Statistical methods

Answer the following questions in the document PFA

1

.

A

researcher is looking at the relationship between periodontal disease and hypertension in a population of men and women.

H

e/she decides to collect relevant information on the following variables as potential confounders in the investigation: gender (M/

F

), education status (

<

>High

School, High School,

>High

School), annual income ($), health status (dissatisfied, somewhat dissatisfied, somewhat satisfied, satisfied),

B

ody Mass

I

ndex (weight kg/height m

2

).

D

escribe each of the relevant co

–

variables as ordinal, categorical, or quantitative

2. Suppose a researcher conducts an analysis of the relationship between cardiovascular disease and type II diabetes. The basic summary of the findings are presented in the following table.

N

Y

Y

Y

A

N

N

Y

Other

Y

N

>High

N

W

Y

Y

Current

Jewish

W

Patient

BMI (kg/m2)

Hypertension ( Y / N )

Diabetes Type II (Y/N)

Smoking status ( Never , Quit , Social , C urrent )

E ducation Status ( , High, >High)

Alcohol (>2 drinks a day? Y/N)

Religious Background ( Catholic , J ewish , Muslim , Other )

Ethnicity ( AA , W , A, H, Other)

A

2 7

N

Current

Y

Catholic

AA

B

3 4

Never

>High

Other

C

21

Quit

High

W

D

2 8

Social

Muslim

E

3 6

A) Describe the following in reference to their status as a variable, observation, or value: column 3, row

5

, column 3/row 2, column

9

.

B) Are any of the variables included in the study ordinal? If so, identify the ordinal variables.

3. Suppose a researcher conducts an experiment to assess the measuring capabilities of a new device aimed at detecting the boiling point of a chemical. The chemical has a known boiling point of 120 degrees Fahrenheit. His measurement device is tested

10

times, and results in the following measurements for boiling point. What can we say about the device with regards to its precision, accuracy, and potential bias?

136

	Measurement	Boiling Point (degrees Fahrenheit)
	1			129
	2	137
	3		136
	4	141
	5	139
	6	142
	7
	8		127
	9	143
	10	123

4. Suppose a researcher is investigating the measurement ability of a new device intended to read the freezing point of a chemical compound. The substance used in the investigation has a known freezing point of

-24

degrees Celsius. The researcher conducted a series of 10 sample measurements of the freezing point, and the results are represented below. What can we say about the device with regards to its precision, and potential bias?

Measurement

1

2

3

4

5

6

-24

7

-24

8

-24

9

10

Freezing Point (degrees Celsius)
-26
-18
-32
-31
			-24
-11
-37

5. A researcher is investigating a new screening tool that is intended to help prevent the onset of breast cancer in young women. Suppose he tests the new device on a group of 10 women. The following table shows the test result and true breast cancer status of each of the women. What can we say about the new device with regards to its accuracy?

Patient

A

+

B

+

+

C

+

D

+

–

E

–

+

–

+

+

–

–

+

–

–

+

–

Test Result	True Cancer Status
										+
								–
		F
		G
H
I
J

6. A surveyor decides to sample students randomly from a classroom in order to get information about teacher satisfaction. There are 29 students in the class, and the surveyor has randomly assigned each of the students a number. The surveyor wishes to randomly select 10 students using the following number table.

741928 65

73

81

104823 57

162

8 021598 204

87

8 123596 8

97

635 234807 646079 659735

A) What kind of sample is this?

B) What assumptions must be made about the population in order to continue with the sampling design?

C) Assuming the above assumptions do hold, what are the numbers corresponding to the 10 students in the sample that would be selected from the classroom?

7. A surveyor is determined to sample homeowners in south Philadelphia before the next local election in order to assess key issues that people want to see changes for this year. Suppose the surveyor decides that he will first collect a list of eligible voters from the county, and separate that list into four groups based on annual income. Then, the surveyor randomly assigns each household a number 01-10 within each group of income. The surveyor will select 4 households from each income group using the following random number table. Once 4 households are selected for one group, the surveyor would continue with the next on the same line of the table.

081203 071072 058436 080695 0

103

54 080951 213607 041573 0

83

947

101

503

78

5409

A) What kind of sampling strategy is this?

B) Which households would be selected for each income group from this table?

8. A surveyor wants to sample a city for the local Public Health Office in order to assess asthma rates annually. In order to get the best estimate for the project, the surveyor first decides to sample 2 of 15 census tracts, and then to sample 5 households from each tract. Assume there are only 10 households in each tract. The surveyor randomly assigns each tract in the city a number 01-15, and each household in each tract a number 01-10. Use the following random number table to select each tract, and then each household, continuing along the line.

0587

91

211403 098746 170528 086401 370614 097810 036418 340514

A) What kind of sampling strategy is this?

B) Which census tracts and households will be selected?

9. A surveyor decides to sample a number of households in a community for a needs assessment project. Suppose he does a sample size calculation and determines that he only needs to sample 15 out of 100 households. What is the sampling fraction?

10. Investigators are interested in the relationship between sleep apnea and Alzheimer’s disease. In order to more thoroughly understand the relationship, these investigators decide to recruit 50 participants with Alzheimer’s and 50 participants without Alzheimer’s, and look at their history of sleep apnea.

A) What type of study design is this?

B) What are the explanatory and response variables?

11.

The following measurements represent the systolic and diastolic blood pressures (mm HG) for a group of individuals awaiting confirmation for enrollment in a study investigating the efficacy of a new anti-hypertensive medication.

129

73

81

132

SYSBP	DIASBP
	118		73
		132		81
147	87
145	91
	126
83
156	97
164	102
162	101
167	103
121	78

A) Create a stem-and-leaf plot for both systolic and diastolic blood pressure.

B) Suppose that Hypertension is categorized by a Systolic blood pressure above 159 mm HG or a diastolic blood pressure above 99 mm HG. What is the relative frequency of the potential participants with hypertension?

12.

The following table reports the fasting glucose levels of a sample of potential participants in a research study investigating the efficacy of a new insulin-type drug.

Patient

Patient

Fasting Glucose (mg/dL)

A

A

B

B

132

C

129

C

118

D

D

E

E

134

F

F

126

G

127

G

	Fasting Glucose (mg/dL)
117	112
125
116	119
	134
108
124

A) Calculate the mean, median, mode, and standard deviation for the group.

B) Are there any potential outliers that may be affecting the statistics calculated in part A?