Name: _
Elementary Biostatistics
BIOS 2010
Spring 2015, Practice Test 1
FOR FULL CREDIT, YOU MUST SHOW ALL WORK AND EXPLAIN ALL REASONING.
1. The following histogram and boxplot show data from a smallpox outbreak in the
community of Abakaliki in southeast
HTN +
36
9
45
Test +
Test Total
HTN 25
230
255
Please calculate the following based on the information provided in the table:
Sensitivity
36/45 = 0.8
Specificity
230/255 = 0.9
Prevalence
45/300 = 0.15
Positive Predictive Value
36/61 = 0.59
Negative Predic
Poisson Distribution Practice Problems
1. Twenty sheets of aluminum alloy were examined for surface flaws. The frequency of the
number of sheets with a given number of flaws per sheet was as follows:
Number of Flaws
0
1
2
3
4
5
6
Frequency
4
3
5
2
4
1
1
W
McNemars Test for Paired Samples
Designs
Data
Paired Samples Independent Samples
Continuous
paired t-test
two-sample t-test
Binary
McNemars Test
Chi-square test
McNemars test is used to compare binary responses in paired samples.
Example: Treatment of Bre
Tests for Independence
So far, we have considered contingency tables in which:
One binary variable can be viewed as an explanatory variable;
Another binary variable can be viewed as the response variable.
Here, we have considered hypothesis tests of the
Inferences About the Population Mean and Variance
Consider inferences about the population mean and population variance 2 .
Two Cases:
1. The data are sampled from a target population of N subjects with mean
N
1
N
xi
i1
and variance
2
N
x i 2
i1
N1
2
Paired t-test
One-Sample t-test: Compares the mean of a single sample to a hypothesized value.
Today: Consider methods for comparing the means of two samples.
Methods:
Paired t-test*. Paired-sample data.
Two-sample t-test. Independent samples.
Definitio
Introductory Biostatistics I
Homework 4
1. The following table gives the probability distribution of family sizes.
Number of Children (x) Probability (p x )
xp x
x2
x2px
0
0.419
0.000
0
0.000
1
0.178
0.178
1
0.178
2
0.230
0.460
4
0.920
3
0.116
0.348
9
1.0
Introductory Biostatistics I
Homework 3 (Solutions)
1. A psychiatric researcher wishes to evaluate a new diagnostic instrument for psychotic
illness. The test is comprised of 20 questions regarding individual psychiatric symptoms.
A positive test is one i
Introductory Biostatistics I
Homework 2
Due: September 5, 2008
1. The Food-Frequency Questionaire (FFQ) is an instrument often used in nutritional
epidemiology to assess consumption of nutrients and vitamins. This questionaire asks
subjects to recall the
Analysis of Variance (ANOVA)
Suppose that we wish to test the effects of three or more treatments. Consider a
completely randomized design.
Definition. Under a completely randomized design, experimental units are randomly
allocated to the treatments.
Proc
Tests for Independence
So far, we have considered contingency tables in which:
One binary variable can be viewed as an explanatory variable;
Another binary variable can be viewed as the response variable.
Here, we have considered hypothesis tests of the f
Introduction to Biostatistics
What is Biostatistics?
The field of statistics is concerned with the collection, summarization, analysis,
and interpretation of information in the presence of uncertainty.
Statistics are also numerical summaries of informat
Two-Sample t-test
We have been looking at methods for comparing two samples.
Methods:
Paired t-test. Paired-sample data.
Two-sample t-test. Independent samples.
Definition: Two samples are said to be paired if each data point in the first sample is
matc
this is not a random sampling design. No manipulations were applied, so this is not a randomized experiment.
1.
2.
Since we are working with volunteers, this is not a random sampling design. However, manipulations were applied (memory enhancement vs. cont
Exploratory Data Analysis
Once the data are obtained from a sample of subjects, the first step of a statistical
analysis is an Exploratory Data Analysis (EDA).
Moreover, the first step in a clinical trial is to obtain baseline characteristics of the
parti
Design of Public Health Surveys and Clinical Trials
Study Types
Prospective
Retrospective
Cross-Sectional
Prospective Studies
Definition. For a prospective study, subjects are recruited before the health outcome
of interest has occurred and then follow
Statistical Inference (Overview)
Definition: Statistical inference is the process of drawing conclusions regarding the
properties of a population or stochastic model from the characteristics of a sample.
Examples:
Estimate the number of people in the Unit
Nonparametric Methods
Wilcoxon Rank-Sum Test
Recall: Nonparametric statistical methods make no assumptions regarding the
distribution of the data.
Nonparametric methods used when:
The data are not normally distributed, especially for small samples;
Ther
Inferences About the Population Mean and Variance
Consider inferences about the population mean and population variance 2 .
Two Cases:
1. The data are sampled from a target population of N subjects with mean
1
N
N
xi
i 1
and variance
2
N
i 1
xi
2
N 1
2. T
Discrete Probability Distributions
Example: Genetics
Background:
In most organisms, chromosomes come in pairs.
At each locus, there are two copies of a gene, one on each member of the pair.
Genes can come in multiply types called alleles.
Suppose that
Inference for the Binomial Distribution
Recall: A random variable X is binomial distributed with parameters p and n if it has
probability mass function
PrX k
n
k
p k 1 p nk
The binomial distribution is used to model the frequency of a trait in a sample o
Hypothesis Testing: Single Population
Example: USDA Womens Health Survey
In 1985, the USDA commissioned a study of womens nutrition. Daily nutrient intake
was measured for a random sample of 737 women aged 25-50 years. The sample
mean calcium intake was
x
Power and Sample Size Determination
Public health investigations require planning before their implementation.
Question: How many subjects do we require to meet the study objectives?
Make sure that data from a sufficient number of subjects is selected to
Comparisons of Proportions or Odds
Binary Variables
So far, we have been concerned with hypothesis testing for continuous, quantitative
variables; for example:
Blood pressure;
Concentration of lead in blood;
Number of minutes of pain relief;
Today, we
Normal Distribution
Question: Why consider the normal distribution?
1. Mathematical Simplicity. This has led to the development of most statistical
methods.
2. Central Limit Theorem. If X 1 , X 2 , , X n are independent, identically distributed
random var
Graphical Methods
One of the first steps in the analysis of any data set is an Exploratory Data Analysis
(EDA), including the graphical display of the data.
Objectives:
Provide a visual summary of the data;
Suggest a plausible model for the data;
Asses
Analysis of R C Contingency Tables
Example: Attitudes of Psychiatrists Regarding the Origins of Schizophrenia*
Procedure:
Survey sent to 1,241 members of the American Psychiatric Association
A total of 339 members responded to the survey.
Responses cro
Introduction to Probability
Probability is the foundation upon which biostatistics is built:
It forms the basis for inferences about the characteristics of a population from
the characteristics of a sample;
Whether or not we reject a null hypothesis is
Screening Tests and Bayes Theorem
Screening Tests:
If diagnosed early, many diseases including cancer can be treated more
effectively than if diagnosed late;
Gold-standard tests (e.g., biopsies) are often expensive or highly invasive;
Public health cos