000%
56.6678
2.4928
0.8588
2.061%
4.2188
0.2088
0.8728
1.412%
Column Total
583
1019
42.3178
806
2408
24.211%
33.472%
Pearson's Chi-squared test
Chi^2 =
38.99484
d.f. =
6
p =
7.17428le-07
Lambda: 0.009359251
Transcribed Image Text:Cell Contents Count Chi-square contribution Row Percent Column Percent Total Percent Total Observations in Table: 2408 gss$fund fundamentalist | gss$class moderate liberal | Row Total lower class 64 1.517 69 90 223 4.173 0.202 30.9428 40.3598 28.7008 9.2618 11.8358 8.8328 7.940% 2.865% 3.7388 2.6588 working class 295 477 328 1100 3.088 0.285 4.387 26.818% 43.3648 29.818% 45.6818 50.600% 46.811% 40.695% 12.2518 19.8098 13.621% middle class 214 431 380 1025 4.703 20.878% 0.017 3.972 42.0498 37.0738 42.5668 36.707% 42.296% 47.146% 8.8878 17.8998 15.7818 upper class 5 21 34 60 6.248 0.759 9.644 8.3338 35.000% 56.6678 2.4928 0.8588 2.061% 4.2188 0.2088 0.8728 1.412% Column Total 583 1019 42.3178 806 2408 24.211% 33.472% Pearson's Chi-squared test Chi^2 = 38.99484 d.f. = 6 p = 7.17428le-07 Lambda: 0.009359251
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