Question

Research Scenario

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?

Answer 1

1. The z-statistic can be used to compare your patient's scores to the population as well as with scores from other tests because the z-statistic tells the standard deviation around the mean.

2.

Participant ID	Weight	FPI	z-scores Weight	z-scores FPI
1	204	115	0.01	0.24
2	198	111	-0.29	-0.53
3	219	119	0.76	1.01
4	250	122	2.32	1.59
5	170	105	-1.70	-1.68
6	232	110	1.42	-0.72
7	178	104	-1.30	-1.87
8	177	107	-1.35	-1.30
9	192	109	-0.60	-0.91
10	198	110	-0.29	-0.72
11	203	115	-0.04	0.24
12	211	114	0.36	0.05
13	198	112	-0.29	-0.34
14	212	120	0.41	1.20
15	215	119	0.56	1.01
16	236	120	1.62	1.20
17	196	115	-0.39	0.24
18	198	115	-0.29	0.24
19	180	112	-1.20	-0.34
20	210	121	0.31	1.39

3. Patient 4's scores are rare.

4. Yes, if the z-score is outside the range of -2 to 2, then it is suffering from any statistically significant deficits.