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Section 1.1
An Overview of
Statistics
What Is Statistics?
Statistics is the science of
collecting, organizing,
analyzing, and interpreting
data in order to make
decisions.
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Important Terms
Population
The collection of all responses,
measurements, or counts that are of interest.
Sample
A portion or subset of the population.
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Important Terms
Parameter
A number that describes a population characteristic.
Example: Average gross income of
all people in the United States in 2002.
Statistic
A number that describes a sample characteristic.
Example: Average gross income of
people from three states in 2002.
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Two Branches of Statistics
Descriptive Statistics
Involves organizing, summarizing, and
displaying data.
Inferential Statistics
Involves using sample data to
draw conclusions about a population.
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Section 1.2
Data Classification
Types of Data
Qualitative Data
-consist of attributes, labels or qualities
Quantitative Data
-consist of measurements, counts or quantities
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Levels of Measurement
A data set can be classified according to the
highest level of measurement that applies. The
four levels of measurement, listed from lowest
to highest are:
1. Nominal
2. Ordinal
3. Interval
4. Ratio
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Levels of Measurement
1. Nominal: Categories, names, labels, or
qualities. Cannot perform mathematical
operations on this data.
Ex: type of car you drive, your major, zip code
2. Ordinal: Data can be arranged in order.
You can say one data entry is greater than
another. Show rank or position
Ex: movie ratings, condition of patient in
hospital
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Levels of Measurement
3. Interval: Data can be ordered and
differences between 2 entries can be
calculated. There is no inherent zero
(a zero that means none).
Ex: Temperature, year of birth
4. Ratio: There is an inherent zero. Data
can be ordered, differences can be found,
and a ratio can be formed so you can say
one data value is a multiple of another.
Ex: Height, weight, age
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Section 1.3
Experimental Design
Data Collection
Observational Study:
Observe and record what the group is doing.
Experiment:
Apply a treatment to a part of the group.
Simulation:
Use a mathematical model (often with a
computer) to reproduce condition.
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Data Collection
Survey:
Asking people questions by interview, mail
or telephone
Census:
A count or measure of the entire population.
Sampling:
A count or measure of part of the population.
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Sampling Techniques
(Simple) Random Sample: Each member of
the population has an equal chance of being selected.
Assign a number to each member of the population.
Random numbers can be generated by a random
number table, computer program or a calculator.
Data from members of the population that
correspond to these numbers become members of
the sample.
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Sampling Techniques
Stratified Sample: when it is important to have
members from each segment of the population
Ex. Income, race, education
Divide the population into groups (strata) and select
a random sample from each group.
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Sampling Techniques
Cluster Sample: when the population falls into
naturally occurring subgroups
Ex. Zip codes, class
Divide the population into clusters and randomly
select one or more clusters. The sample consists of
all members from selected cluster(s).
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Sampling Techniques
Systematic Sample: each member is assigned a
number and every kth member is chosen
Choose a starting value at random. Then choose
sample members at regular intervals. If k = 5,
every 5th member of the population is selected.
Random.org
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Sampling Techniques
Convenience Sample: Choose readily
available members of the population for
your sample.
This often leads to biased results so it is
not used very often.
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Bias
Biased sample: the sample does not
represent the entire population
Ex: a sample of 18-22 year old college
students does not represent the population
of 18-22 year olds
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Bias
Biased question: using a survey
question that encourages people
to answer a certain way
Ex: Do people have the right to possess
loaded guns in their homes to protect
themselves and their families?
Or: Do people have the right to
possess loaded guns in their homes?
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