Question

Specify completely two potential stratification variables for grade goal; describe all levels of the variables(Levels refer to the various categories. E.g. if you stratified the year according to months, the levels would be Jan, Feb,..., Dec.). Discuss one advantage and one disadvantage of stratifying in comparison to simple random sampling.

index	goal
1	100
2	100
3	100
4	100
5	100
6	100
7	100
8	100
9	100
10	100
11	100
12	100
13	100
14	100
15	100
16	100
17	100
18	100
19	100
20	100
21	99
22	98
23	95
24	95
25	95
26	95
27	95
28	95
29	95
30	95
31	95
32	90
33	90
34	90
35	90
36	90
37	90
38	90
39	90
40	90
41	90
42	90
43	90
44	90
45	90
46	90
47	90
48	90
49	90
50	90
51	90
52	90
53	90
54	90
55	90
56	90
57	90
58	90
59	90
60	90
61	90
62	90
63	90
64	90
65	90
66	90
67	89
68	89
69	88
70	88
71	88
72	87
73	87
74	86
75	86
76	86
77	86
78	86
79	85
80	85
81	85
82	85
83	85
84	85
85	85
86	85
87	85
88	85
89	85
90	85
91	85
92	85
93	85
94	85
95	85
96	85
97	85
98	85
99	85
100	85
101	85
102	85
103	85
104	85
105	85
106	85
107	85
108	85
109	85
110	85
111	85
112	85
113	85
114	85
115	85
116	85
117	85
118	85
119	85
120	85
121	85
122	85
123	85
124	85
125	85
126	85
127	85
128	85
129	85
130	85
131	85
132	85
133	85
134	85
135	85
136	85
137	85
138	85
139	85
140	85
141	85
142	85
143	85
144	85
145	85
146	83
147	83
148	83
149	82
150	80
151	80
152	80
153	80
154	80
155	80
156	80
157	80
158	80
159	80
160	80
161	80
162	80
163	80
164	80
165	80
166	80
167	80
168	80
169	80
170	80
171	80
172	80
173	80
174	80
175	80
176	80
177	80
178	80
179	80
180	80
181	80
182	80
183	80
184	80
185	80
186	80
187	80
188	80
189	80
190	80
191	80
192	80
193	80
194	80
195	80
196	80
197	80
198	80
199	80
200	80
201	80
202	80
203	80
204	80
205	80
206	80
207	80
208	80
209	80
210	80
211	80
212	80
213	80
214	80
215	80
216	78
217	75
218	75
219	75
220	75
221	75
222	75
223	75
224	75
225	75
226	75
227	75
228	75
229	75
230	73
231	73
232	70
233	70
234	70
235	70
236	70
237	70
238	70
239	70
240	70
241	70
242	70
243	70
244	70
245	70
246	70
247	70
248	68
249	62
250	60
251	50

Answer 1

We are having data on index and goal.

(1) stratification variable

(i) firstly consider an index variable which must have some order i.e. it is an ordinal scale. Then just divide the total number of observation(251) in some say 5 catagories each having 50 approximately observations hence this can be a stratification factor.

(ii) now sort the data on 'goal' find the quartiles say Q1 Q2 and Q3 which will divide the data into four parts then just treat them as stratas.

ADVANTAGE: stratification accurately reflects the population. In short it insures the all subgroups of population to be considered it does not ignore any part of population which is not exactly done in case of simple random sampling. In simple random sampling there is no guarantee that the all subgroups of population might be included in sample.

e.g in income study of a society simple random sampling draws a sample which may or may not include the highest and lowest income classes but in stratified sampling first make stratas according to there income then draw a sample from each stratum which insures that all subgroups have been considered.

DISADVANTAGE: Time consuming and tedious

Stratified sampling requires several conditions like non overlapping stratas, each unit must belong to one and only one strata, heterogeneity between strata and homogeneity within strata etc. And hence it is time consuming and tedious on the other hand simple random sampling is not that time consuming it exicuted with less efforts.