18 Oct Certain basic assumptions are necessary to allow for the statistical analysis of public health data.
Sample Size and Statistical Assumptions
Certain basic assumptions are necessary to allow for the statistical analysis of public health data. However, the validity of these assumptions can be affected by the sample size being analyzed. The purpose of this assignment is to refresh your knowledge of the basic assumptions underlying the biostatistical analysis and to consider how these assumptions are affected by the sample size being analyzed.
Using the South University Online Library, the Internet, and your text readings, research the following statistical topics:
Statistical power
Central limit theorem (CLT)
On the basis of your research and understanding, respond to the following:
Find and state the definition of statistical power that you identify with.
State the definition of statistical power in your own words.
Compare and contrast type I and type II errors.
Explain how power is affected by sample size.
Find and state the definition of CLT that you identify with.
State the definition of CLT in your own words.
Summarize the basic assumptions underlying hypothesis testing and confidence interval methods.
Explain how these assumptions are affected by sample size.
Explain the relation of a sample size to the basic assumptions underlying biostatistical analysis.
PHE5020 Biostatistical Methods
Week 2 Discussion
Parametric vs. Nonparametric Methods
The purpose of this assignment is to differentiate between parametric and nonparametric statistical methods. In addition, this assignment will help you understand and implement parametric or nonparametric statistical methods.
Using the South University Online Library, the Internet, and your text readings, research the following statistical topics:
Levels of measurement
Parametric and nonparametric methods
On the basis of your research and understanding, respond to the following:
Find and state the definition of levels of measurement that distinguishes the five types of data used in statistical analysis.
In your own words, compare the five types of data and explain how they differ.
Find and state a definition of parametric and nonparametric methods that distinguishes between the two.
In your own words, explain the difference between parametric and nonparametric methods.
Explain which types of data require parametric statistics to be used and which types of data require nonparametric statistics to be used and why.
Compare the advantages and disadvantages of using parametric and nonparametric statistics.
Describe how the level of measurement helps determine which of these methods to use on the data being analyzed.
PHE5020 Biostatistical Methods
Week 3 Discussion
Statistics for Contingency Tables
The purpose of this assignment is to learn about categorical data and the statistics used to analyze this type of data.
You can expect to research and provide your own definitions of these concepts. You will also discuss in what situations to use each statistic, how these statistics are used to test for significance of relations among the data, and how to interpret each statistic. The takeaways from this assignment are an understanding of contingency tables as a representation of categorical data, two statistics used to analyze this type of data, and an understanding of how to interpret these statistics in the context of a public health analysis.
Using the South University Online Library, the Internet, and your text readings, research the following statistical topics:
Contingency tables
The chi-square
Fisher’s exact test (FET)
On the basis of your research, respond to the following:
Find and state a definition of a contingency table that you feel is easy to understand.
In your own words, explain what contingency tables are and what they are used for.
Explain what type of data is displayed in contingency tables.
Explain how contingency tables and their related statistics are used to test for significance of relations among the data.
Two statistics that can be used in contingency tables are chi-square and FET. Distinguish between the two statistics.
Explain when you would use the chi-square and when you would use the FET.
Explain how you would interpret each statistic.
PHE5020 Biostatistical Methods
Week 4 Discussion
Coefficient of Determination
The purpose of this assignment is to learn about the coefficient of determination (R2) statistic as a measure of the fit of a regression line.
R2 is a statistical measure of how close the data are to a fitted regression line. In general, the higher the R2, the better the model fits your data. However, while R2 measures goodness of fit, it does not indicate whether a regression model is adequate. You can have a low R2 value for a good model or a high R2 value for a model that does not fit the data.
Using the South University Online Library, the Internet, and your text readings, research about R2.
On the basis of your research and your involvement in public health functions, respond to the following:
Find and state a definition of R2 that you feel is easy to understand.
In your own words, provide a substantive explanation of what R2 represents.
Explain what the statistic R2 is used for in regression analysis.
Explain how R2 is affected by sample size.
Describe whether a large R2 value means that a regression is significant. Provide reasons for your answer.
Describe how you would substantively interpret R2.
PHE5020 Biostatistical Methods
Week 5 Discussion
ORs and RRs
This assignment will help you analyze the relationship of risk (of an illness) to exposure in public health regression analyses. Both ORs and RRs can be used to demonstrate the relationship between exposure and risk. However, each has its own advantages and disadvantages. While ORs are often used in professional papers, they are also often mistaken for RRs. RRs would often be the better choice as they are less complex than ORs and the interpretation is straightforward.
Using the South University Online Library, the Internet, and your text readings, research the following:
ORs
RRs
On the basis of your research, respond to the following:
Identify and state the definition of an OR that you feel is easy to understand.
In your own words, explain what an OR is and for what it is used.
Identify and state the definition of an RR that you feel is easy to understand.
In your own words, explain what an RR is and for what it is used.
Compare and contrast ORs and RRs and how they are used for multisample inferences.
Explain the advantages and disadvantages of using each ratio.
PHE5020 Biostatistical Methods
Week 1 Project
Hypothesis Testing and Inference
This assignment focuses on estimation and hypothesis testing with one-sample and two-sample inferences.
The essence of parametric testing is the use of standard normal distribution tables of probabilities. For each exercise, there will be a sample problem that shows how the calculations are done and at least one problem for you to work out.
For the first assignment, you will not need any statistical software. However, you will use a standardized normal distribution table (a z-score table) provided in the course textbook (Table 3—The normal distribution—in the Tables section in APPENDIX) to obtain your responses.
Click here to access the standardized normal distribution table from your course textbook.
Problem 1: Probability Using Standard Variable z and Normal Distribution Tables
Variables are the things we measure. A hypothesis is a prediction about the relationship between variables. Variables make up the words in a hypothesis.
In the attention-deficit/hyperactivity disorder’s (ADHD’s) hypothetical example provided in the tables below, the research question was: What is the most effective therapy for ADHD? One of the variables is type of therapy. Another variable is change in ADHD-related behavior, given exposure to therapy. You might measure change in the mean seconds of concentration time when children read. This experiment is designed to obtain children’s concentration times while they read a science textbook and to find out whether the therapy used worked on any of the children.
Use the stated µ and σ to calculate probabilities of the standard variable z to get the value of p (up to three decimal places). In addition, respond to the following questions for each pair of parameters:
Which child or children, if any, appeared to come from a significantly different population than the one used in the null hypothesis?
What happens to the “significance” of each child’s data as the data are progressively more dispersed?
In addition to the above, write a formal statement of conclusion for each child in APA style. A report template is provided for submission of your work.
Note: Tables 1 and 2 are practice tables with answers. Tables 3 and 4 are the assignment tables for you to work on.
Table 1 (µ = 100 seconds and σ = 10)
Table 1 (µ = 100 seconds and σ = 10)
Child
Mean seconds of concentration in an experiment of reading
z-score
(z = [X – µ]/σ)
p-value
1
75
-2.50
0.0
2
81
-1.90
0.0
3
89
-1.10
0.1
4
99
-0.10
0.4
5
115
1.50
0.0
6
127
2.70
0.0
7
138
3.80
<0.0
8
139
3.90
<0.0
9
142
4.20
<0.0
10
148
4.80
<0.0
Table 2 (µ = 100 seconds and σ = 20)
Child
Mean seconds of concentration in an experiment of reading
z-score
(z = [X – µ]/σ)
p-value
1
75
-1.25
0.1
2
81
-0.95
0.1
3
89
-0.55
0.2
4
99
-0.05
0.4
5
115
0.75
0.2
6
127
1.35
0.0
7
138
1.90
0.0
8
139
1.95
0.0
9
142
2.10
0.0
10
148
2.40
0.0
Table 3 (µ = 100 seconds and σ = 30)
Child
Mean seconds of concentration in an experiment of reading
z-score
p-value
1
75
-0.83
2
81
-0.63
3
89
-0.37
4
99
-0.03
5
115
0.50
6
127
0.09
7
138
1.27
8
139
1.30
9
142
1.40
10
148
1.60
Table 4 (µ = 100 seconds and σ = 40)
Child
Mean seconds of concentration in an experiment of reading
z-score
p-value
1
75
-0.63
2
81
-0.48
3
89
-0.28
4
99
-0.03
5
115
0.38
6
127
0.68
7
138
0.95
8
139
0.98
9
142
1.05
10
148
1.20
Click here for a template to provide your answers and submit the assignment.
Refer to the Assignment Resources on this page for Two Independent Samples of t-Test to view an example of probability using standard variable and normal distribution tables. The same resource is also available under lecture Estimation and Hypothesis Testing.
Problem 2: Two-Sample Inferences
A two-sample inference deals with dependent and independent inferences. In a two-sample hypothesis testing problem, underlying parameters of two different populations are compared. In a longitudinal (or follow-up) study, the same group of people is followed over time. Two samples are said to be paired when each data point in the first sample is matched and related to a unique data point in the second sample.
This problem demonstrates inference from two dependent (follow-up) samples using the data from the hypothetical study of new cases of tuberculosis (TB) before and after the vaccination was done in several geographical areas in a country in sub-Saharan Africa. Conclusion about the null hypothesis is to note the difference between samples.
The problem that demonstrates inference from two dependent samples uses hypothetical data from the TB vaccinations and the number of new cases before and after vaccination.
Table 5: Cases of TB in Different Geographical Regions
Geographical regions
Before vaccination
After vaccination
1
85
11
2
77
5
3
110
14
4
65
12
5
81
10
6
70
7
7
74
8
8
84
11
9
90
9
10
95
8
Using the Minitab statistical analysis program to enter the data and perform the analysis, complete the following:
Construct a one-sided 95% confidence interval for the true difference in population means.
Test the null hypothesis that the population means are identical at the 0.05 level of significance.
Click here to install Minitab Software.
In addition, in a Microsoft Word document, provide a written interpretation of your results in APA format.
Problem 3: Cross-Sectional Study
In a cross-sectional study, the participants are seen at only one point of time. Two samples are said to be independent when the data points in one sample are unrelated to the data points in the second sample.
The problem that demonstrates inference from two independent samples will use hypothetical data from the American Association of Poison Control Centers.
There are two groups of independent data collected in different regions, which also calls for a t-test. The numbers represent the number of recorded cases of poisoning with chemicals in the homes of 100,000 people in two regions.
Table 6: Cases of Poisoning With Chemicals
Year Region 1 Region 2
1 150 11
2 160 10
3 132 14
4 110 12
5 85 10
6 45 11
7 123 9
8 180 11
9 143 10
10 150 14
Using the Minitab statistical analysis program to enter the data and perform the analysis, complete the following:
Formulate a null and an alternative hypothesis for a two-sided test.
Conduct the test at the 0.05 level of significance.
In addition, in a Microsoft Word document, provide a written interpretation of your results in APA format.
PHE5020 Biostatistical Methods
Week 2 Project
Instructions
Week 2: Project Assignment
This assignment focuses on nonparametric methods. When a researcher is not in a situation to be able to assume parametric statistical methods requirements, known distribution, or dealing with small sample size, then nonparametric statistical methods need to be used, which make fewer assumptions about the distributional shape.
Click here to install Minitab Software.
Nonparametric Methods
In this assignment, we will use the following nonparametric methods:
The Wilcoxon signed-rank test: The Wilcoxon signed-rank test is the nonparametric test analog of the paired t-test.
The Wilcoxon rank-sum test or the Mann-Whitney U test: The Wilcoxon rank-sum test is an analog to the two-sample t-test for independent samples.
For each exercise, there will be a sample problem that shows how the calculations are done and the problems for you to work on.
Part 1: Wilcoxon Signed-Rank Test
Let’s take a hypothetical situation. The World Health Organization (WHO) wants to investigate whether building irrigation systems in an African region helped reduce the number of new cases of malaria and increased the public health level.
Data was collected for the following variables from ten different cities of Africa:
The number of new cases of malaria before the irrigation systems were built
The number of new cases of malaria after the irrigation systems were built
Table 1: Cases of Malaria
City
Before
After
1
110
55
2
240
75
3
68
15
4
100
10
5
120
21
6
110
11
7
141
41
8
113
5
9
112
13
10
110
8
Using the Minitab statistical analysis program to enter the data and perform the analysis, complete the following:
Run a sample Wilcoxon signed-rank test to show whether there is a statistically significant difference between the number of cases before and after the irrigation systems were built.
Obtain the rank-sum.
Determine the significance of the difference between the groups.
Determine whether building these systems helped reduce new cases of malaria.
In addition, in a Microsoft Word document, provide a written interpretation of your results in APA format. Refer to the Assignment Resources: Wilcoxon Signed-Rank Test Example to view an example of the Wilcoxon signed-rank test. The same resource is also available under lecture Nonparametric Methods.
Part 2: Wilcoxon Rank-Sum Test
Let us consider another hypothetical situation. The WHO wants to compare the mortality rates of children under the age of five years of underdeveloped and developed regions of the world. There were two independent samples of ten countries from each of the groups drawn at the same time, and the yearly mortality rates of children under the age of five years (per 100,000) inhabitants were reported (MRate1 and MRate2).
Table 2: Mortality Rates of Children
Country
MRate1
MRate2
1
120
11
2
110
9
3
105
13
4
61
11
5
45
14
6
114
11
7
118
10
8
138
8
9
85
6
10
70
6
Using the Minitab statistical analysis program to enter the data and perform the analysis, complete the following:
Run the Wilcoxon rank-sum test to show whether there is a statistically significant difference between the mortality rates of children under the age of five years of the regions. Results may be used in making decisions regarding which region needs to receive help to improve the public health issues of morality.
Obtain the difference in the mortality rates and whether there is a statistically significant difference.
In addition, in a Microsoft Word document, provide a written interpretation of your results in APA format.
PHE5020 Biostatistical Methods
Week 3 Project
Week 3: Project Assignment
Statistics for Categorical Data: Odds Ratios and Chi-Square
This assignment focuses on categorical data. Two of the statistics most often used to test hypotheses about categorical data are odds ratios (ORs) and the chi-square. The disease-OR refers to the odds in favor of disease in the exposed group divided by the odds in favor of the unexposed group. Chi-square statistics measure the difference between the observed counts and the corresponding expected counts. The expected counts are hypothetical counts that would occur if the null hypothesis were true.
Part 1: ORs
A study conducted by López-Carnllo, Avila, and Dubrow (1994) investigated health hazards associated with the consumption of food local to a particular geographic area, in this case chili peppers particular to Mexico. It was a population-based case-control study in Mexico City on the relationship between chili pepper consumption and gastric cancer risk. Subjects for the study consisted of 213 incident cases and 697 controls randomly selected from the general population. Interviews produced the following information regarding chili consumption:
Table 1: Chili Pepper Consumption and Gastric Cancer Risk
Chili pepper consumption
Case of gastric cancer
Controls
Yes
A = 204
B = 552
No
C = 9
D = 145
Reference:
López-Carnllo, L., Avila, M. H., & Dubrow, R. (1994). Chili pepper consumption and gastric cancer in Mexico: A case-control study. American Journal of Epidemiology, 139(3), 263–271.
Note: You do not need to use the Minitab software to complete this assignment.
In a Microsoft Excel worksheet, calculate the odds of having gastric cancer.
In addition, provide a written interpretation of your results in APA format.
Refer to the Assignment Resources: Odds Ratio to view an example of odds ratio. The same resource is also available under lecture Testing Hypotheses.
Part 2: Chi-Square
Bain, Willett, Hennekens, Rosner, Belanger, and Speizer (1981) conducted a study of the association between current postmenopausal hormone use and risk of nonfatal myocardial infarction (MI), in which 88 women reporting a diagnosis of MI and 1,873 healthy control subjects were identified from a large population of married female registered nurses aged thirty to fifty-five years. To test the hypothesis that there is no association between use of postmenopausal hormones and risk of MI, chi-square statistics need to be calculated.
The data are presented as follows:
Table 2: Association between Postmenopausal Hormone Use and Risk of Nonfatal MI
Cases
Controls
Total
Currently use
32
825
857
Never use
56
1,048
1,104
Total
88
1,873
1,961
Reference:
Bain, C., Willett, W., Hennekens, C. H., Rosner, B., Belanger, C., & Speizer,
F. E. (1981). Use of postmenopausal hormones and risk of myocardial
infarction. Circulation, 64(1), 42–46.
Using the Minitab procedure, enter the data, perform appropriate procedures, and provide calculations from the table.
In addition, in a Microsoft Word document, provide a written interpretation of your results in APA format.
PHE5020 Biostatistical Methods
Week 4 Project
Regression and Correlation Methods: Correlation, ANOVA, and Least Squares
This is another way of assessing the possible association between a normally distributed variable y and a categorical variable x. These techniques are special cases of linear regression methods. The purpose of the assignment is to demonstrate methods of regression and correlation analysis in which two different variables in the same sample are related.
The following are three important statistics, or methodologies, for using correlation and regression:
Pearson’s correlation coefficient
ANOVA
Least squares regression analysis
In this assignment, solve problems related to these three methodologies.
Part 1: Pearson’s Correlation Coefficient
For the problem that demonstrates the Pearson’s coefficient, you will use measures that represent characteristics of entire populations to describe disease in relation to some factor of interest, such as age; utilization of health services; or consumption of a particular food, medication, or other products. To describe a pattern of mortality from coronary heart disease (CHD) in year X, hypothetical death rates from ten states were correlated with per capita cigarette sales in dollar amount per month. Death rates were highest in states with the most cigarette sales, lowest in those with the least sales, and intermediate in the remainder. Observation contributed to the formulation of the hypothesis that cigarette smoking causes fatal CHD. The correlation coefficient, denoted by r, is the descriptive measure of association in correlational studies.
Table 1: Hypothetical Analysis of Cigarette Sales and Death Rates Caused by CHD
State
Cigarette sales
Death rate
1
102
5
2
149
6
3
165
6
4
159
5
5
112
3
6
78
2
7
112
5
8
174
7
9
101
4
10
191
6
Using the Minitab statistical procedure:
Calculate Pearson’s correlation coefficient.
Create a two-way scatter plot.
In addition to the above:
Explain the meaning of the resulting coefficient, paying particular attention to factors that affect the interpretation of this statistic, such as the normality of each variable.
Provide a written interpretation of your results in APA format.
Refer to the Assignment Resources: Dot Plots and Correlation and Resources: Performing Regression Analysis to view an example of Pearson’s correlation coefficient. This same resources are also available under lecture Correlation and Regression Methods.
Part 2: ANOVA
Let’s take hypothetical data presenting blood pressure and high fat intake (less than 3 grams of total fat per serving) or low fat intake (less than 1 gram of saturated fat) of an individual.
Table 2: Blood Pressure and Fat Intake
Individual
Blood Pressure
Fat Intake
1
135
1
2
130
1
3
135
1
4
128
0
5
121
0
6
133
0
7
145
1
8
137
1
9
148
1
10
134
0
11
150
0
12
121
0
13
117
1
14
128
1
15
121
0
16
124
1
17
132
0
18
121
0
19
120
0
20
124
0
Using the Minitab statistical procedure:
Calculate a one-way ANOVA to test the null hypothesis that the mean of each group is the same.
Use different variables as grouping variables (fat intake high 1; fat intake low 0) and compare the results.
Calculate an F-test for an overall comparison of means to see whether any differences are significant.
In addition, in a Microsoft Word document, provide a written interpretation of your results in APA format.
Visit the media Resources: One-Way ANOVA on lecture Correlation and Regression Methods to view an example of ANOVA.
Using the Minitab statistical procedure:
Apply least squares analysis to fit a regression line to the data.
Calculate an F-test and a t-test to test for the significance of the regression.
Test for goodness of fit using R2.
In addition, in a Microsoft Word document, provide a written interpretation of your results in APA format.
PHE5020 Biostatistical Methods
Week 5 Project
Analysis of Biostatistical Article
Identify a peer-reviewed article from the South University Online Library that presents statistical analysis of a pertinent topic of public health interest or importance. Provide a link to this article and give a brief summary of the article, including hypotheses, methods, and findings. Research the topic and available data sources. On the basis of the biostatistical methods you have learned about in this course, analyze the article and its findings.
Here are some points to consider in your analysis:
What data are available on this topic?
What data does the article use?
Discuss the level of measurement, assumptions that can be made, statistics that can be calculated from these data, and the general quality of the data.
What is the type of study or study design used?
Explain the type of biostatistical study design that the author has used.
Describe the hypothesis or hypotheses that the author intends to test.
Explain the statistics that the author uses to test these hypotheses.
What are the article’s statistical findings?
Describe the statistical results of the author’s analysis.
Provide a substantive interpretation of these findings (What do the results mean in relation to the hypotheses and the public health topic?).
Describe the author’s recommendations about this topic based on his or her findings and hypotheses.
If you had been the author, what changes, if any, would you have made in the study you analyzed?
Discuss whether the author made any statistical errors.
Were the correct data used for the questions asked?
Were the correct data available?
Were the correct statistics used for the data available?
What other data might you want to collect and why?
Do the statistical findings support the author’s conclusions?
Write a 15–20-page, double-spaced paper in Word format. Apply APA standards to citation of sources. Utilize at least 7–10 scholarly sources in your research and be sure to include a references page. Write in a clear, concise, and organized manner; demonstrate ethical scholarship in accurate representation and attribution of sources; and display accurate spelling, grammar, and punctuation.
PHE5020 Biostatistical Methods
Week 1 Knowledge Check
Question 1 The statistical process of using samples to estimate population parameters is known as:
Statistical interference.
Statistical inference.
Statistical confidence.
Descriptive statistics.
Question 2 If a researcher wishes to determine whether there is evidence that the mean fasting glucose level in adults with type 2 diabetes is different from 110mg/dL, then
a two-dependent samples t-test should be considered.
a two-independent sample t-test should be considered.
a one-sample t-test should be considered.
either a one-sample or two-dependent samples t-test should be considered.
Question 3 Power is defined as:
the probability that you will retain/keep the null hypothesis if it is false.
the probability that you will reject the null hypothesis if it is true.
by your research hypothesis only.
the probability that you will reject the null hypothesis if it is false.
PHE5020 Biostatistical Methods
Week 2 Knowledge Check
Question 1 Which of the following statements is not true of parametric statistics?
They are inferential tests.
They assume certain characteristics of population parameters.
They assume normality of the population.
They are distribution-free.
Question 2 Assume you are conducting a study and find that the data violate all the assumptions of the statistic you had planned to conduct, what are your alternatives?
Conduct the statistical test since there will be no evidence of the error.
Run the study again and hope the data are better.
Conduct a nonparametric statistical test.
Change the research question.
Question 3 Under what circumstances would you use a non- parametric test?
In a pilot study.
When your data does not meet the assumptions for a parametric test.
When you think your sample size is too big.
When you do not really understand a parametric test.
PHE5020 Biostatistical Methods
Week 3 Knowledge Check
Question 1: Chi-square test for independence assesses which of the following?
It assesses whether there is a relationship between the population and the sample.
It assesses whether there is a relationship between two categorical variables.
It assesses whether there is significant difference between scores taken at time 1 and those taken at time 2.
It assesses whether the minimum number of cases exceeds recommended boundaries.
Question 2: Which tests could be used if in a contingency table your expected cases were fewer than what is required for the Chi-square test?
Chi-square test for independence.
Two-independent sample t-test.
Fisher’s Exact Probability Test.
Paired-samples t-tests.
Question 3: Contingency tables and degrees of freedom are key elements of the chi-square test.
Question 3 options:
True
False
PHE5020 Biostatistical Methods
Week 4 Knowledge Check
Question 1: Correlation refers to:
The causal relationship between two variables.
The linear relationship between two variables.
The proportion of variance that two variables share.
A statistical method that can only be used with a correlational research design.
Question 2: If two variables are highly correlated, what do you know?
That they always go together.
That high values on one variable lead to high values on the other variable.
That there are no other variables responsible for the relationship.
That changes in one variable are accompanied by predictable changes in the other.
Question 3: The coefficient of determination tells us:
The proportion of variance in X accounted for by the mean of Y.
The proportion of variance in Y accounted for by X.
The mean value of Y.
The mean value of X.
PHE5020 Biostatistical Methods
Week 5 Knowledge Check
Question 1 All the following statements are true for the odds ratio except:
can be calculated obtained from case-control studies.
it is the incidence between the exposed divided the incidence between the un-exposed.
it is an estimate of relative risk.
it tends to be biased towards 1.
Question 2 : The analysis of epidemiological studies is based on the following except:
contingency tables
statistics that measure effects
measuring the confounders
experimental effect size.
Question 3 Epidemiology describes the distribution of disease in terms of Person, Place and Time.
True
False
Question 4 Epidemiological studies usually describe the characteristics of people in terms of age, gender, race, ethnicity, socioeconomic status and religion, among others.
True
False
Question 5 The most important difference between odds ratios and relative risks is that odds ratios measure incidence directly from the observed data.
True
False
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