Chapter One
Notes
created by Prof.
Dane McGuckian
Sections 1.1 – 1.3
Statistics
is a collection of methods for planning experiments, obtaining data, and then organizing,
summarizing, presenting, analyzing, interpreting and drawing conclusions based on the data.
It is the science
of data.
Statistical thinking
involves applying rational thought and the science of statistics to critically assess data
and inferences.
In this course we will divide our study of statistics into two categories:
Descriptive statistics,
is where we will organize and summarize the data to present that information in a
convenient form.
Inferential statistics
is where we use data to make predictions and decisions about a population based on
information from a sample.
Descriptive statistics
utilizes numerical and graphical methods to look for patterns in a data set, to
summarize the information revealed in a data set and to present that information in a convenient
form.
Inferential statistics
utilizes sample data to make estimates, decisions, predictions or other
generalizations about a larger set of data.
Above, we mentioned the word population.
Let’s define two important terms used in this course:
The
population
is the set of
all
measurements of interest to the investigator.
Typically, there are too many
experimental units in a population to consider
every
one.
However, if we can examine every single one, we
conduct what is called a
census
.
A
sample
is a subset of measurements selected from the population of interest.
Example 1: In a study of household incomes in a small town of 1000 households, one might conceivably
obtain the income of every household. However, it is probably very expensive and time consuming to do
this.
Therefore, a better approach would be to obtain the data from a portion of the households (let’s say 125
households). In this scenario, the 1000 households are referred to as the population and the 125 households
are referred to as a sample.
A
parameter
is a numerical measurement describing some characteristic of a
population
and computed from
all of the population measurements.
For example, a population average (mean), the average obtained from
every item in the population, is a parameter.
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A
statistic
is a numerical measurement describing some characteristic of a
sample
drawn from the
population.
The example below will illustrate these ideas.
One way to remember where parameters and statistics come
from is to notice that the letter P is the first letter of Population and Parameter and S is the first letter of
Sample and Statistic.
Example 2: In the household incomes example from above, the average (mean) income of all 1000
households is a parameter, whereas the average (mean) income of the 125 households is a statistic.
Example 3
(parameter vs. statistic)  Determine whether the given value is a statistic or a parameter.
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 Fall '08
 STAFF
 Statistics, Level of measurement

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