Transcript 5 Minute Check, 26 Sep

Prob and Stats, Aug 26
Unit 1 Review - Fundamental Terms and
Definitions
Book Sections: N/A
Essential Questions: What are the building blocks of Statistics, what do
I call them, and what do they mean?
Standards: PS.SPMJ.3, PS.SPMJ.5
Statistics
As a Branch of Mathematics
Statistics – The science of collecting, organizing,
analyzing, and interpreting data in order to make
decisions.
Data - Information that pertains to some population
Statistics Relationships
Statistics
A Mathematical Science
Descriptive
Statistics
Inferential
Statistics
Reporting the Facts
Outside of the Facts
Predicting
Common Manifestations
Descriptive or Inferential?
The most common use of descriptive statistics is a statistical
graph or visual representation.
The most common use of inferential statistics is a prediction.
More Key Words for Statistics
Data Sets – populations and samples.
Population – An entire group (all of them, whatever
they are)
Sample – A subset of a population
Computed or Observed Quantities
Parameter – A description of a population
characteristic.
A statistic – A description of a sample characteristic.
The Types of Data
Qualitative Data –Words
Quantitative Data –Numbers
Quantitative Data (Numbers)
Quantitative Data are further separated into two
categories: Discrete and Continuous.
• Discrete – Data that assume values that can be
counted. They are always whole numbers.
• Continuous – Data that can assume any value
between two specific boundaries. They are
obtained by measuring. They can be rational
numbers.
Data Classification
Data
Qualitative
Words
Quantitative
Numbers
Discreet Values
Whole Numbers
Continuous Values
Rational Numbers
A Good Sample
A good sample of a population is one whose target
statistics are very close in value to the
corresponding population parameters. There are
four generally accepted methods that have proven
to be good sampling techniques over time.
Note that none of them is perfect.
Sampling Techniques
• There are four sampling methods that usually
make the process as random as possible The
sampling techniques are:
 Random Sampling
 Systematic Sampling
 Stratified Sampling
 Cluster Sampling
These four methods of
sampling will usually
lead to an unbiased
sample.
Random Sampling
Random samples are selected by using some random
method to select a sample. It must use some
technique designed to give every population
member an equal chance of being selected.
• For a smaller sized population, a true random
sample is attainable; but as the population grows
true randomness becomes impossible.
Systematic Sampling
Systematic sampling results from using a timing or
item interval to select the sample from a
population.
• Although not perfectly random, a consistent
system will usually produce a good cross-section
of a target population.
Stratified Sampling
Stratified sampling is a process of dividing a
population into non-overlapping groups and then a
simple random sample is selected from each group
and surveyed.
• The groups in this process are called the strata.
• If the stratified groups are too large, all the
problems of a random sample are still present.
Also, some grouping strategies (such as using
geography) can introduce biases into the data.
Cluster Sampling
Cluster sampling is using an intact group that is
representative of the population and surveying the
entire group.
• A good diverse group that is representative of the
population is hard to come by and the common
bond of the group could reduce true group
diversity.
Biased Sampling
There are two types of sampling often used that
are not random and usually lead to biased
statistics. They are:
• Convenience Sampling: Sampling only members
of a population that are easily accessed.
• Voluntary Response Sample: A sample that only
consists of respondents who want to participate in
the survey.
The Survey
A survey – is an investigation of one or more
characteristics of a population.
• Most often surveys are carried out on people by
asking them questions.
• Common types of surveys:
 Interview
 Mail
 Telephone
 On-Line
The Survey II
A survey – is an investigation of one or more
characteristics of a population.
• This can apply to any population
People – previous slide
Animals – they can’t answer questions – you can
get information from measurements, DNA, etc.
Objects – manufacturing – test until failure
Besides a Survey
The Controlled Experiment (usually medically
related)– Two groups are tracked by a specified
drug or treatment.
• In the experiment the first group is administered
the treatment or drug and are observed and tracked
over time.
• A second group, called the Control Group, are not
administered the treatment and they are observed
and compared to the other group over time.
 Usually a placebo is administered to the control group
to simulate the treatment.
Besides a Survey 2
Observational Study – Researchers observe and
measure characteristics of interest of part of a
population but do not change existing conditions.
Researchers are usually in the background, those
being observed are better off not even knowing
about it
Besides a Survey 3
Simulation – Use of a mathematical or physical
model to reproduce the conditions of a situation or
process. Simulations allow the study situations
that are impractical or even dangerous to create in
real life and can save time and money.
Classwork: CW 8/26/15, 1-25
Homework – HW Due 8/27/15, 1-12
Classwork Solutions
1a) Stratified 1b) Random 1c) Cluster 1d) Systematic
1e) convenience 2) Qualitative 3) Quantitative,
continuous 4) Quantitative, discrete, 5) Qualitative
6) Descriptive 7) Sample 8) population 9) parameter
10) Statistic 11) Survey 12) Observational study
13) Simulation