Question

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 College	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 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?

Answer 1

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Answer:

The democrat numbers for none are obtained by adding Strong democrat, Not stron democrat and Independent near democrat = 53 + 52 + 40 = 145

The Republicans numbers for none are obtained by adding Strong Republicans , Not strong republicans and Independent near republicans= 24 + 19 + 18 = 61.

Similarly the calculations are followed across the table for high school, Junior high etc.

From the table we can see that the support is high for Democrats. It is provided maximum by the students having the education High School.

Chi Squared Table:

		NONE	HS	JH	BACHELOR	GRADUATE
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

=> We can conclude there is a difference in political party support among different stages of education