In: Statistics and Probability
Political parties want to know what groups of people support them. The General Social Survey (GSS) asked its 2014 sample, "Generally speaking, do you usually think of yourself as a Republican, Democrat, Independent, or what?" The GSS is essentially an SRS of American adults. Here is a large two-way tale breaking down the responses by the highest degree the subject held:
None | High School | Junior High | Bachelor | Graduate | |
Strong Democrat | 53 | 198 | 23 | 81 | 64 |
Not strong Democrat | 52 | 204 | 31 | 70 | 49 |
Independent, near Dem. | 40 | 163 | 26 | 66 | 42 |
Independent | 118 | 251 | 36 | 67 | 30 |
Independent, near Rep. | 24 | 136 | 19 | 45 | 25 |
Not strong Republican | 19 | 142 | 30 | 71 | 30 |
Strong Republican | 18 | 131 | 15 | 53 | 28 |
Other Party | 5 | 31 | 3 | 15 | 8 |
1. Make a 2x5 table by combining the counts in the three rows that mention Democrats, Republicans and ignoring strict independents and supporters of other parties. We might think of this table as comparing all adults who lean Democrat or Republican. How does support for the two major parties differ among adults with different levels of education?
2. Use the full table to analyze the differences in political party support among levels of education. The sample is so large that the differences are bound to be highly significant. but give the χ2χ2 test statistic and p-value nonetheless. The main challenge is in seeing what the data say. Does the full table yield any insights not found in the compressed table analyzed in part 1?
1. The 2x5 table is:
None | High School | Junior High | Bachelor | Graduate | Total | |
Democrat | 145 | 565 | 80 | 217 | 155 | 1162 |
Republican | 61 | 409 | 64 | 169 | 83 | 786 |
Total | 206 | 974 | 144 | 386 | 238 | 1948 |
The support is more for Democrats. The support is provided maximum by the people having the education level High School.
2. The output is:
None | High School | Junior High | Bachelor | Graduate | Total | ||
Strong Democrat | Observed | 53 | 198 | 23 | 81 | 64 | 419 |
Expected | 54.88 | 209.50 | 30.52 | 78.06 | 46.04 | 419.00 | |
O - E | -1.88 | -11.50 | -7.52 | 2.94 | 17.96 | 0.00 | |
(O - E)² / E | 0.06 | 0.63 | 1.85 | 0.11 | 7.01 | 9.67 | |
Not strong Democrat | Observed | 52 | 204 | 31 | 70 | 49 | 406 |
Expected | 53.17 | 203.00 | 29.58 | 75.64 | 44.61 | 406.00 | |
O - E | -1.17 | 1.00 | 1.42 | -5.64 | 4.39 | 0.00 | |
(O - E)² / E | 0.03 | 0.00 | 0.07 | 0.42 | 0.43 | 0.95 | |
Independent, near Dem. | Observed | 40 | 163 | 26 | 66 | 42 | 337 |
Expected | 44.14 | 168.50 | 24.55 | 62.79 | 37.03 | 337.00 | |
O - E | -4.14 | -5.50 | 1.45 | 3.21 | 4.97 | 0.00 | |
(O - E)² / E | 0.39 | 0.18 | 0.09 | 0.16 | 0.67 | 1.49 | |
Independent | Observed | 118 | 251 | 36 | 67 | 30 | 502 |
Expected | 65.75 | 251.00 | 36.57 | 93.53 | 55.16 | 502.00 | |
O - E | 52.25 | 0.00 | -0.57 | -26.53 | -25.16 | 0.00 | |
(O - E)² / E | 41.53 | 0.00 | 0.01 | 7.52 | 11.47 | 60.53 | |
Independent, near Rep. | Observed | 24 | 136 | 19 | 45 | 25 | 249 |
Expected | 32.61 | 124.50 | 18.14 | 46.39 | 27.36 | 249.00 | |
O - E | -8.61 | 11.50 | 0.86 | -1.39 | -2.36 | 0.00 | |
(O - E)² / E | 2.27 | 1.06 | 0.04 | 0.04 | 0.20 | 3.62 | |
Not strong Republican | Observed | 19 | 142 | 30 | 71 | 30 | 292 |
Expected | 38.24 | 146.00 | 21.27 | 54.40 | 32.08 | 292.00 | |
O - E | -19.24 | -4.00 | 8.73 | 16.60 | -2.08 | 0.00 | |
(O - E)² / E | 9.68 | 0.11 | 3.58 | 5.06 | 0.14 | 18.57 | |
Strong Republican | Observed | 18 | 131 | 15 | 53 | 28 | 245 |
Expected | 32.09 | 122.50 | 17.85 | 45.64 | 26.92 | 245.00 | |
O - E | -14.09 | 8.50 | -2.85 | 7.36 | 1.08 | 0.00 | |
(O - E)² / E | 6.19 | 0.59 | 0.45 | 1.19 | 0.04 | 8.46 | |
Other Party | Observed | 5 | 31 | 3 | 15 | 8 | 62 |
Expected | 8.12 | 31.00 | 4.52 | 11.55 | 6.81 | 62.00 | |
O - E | -3.12 | 0.00 | -1.52 | 3.45 | 1.19 | 0.00 | |
(O - E)² / E | 1.20 | 0.00 | 0.51 | 1.03 | 0.21 | 2.95 | |
Total | Observed | 329 | 1256 | 183 | 468 | 276 | 2512 |
Expected | 329.00 | 1256.00 | 183.00 | 468.00 | 276.00 | 2512.00 | |
O - E | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | |
(O - E)² / E | 61.35 | 2.58 | 6.60 | 15.54 | 20.17 | 106.24 | |
106.24 | chi-square | ||||||
28 | df | ||||||
4.82E-11 | p-value |
Therefore, we can say that there is a difference in political party support among levels of education.