AMS 7 – BIOSTATISTICS

382 Pages·2009·5.65 MB·English

by  Abel Rodriguez

AMS 7 – B
IOSTATISTICS
1 Abel Rodriguez
Spring 2009
W ?
HAT IS STATISTICS
A collection of methods for planning experiments,
obtaining data and then organizing, summarizing,
analyzing, interpreting, presenting and drawing
conclusions based on data.
The word statistics comes from status (meaning “state”).
Early uses involved compilations of data (numbers)
describing various aspects of a state or country.
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L
EARNING FROM DATA
Steps in learning from data:
Designing the data collection process (study
 
design / experimental design).
Preparing and analyzing the data (descriptive
 
statistics, models).
Reporting conclusions.
 
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S E N
TUDY OF THE FFECTS OF ITROGEN
F
ERTILIZER IN WHEAT PRODUCTION
Setting: 15 fields and 5 nitrogen rates. Three
 
fields were randomly assigned to each of the
nitrogen rates. The same variety of wheat was
planted in all fields and they were cultivated in
the same manner. The number of pounds of
wheat per acre was recorded.
Goal: to determine the amount of nitrogen that
 
yielded the largest production of wheat, the
experimenter concluded that similar results
would hold for fields with the same
characteristics as the ones in the study. Is this
conclusion justified?
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P S
OPULATION AND AMPLE
In this case it is important to measure soil
 
characteristics of the fields and environmental
conditions to obtain results that can be
generalized to fields not included in the study 
the design of the experiment is crucial.
A population is the set of all elements of interest
 
to the sample collector.
A sample is any subset of elements selected from
 
the population.
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P S
OPULATION AND AMPLE
We typically refer to the values of the variables
 
on the N individuals of the population as X , …,
1
X . Sometimes N can be infinite.
N
We typically refer to the observations as in a
 
sample of size n as x , …, x
1 n
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P S
OPULATION AND AMPLE
The descriptive characteristics of a population
 
can be summarized by some population
parameters. These are measures that are typical
of each population. Usual examples are the
central tendency of the population or its
dispersion. Parameters are usually unknown
quantities.
Parameters are estimated using values from a
 
sample. Sample values are used to obtain a
statistic. Actually, any function of a sample is
called a statistic. The observed value of a statistic
depends on how the sample is obtained, thus
statistics are random variables.
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D T
ATA YPES
Quantitative data consists of numbers
 
representing counts or measurements.

Discrete data: the number of possible values is either
 
a finite number or a countable number.
Continuous data: are the result from infinitely many
 
possible values not restricted to certain specified
values (such as integers).
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D T
ATA YPES
Qualitative data, also called categorical or
 
attribute data. These can be separated into
different categories that are distinguished by
some non-numeric characteristics.
Nominal data consist of names, labels or categories
 
only. There is no natural ordering to this categories.
Ordinal data can be arranged in some order but
 
differences between data values either cannot be
determined or are meaningless.
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E
XAMPLES
This scale is used to classify the performance
status of patients in a clinical trial.
Description
0 Fully active, able to carry on all pre-disease performance without restriction.
1 Restricted in physically strenuous activity but ambulatory and able to carry
out work of a light or sedentary nature.
2 Ambulatory and capable of all self-care but unable to carry out any work
activities; up and about more than 50% of waking hours.
3 Capable of only limited self-care; confined to bed or chair more than 50% of
waking hours.
5 Completely disabled; not capable of any self-care; totally confined to bed or
chair.
Note that differences in magnitude are
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meaningless this is an example of ordinal data.