Project in Applied statistics

APPLIED STATISTICS

PROJECT I: EFFECTS OF EXERCISE INTERVENTION WITH OVERWEIGHT ADOLESCENTS – 75 points

Purpose:

To assess your ability to transform a real-world problem in to related statistical tests, to interpret test results and to report them as a managerial or research summary.

Overview:

You are part of a research team investigating the effects of aerobic cardiovascular and moderate weight resistance training on the BMI (Body Mass Index) of moderately overweight but not obese teens (BMI range: 25.0 – 29.9).Your team has carefully recruited four random samples of about fifty overweight adolescents each.All subjects were given access to a local gym, had an initial fitness session in which they were introduced to the facilities and their use, and passed a medical exam to ensure they were healthy enough for an exercise program.They were randomly assigned to one of four groups:

Group A: Not assigned to any specific exercise program (‘control’ or ‘no treatment’ group)

Group B: Asked to follow a cardiovascular exercise program 3 times per week

Group C: Asked to follow a moderate weight resistance training program 3 times per week

Group D: Asked to follow an exercise program that incorporated both cardiovascular activity and resistance training 3 times per week

The adolescents’ BMI’s were measured by their general practitioner or another medical professional before they began the study and again two months later.  You have been asked to provide the top-line summary of preliminary results for your team to review based on the data file you have received, using a confidence level of 95%.

The data file for this project includes the following variables:

Id: The identification number given to each participant for confidentiality

Group: The treatment group the individual is assigned to (A, B, C or D)

BMI_1: BMI measurement of participants before they began the study

BMI_2: BMI measurement of participants 2 months later

Your research summary should answer the following questions:

a. What was the average change in BMI for subjects in each of the four groups?(These averages should be expressed as confidence intervals. i.e. Provide a 95% confidence interval for the change in BMI for subjects in each group)

Which exercise program was more effective in reducing BMI: the cardiovascular exercise or weight resistance training programs? Your response should include a decision (based on a test) whether or not to assume equal variances.

What can you conclude about the variances of the change in BMI for the cardio and weight training group compared to the group that was not asked to follow a specific exercise program?

a. Verify or disprove that the average starting BMIs (BMI_1) of the four groups were the same.

b. Perform a hypothesis test to determine which groups showed a significant reduction in BMI.  (Provide p-values for each group for this specific test.)

c. Compare the confidence intervals (from part a) and the hypothesis test results (from part b) and make connections between the two.

Include a discussion as to why you selected the test you did and verify its assumptions.

Describe the test you use to answer this question. Feel free to include any graphs that support your conclusion.

Describe the test being used and verify its assumptions. (You may use other tests or graphs to verify the assumptions)

b. What impact does this have on the reliability of your results above?

In addition to providing your answers to the above questions, your report should make it clear what statistical tests or methods you used to answer each question and address any assumptions required for those tests to be valid (you may need to provide other tests, graphical summaries or other analysis to do this).You should also carefully examine your data set for data quality issues.

id
Group
1A
2A
3A
4A
5A
6A
7A
8A
9A
10 A
11 A
12 A
13 A
14 A
15 A
16 A
17 A
18 A
19 A
20 A
21 A
22 A
23 A
24 A
25 A
26 A
27 A
28 A
29 A
30 A
31 A
32 A
33 A
34 A
35 A
36 A
37 A
38 A
39 A
40 A
41 A
42 A
43 A
44 A
45 A
46 A
BMI_1
BMI_2
27,5
27,9
29,2
29,4
28,7
29,6
26,3
27,5
28,2
29
25
24
27
26,1
28,1
26,6
27,8
27
27,5
27,5
27,8
28,3
28,7
30,1
27,7
27,5
28,1
27,7
27,3
26,3
27
27,2
26
25,3
26,5
26,6
28,5
28,3
28,3
28,1
26,1
27
27,1
25,9
27,5
27,7
27,2
26,6
25,8
27,4
26,1
26,5
27,2
26,5
28
28,1
27,9
26,6
27,3
26,9
28,5
27,3
28,1
27,1
29,3
28,1
27,9
27,3
25,9
25,1
26,8
27,2
26,6
25,6
27,1
28,2
27,6
27
27,8
28
28,2
27,6
26,6
26,2
29
29,6
26,6
28,1
28,4
28,6
27,7
28,5
47 A
48 A
49 A
50 A
51 A
52 A
53 A
54 A
55 B
56 B
57 B
58 B
59 B
60 B
61 B
62 B
63 B
64 B
65 B
66 B
67 B
68 B
69 B
70 B
71 B
72 B
73 B
74 B
75 B
76 B
77 B
78 B
79 B
80 B
81 B
82 B
83 B
84 B
85 B
86 B
87 B
88 B
89 B
90 B
91 B
92 B
93 B
28,8
28,2
27,6
27
26,1
26,2
29
28
29,3
26,7
27,4
28
26,2
27,8
29,6
28,4
26,4
27,2
27,8
26,7
27,4
28,6
25,6
28
27,2
26,4
25,3
26,8
28
28,6
27,8
26,9
26,7
28,8
27,2
27,1
27,4
26
26,9
28,1
25,7
26,5
26,3
29
28,7
27,9
29,5
27,1
26,7
27,9
26,2
25,9
26,9
28,5
28,1
28,6
26,3
26,6
27,7
25,1
27,1
29
27,5
25,6
26,5
27,7
26,3
26,7
28,3
25,2
27,4
26,6
25,4
24,2
26,1
26,9
28,3
27,1
26
26,3
28,8
26,6
26,4
26,6
25,4
26,3
28,2
25,4
26,4
25,5
29
27,9
26,8
29,1
94 B
95 B
96 B
97 B
98 B
99 B
100 B
101 B
102 B
103 B
104 B
105 B
106 B
107 B
108 B
109 B
110 B
111 C
112 C
113 C
114 C
115 C
116 C
117 C
118 C
119 C
120 C
121 C
122 C
123 C
124 C
125 C
126 C
127 C
128 C
129 C
130 C
131 C
132 C
133 C
134 C
135 C
136 C
137 C
138 C
139 C
140 C
27,4
25,7
26,6
26,6
27,7
27,8
27,5
28,3
28,5
27,5
28,9
28,7
27,2
27,9
27,8
26,8
27,6
27,7
27,3
27,1
27,9
26,9
29,2
27,5
27,6
26,9
27,4
27,8
28,6
27,6
26,9
29,6
26,8
27
27,1
27,4
27,3
27,7
29
26,5
28,7
29,3
27,5
28
26
26,9
27,6
26,5
24,6
26
26,2
26,2
26,8
26,9
27,9
28
26,7
28,4
28,5
26,2
27,1
26,7
25,8
27,3
27,6
26,7
26,6
27,2
27,3
29,6
26,6
27,1
26,2
27,6
27,8
28,8
26,5
26,9
28,9
26,5
27,1
26,1
27
27
27,5
28,4
25,8
28,5
28,5
27,1
27,4
26
27,5
27,6
141 C
142 C
143 C
144 C
145 C
146 C
147 C
148 C
149 C
150 C
151 C
152 C
153 C
154 C
155 C
156 C
157 C
158 C
159 C
160 C
161 C
162 D
163 D
164 D
165 D
166 D
167 D
168 D
169 D
170 D
171 D
172 D
173 D
174 D
175 D
176 D
177 D
178 D
179 D
180 D
181 D
182 D
183 D
184 D
185 D
186 D
187 D
27,4
28,3
27
28,9
26,4
28,1
28,5
26,3
27,5
27,8
28,3
26,8
29
26,3
28,5
27,2
28,1
27,7
26,2
27,3
27,5
28,7
27,8
27,9
28,7
26,1
27,5
26,6
27,7
28,3
27,3
28,4
26,7
27,7
26,7
27,9
29,7
27,6
25,8
26,6
28,2
29,2
28,3
27,9
27,2
25
27,5
27,4
27,6
26,9
28,7
26,2
27,5
28
25,3
27,1
26,6
27,6
26,6
29,1
25,6
28
27,5
28,2
27,1
25,9
27,6
27,2
27,8
26,7
27,6
27,8
25,9
27,1
25,3
28,1
27
26,7
27,7
26,6
26,8
26,3
26,6
29,8
26,4
24,8
25,4
27,6
28,2
27,4
27,7
26,5
24,6
26,7
188 D
189 D
190 D
191 D
192 D
193 D
194 D
195 D
196 D
197 D
198 D
199 D
200 D
201 D
202 D
203 D
204 D
205 D
206 D
207 D
208 D
209 D
210 D
211 D
212 D
213 D
214 D
215 D
216 D
26,7
27,1
28
27
27
28,6
27,8
26,1
28,2
25,7
26,3
29,3
27,6
27,5
28,6
26,3
27,9
25,5
28,5
28
26
27,9
27,1
26,5
26,8
27,3
25,6
25,5
28,5
25,8
26,6
27,7
26,7
26,2
28,5
27,4
25,3
27,5
25,8
25,3
28,4
26,9
27,6
28,1
26
28,1
25,5
28,2
27,5
25,8
27,3
25,9
25,8
25,9
27,2
25,1
24,6
28,2
id
Group
1A
2A
3A
4A
5A
6A
7A
8A
9A
10 A
11 A
12 A
13 A
14 A
15 A
16 A
17 A
18 A
19 A
20 A
21 A
22 A
23 A
24 A
25 A
26 A
27 A
28 A
29 A
30 A
31 A
32 A
33 A
34 A
35 A
36 A
37 A
38 A
39 A
40 A
41 A
42 A
43 A
44 A
45 A
46 A
BMI_1
BMI_2
27.5
27.9
29.2
29.4
28.7
29.6
26.3
27.5
28.2
29
25
24
27
26.1
28.1
26.6
27.8
27
27.5
27.5
27.8
28.3
28.7
30.1
27.7
27.5
28.1
27.7
27.3
26.3
27
27.2
26
25.3
26.5
26.6
28.5
28.3
28.3
28.1
26.1
27
27.1
25.9
27.5
27.7
27.2
26.6
25.8
27.4
26.1
26.5
27.2
26.5
28
28.1
27.9
26.6
27.3
26.9
28.5
27.3
28.1
27.1
29.3
28.1
27.9
27.3
25.9
25.1
26.8
27.2
26.6
25.6
27.1
28.2
27.6
27
27.8
28
28.2
27.6
26.6
26.2
29
29.6
26.6
28.1
28.4
28.6
27.7
28.5
47 A
48 A
49 A
50 A
51 A
52 A
53 A
54 A
55 B
56 B
57 B
58 B
59 B
60 B
61 B
62 B
63 B
64 B
65 B
66 B
67 B
68 B
69 B
70 B
71 B
72 B
73 B
74 B
75 B
76 B
77 B
78 B
79 B
80 B
81 B
82 B
83 B
84 B
85 B
86 B
87 B
88 B
89 B
90 B
91 B
92 B
93 B
28.8
28.2
27.6
27
26.1
26.2
29
28
29.3
26.7
27.4
28
26.2
27.8
29.6
28.4
26.4
27.2
27.8
26.7
27.4
28.6
25.6
28
27.2
26.4
25.3
26.8
28
28.6
27.8
26.9
26.7
28.8
27.2
27.1
27.4
26
26.9
28.1
25.7
26.5
26.3
29
28.7
27.9
29.5
27.1
26.7
27.9
26.2
25.9
26.9
28.5
28.1
28.6
26.3
26.6
27.7
25.1
27.1
29
27.5
25.6
26.5
27.7
26.3
26.7
28.3
25.2
27.4
26.6
25.4
24.2
26.1
26.9
28.3
27.1
26
26.3
28.8
26.6
26.4
26.6
25.4
26.3
28.2
25.4
26.4
25.5
29
27.9
26.8
29.1
94 B
95 B
96 B
97 B
98 B
99 B
100 B
101 B
102 B
103 B
104 B
105 B
106 B
107 B
108 B
109 B
110 B
111 C
112 C
113 C
114 C
115 C
116 C
117 C
118 C
119 C
120 C
121 C
122 C
123 C
124 C
125 C
126 C
127 C
128 C
129 C
130 C
131 C
132 C
133 C
134 C
135 C
136 C
137 C
138 C
139 C
140 C
27.4
25.7
26.6
26.6
27.7
27.8
27.5
28.3
28.5
27.5
28.9
28.7
27.2
27.9
27.8
26.8
27.6
27.7
27.3
27.1
27.9
26.9
29.2
27.5
27.6
26.9
27.4
27.8
28.6
27.6
26.9
29.6
26.8
27
27.1
27.4
27.3
27.7
29
26.5
28.7
29.3
27.5
28
26
26.9
27.6
26.5
24.6
26
26.2
26.2
26.8
26.9
27.9
28
26.7
28.4
28.5
26.2
27.1
26.7
25.8
27.3
27.6
26.7
26.6
27.2
27.3
29.6
26.6
27.1
26.2
27.6
27.8
28.8
26.5
26.9
28.9
26.5
27.1
26.1
27
27
27.5
28.4
25.8
28.5
28.5
27.1
27.4
26
27.5
27.6
141 C
142 C
143 C
144 C
145 C
146 C
147 C
148 C
149 C
150 C
151 C
152 C
153 C
154 C
155 C
156 C
157 C
158 C
159 C
160 C
161 C
162 D
163 D
164 D
165 D
166 D
167 D
168 D
169 D
170 D
171 D
172 D
173 D
174 D
175 D
176 D
177 D
178 D
179 D
180 D
181 D
182 D
183 D
184 D
185 D
186 D
187 D
27.4
28.3
27
28.9
26.4
28.1
28.5
26.3
27.5
27.8
28.3
26.8
29
26.3
28.5
27.2
28.1
27.7
26.2
27.3
27.5
28.7
27.8
27.9
28.7
26.1
27.5
26.6
27.7
28.3
27.3
28.4
26.7
27.7
26.7
27.9
29.7
27.6
25.8
26.6
28.2
29.2
28.3
27.9
27.2
25
27.5
27.4
27.6
26.9
28.7
26.2
27.5
28
25.3
27.1
26.6
27.6
26.6
29.1
25.6
28
27.5
28.2
27.1
25.9
27.6
27.2
27.8
26.7
27.6
27.8
25.9
27.1
25.3
28.1
27
26.7
27.7
26.6
26.8
26.3
26.6
29.8
26.4
24.8
25.4
27.6
28.2
27.4
27.7
26.5
24.6
26.7
188 D
189 D
190 D
191 D
192 D
193 D
194 D
195 D
196 D
197 D
198 D
199 D
200 D
201 D
202 D
203 D
204 D
205 D
206 D
207 D
208 D
209 D
210 D
211 D
212 D
213 D
214 D
215 D
216 D
26.7
27.1
28
27
27
28.6
27.8
26.1
28.2
25.7
26.3
29.3
27.6
27.5
28.6
26.3
27.9
25.5
28.5
28
26
27.9
27.1
26.5
26.8
27.3
25.6
25.5
28.5
25.8
26.6
27.7
26.7
26.2
28.5
27.4
25.3
27.5
25.8
25.3
28.4
26.9
27.6
28.1
26
28.1
25.5
28.2
27.5
25.8
27.3
25.9
25.8
25.9
27.2
25.1
24.6
28.2