In: Statistics and Probability
With increases in obesity rates over the past several decades, health care providers have become concerned about the effects of obesity on health. As a health psychologist, you are interested in people’s perceptions and responses to food as this might influence obesity. You are curious if people that are impulsive or have difficult with impulse control are more likely to be obese and if they perceive sweet, high calorie foods as being more desirable than the general population. Given this, you screen a group of participants and recruit participants (n=20) that have high impulsivity scores (that is, they are more impulsive). From your sample, you collect participant’s weight and scores on the Food Perception Inventory (FPI) which measures individual’s preference for high calorie foods. For obesity, you know the national mean (168) and standard deviation (26.38), but you only know the population mean (103) for the FPI. Using the data below, answer the following questions:
Participant ID |
Weight |
FPI |
1 |
204 |
115 |
2 |
198 |
111 |
3 |
219 |
119 |
4 |
250 |
122 |
5 |
170 |
105 |
6 |
232 |
110 |
7 |
178 |
104 |
8 |
177 |
107 |
9 |
192 |
109 |
10 |
198 |
110 |
11 |
203 |
115 |
12 |
211 |
114 |
13 |
198 |
112 |
14 |
212 |
120 |
15 |
215 |
119 |
16 |
236 |
120 |
17 |
196 |
115 |
18 |
198 |
115 |
19 |
180 |
112 |
20 |
210 |
121 |
Questions:
1. What type of statistic can you use to compare your patients scores to the population as well as with scores from other tests? Explain.
2. Convert your patient’s raw scores into z-scores and report them.
3. Describe your patient’s scores in terms of uniqueness or rareness.
4. Is your patient suffering from any statistically significant deficits and how do you know?
Sl No | FPI (x) | z=(x-168)/26.38 |
1 | 115 | -2.008336491 |
2 | 111 | -2.159909056 |
3 | 119 | -1.856763926 |
4 | 122 | -1.743084502 |
5 | 105 | -2.387267905 |
6 | 110 | -2.197802198 |
7 | 104 | -2.425161046 |
8 | 107 | -2.311481622 |
9 | 109 | -2.235695339 |
10 | 110 | -2.197802198 |
11 | 115 | -2.008336491 |
12 | 114 | -2.046229632 |
13 | 112 | -2.122015915 |
14 | 120 | -1.818870784 |
15 | 119 | -1.856763926 |
16 | 120 | -1.818870784 |
17 | 115 | -2.008336491 |
18 | 115 | -2.008336491 |
19 | 112 | -2.122015915 |
20 | 121 | -1.780977643 |
3. Describe your patient’s scores in terms of uniqueness or rareness.
Ans: The patient's scores which fall outside the 3Sigma that is outside the -3 and 3 limits for z-score can be considered as uniqueness or rareness terms. Hence, the given data set does not include any uniqueness or rareness term.
4. Is your patient suffering from any statistically significant deficits and how do you know?