Transcript Fundamentals of Research Project Planning: Hypotheses

Introduction to Biostatistics
Dr. M. H. Rahbar
Professor of Biostatistics
Department of Epidemiology
Director, Data Coordinating Center
College of Human Medicine
Michigan State University
What does “STATISTICS” mean?
The word “Statistics” has several meanings:
• It is frequently used in referring to recorded
data
2. Statistics also denotes characteristics calculated
for a set of data, for example, sample mean
3. Statistics also refers to statistical methodology,
techniques and procedures dealing with the
design of experiments, collection, organization,
analysis of the information contained in a data
set to make inferences about the population
parameters
What do statisticians do?
• To guide the design of an experiment or
survey prior to the data collection
2. To analyze data using proper statistical
procedures and techniques
3. To present and interpret results to the
researchers and other decision makers
including the government and industries
WHY STUDY STATISTICS?
• Knowledge of statistics is essential for people
going into research, management or graduate
study
2. Basic understanding of statistics is useful for
conducting investigations and an effective
presentation
3. Understanding of statistics can help anyone
discriminate between fact and fancy in daily
life
• A course in statistics should help one know
when, and for what, a statistician should be
consulted
Definition of Population & Sample
A population is a set of measurements of interest
to the researcher.
Examples:
1. Income of households living in Karachi
2. The number of children in families living
Pakistan
3. The health status of adults in a community
A subset of the population is called sample.
A sample is usually selected such that it is
representative of the population
Descriptive & Inferential Statistics
1. Descriptive Statistics deal with the
enumeration, organization and graphical
representation of data
2. Inferential Statistics are concerned with
reaching conclusions from incomplete information,
that is, generalizing from the specific sample
An example of inferential statistics include using
available information about the health status of
people in a sample to draw inferences about the
underlying population from which the sample is
selected
INFERENTIAL STATISTICS
The objective of inferential statistics is to make
inference about the population parameters
based on the information contained in the
sample.
1. Estimation (e.g., Estimating the prevalence of
hypertension among adults living in Karachi)
2. Testing Hypothesis (e.g., Testing the
effectiveness of a new drug for reducing
cholesterol levels)
Sources of Data
1.
2.
3.
4.
5.
6.
Data may come from different sources:
Surveillance systems (e.g., NIH)
Planned surveys (Government, Universities,
NGOs)
Experiments (Pharmaceutical Companies)
Health Organizations (Administrative Data sets)
Private sector (Banks, Companies, etc)
Government (All government agencies)
Here we will focus on surveys and experiments
What is the difference between a survey and an
experiment?
Difference between Surveys &
Experiments
A Survey Data represent observations of
events or phenomena over which few, if any,
controls are imposed.
(e.g., Assessing the association between
different lifestyles and heart disease)
In an experiment we design a research plan
purposely to impose controls over the
amount of exposure (treatment) to a drug.
(e.g., Clinical Trials)
Sampling Methods
• Random Sampling (Simple)
• Systematic Sampling
• Stratified Sampling
4. Cluster Sampling
5. Convenience Sampling
6. More complex sampling
Some Epidemiologic Studies
Retrospective Studies:
Retrospective Studies gather past data from
selected cases and controls to determine
difference, if any, in the exposure to a suspected
factor. They are commonly referred to as casecontrol studies
Prospective Studies:
Prospective studies are usually cohort studies in
which one enrolls a group of healthy people and
follows them over a certain period to determine
the frequency with which a disease develops
Qualitative and Quantitative
Variables
Examples of qualitative variables are
occupation, sex, marital status, and etc
Variables that yield observations that can be
measured are considered to be quantitative
variables. Examples of quantitative variables
are weight, height, and age
Quantitative variables can further be
classified as discrete or continuous
VARIABLES TYPES
1. Categorical variables (e.g., Sex, Marital
Status, income category)
2. Continuous variables (e.g., Age, income,
weight, height, time to achieve an outcome)
3. Discrete variables (e.g.,Number of Children
in a family)
4. Binary or Dichotomous variables (e.g.,
response to all Yes or No type of questions)
VARIABLES SCALE
• SCALE OF VARIABLE
– Nominal Scale
– Ordinal Scale
– Interval Scale
– Interval Ratio Scale
Scale of Data
1. Nominal: These data do not represent an amount
or quantity (e.g., Marital Status, Sex)
2. Ordinal: These data represent an ordered series
of relationship (e.g., level of education)
3. Interval: These data is measured on an interval
scale having equal units but an arbitrary zero
point. (e.g.: Temperature in Fahrenheit)
4. Interval Ratio: Variable such as weight for which
we can compare meaningfully one weight versus
another (say, 100 Kg is twice 50 Kg)
VARIABLES IN THE PROTOCOL
• TYPES OF VARIABLE
– independent
– dependent
– intermediate
– confounding
Independent Variable
• The characteristic being observed and/or
measured that is hypothesized to influence
an event or outcome (dependent variable).
• NOTE
– The independent variable is not influenced
by the event or outcome, but may cause it or
contribute to its variation.
Dependent Variable
• A variable whose value is dependent on
the effect of other variables (ie.,
“independent variables”) in the
relationship being studied. Synonyms:
outcome or response variable.
• NOTE
– an event or outcome whose variation we
seek to explain or account for by the
influence of independent variables.
Intermediate Variable
• A variable that occurs in a causal pathway
from an independent to a dependent variable.
Synonyms: intervening, mediating
• NOTES
– it produces variation in the dependent
variable, and is caused to vary by the
independent variable.
– such a variable is “associated” with both the
dependent and independent variables.
Confounding Variable
• A factor (that is itself a determinant of
the outcome), that distorts the apparent
effect of a study variable on the outcome.
• NOTE
– such a factor may be unequally
distributed among the exposed and the
unexposed, and thereby influence the
apparent magnitude and even the
direction of the effect.
Organizing Data
1.
2.
3.
4.
5.
6.
7.
8.
9.
Frequency Table
Frequency Histogram
Relative Frequency Histogram
Frequency polygon
Relative Frequency polygon
Bar chart
Pie chart
stem-and-leaf display
Box Plot
Frequency Table
Suppose we are interested in studying the
number of children in the families living in a
community. The following data has been
collected based on a random sample of n = 30
families from the community.
2, 2, 5, 3, 0, 1, 3, 2, 3, 4, 1, 3, 4, 5, 7, 3, 2, 4, 1, 0,
5, 8, 6, 5, 4 , 2, 4, 4, 7, 6
Organize this data in a Frequency Table!
X=No. of
Children
0
1
2
3
4
5
6
7
8
Count
(Freq.)
2
3
5
5
6
4
2
2
1
Relative Freq.
2/30=0.067
3/30=0.100
5/30=0.167
5/30=0.167
6/30=0.200
4/30=0.133
2/30=0.067
2/30=0.067
1/30=0.033
6
5
4
Freq.
3-D Column 2
3-D Column 3
3
2
1
0
0
1
2
3
4
5
6
7
8
Frequency Table
Now suppose we need to construct a similar
frequency table for the age of patients with Heart
related problems in a clinic.
The following data has been collected based on a
random sample of n = 30 patients who went to the
emergency room of the clinic for Heart related
problems.
The measurements are: 42, 38, 51, 53, 40, 68, 62,
36, 32, 45, 51, 67, 53, 59, 47, 63, 52, 64, 61, 43, 56,
58, 66, 54, 56, 52, 40, 55, 72, 69.
Age Groups
Frequency
Relative
Frequency
32 -36.99
37- 41.99
42-46.99
47-51.99
52-56.99
57-61.99
62-66.99
67-72
Total
2
3
4
3
8
3
4
3
n=30
2/30=0.067
3/30=0.100
4/30=0.134
3/30=0.100
8/30=0.267
3/30=0.100
4/30=0.134
3/30=0.100
1.00
Measures of Central Tendency
Where is the heart of distribution?
1. Mean
2. Median
3. Mode
Sample Mean
The arithmetic mean (or, simply, mean) is
computed by summing all the observations in the
sample and dividing the sum by the number of
observations.
For a sample of five household incomes, 6000,
10,000, 10,000, 14000, 50,000 the sample mean is,
6000 + 10000 + 10000 + 14000 + 50000
X =
= 18000
5
Sample Median
In a list ranked from smallest
measurement to the highest, the median is
the middle value
In our example of five household incomes,
first we rank the measurements
6,000, 10,000, 10,000, 14,000, 50,000
Sample Median is 10,000
Measures of Dispersion or
Variability
1. Range
2. Variance
3. Standard deviation
Formula for Sample Variance &
Standard deviation S
n
 ( xi - x )
2
s =
2
i=1
n -1
Standard deviation = S
Calculation of Variance and
Standard deviation
2
2
2
2
2 (6000-18000 ) +(10000-18000 ) +(10000-18000 ) +(14000-18000)+(50000-18000 )
=
S=
5-1
2
S = 328,000,000
S  18110.77
Empirical Rule
For a Normal distribution approximately,
a) 68% of the measurements fall within one
standard deviation around the mean
b) 95% of the measurements fall within two
standard deviations around the mean
c) 99.7% of the measurements fall within three
standard deviations around the mean
Suppose the reaction time of a particular drug
has a Normal distribution with a mean of 10
minutes and a standard deviation of 2 minutes
Approximately,
a) 68% of the subjects taking the drug will have
reaction tome between 8 and 12 minutes
b) 95% of the subjects taking the drug will have
reaction tome between 6 and 14 minutes
c) 99.7% of the subjects taking the drug will have
reaction tome between 4 and 16 minutes