Biostatistics I: Unit 02 – Parameters and Statistics Notes

Slide 1

In this learning unit, we will cover parameters and statistics.

Slide 2
In biostatistics, we use different terminology to refer to characteristics that summarize
data obtained from populations and samples: parameters and statistics.Parameters
and Statistics are characteristics that summarize data obtained from populations and
samples.You will learn about the notation used by statisticians to differentiate characteristics
of populations from characteristics of samples. Because populations and samples form the basis
of statistics, knowing how they are defined and what kinds of notations are used is essential.

Slide 3
Summary characteristics of populations are called parameters.

Slide 4
Estimates of parameters obtained from samples are called statistics.

Slide 5
If the population of interest is the blood pressures of all of the students at USF,
then the mean blood pressure of all of the students would be a parameter
of that population.If one were to take a random sample of 100 students
from USF, the mean blood pressure of that sample would be a statistic
and would provide an estimate of the mean blood pressure among
the population of all USF students.

Slide 6

Self assessment

Slide 7
The word statistic often is used incorrectly in the popular press. For example,
the number of people who died of a reportable illness, for example, AIDS,
in Florida last year is frequently described as a statistic. Assuming that
all deaths were reported, this number would be a parameter, not a statistic.
We might look at number of people with AIDS who died in January and
use it to estimate how many people died of AIDS in that year. In that case,
the number of people who died of AIDS in January would be a statistic
from which we could estimate the parameter representing the number
of people died of AIDS in that year.

Slide 8
The definition of populations and samples can seem quite arbitrary. If the population
of interest is the number of people who died of the flu in Florida last year, this number
is a parameter. If the population is the number of people with flu who died
in the United States last year, then the number who died in Florida could be
a statistic that could be used to estimate the number of who died
in the United States.

Slide 9
In statistics, we have adopted certain conventions for representing parameters
and statistics.One convention in common use is to employ Greek letters for
parameters and letters of the Roman (English) alphabet for statistics. For example,
the Greek letter s is used to represent the standard deviation of the population,
whereas the English letter s is used to represent the standard deviation of a sample
(an estimate for s.)

Slide 10
Parameters can also be represented by capital letters, statistics by the same
capital letters with a ‘cap’ or ‘hat’ over them. For example, RR stands for
the risk ratio of the population, whereas RR with a hat over it is a statistic
from a sample used to estimate the population relative risk.

Slide 11
Sometimes, both conventions are combined, so that parameters are represented
by Greek letters and the corresponding statistics by Roman letters with a hat.
An example of a combined notation is p with a hat over it, which is a representation
for the estimate for a proportion.

Slide 12
Self-Assessment

Slide 13
We can use samples to estimate characteristics of populations, which we call parameters.
For example, the mean of a sample can be used to estimate the mean of the population
from which the sample was taken. Characteristics of samples are called statistics. Statistics
are estimates for population parameters. Parameters are usually represented by capital letters
or Greek letters. Statistics are usually represented by English letters or by letters with “hats”
over them. For example, alpha is a parameter and p with a hat over it is a statistic.