Stats 244.3

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Stats 244.3

• Elementary Statistical Concepts

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Marks will be distributed in this manner

• 6 Term Tests in the lab every two weeks
• the lowest mark out of 6 tests will be dropped
• Term tests will be worth 30
• 4 computer assignments
• Worth 10
• Final Exam
• Worth 60

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Dates for term tests Stats 244

• Thursday, Jan 17 - 230-320 (in Lab)
• Thursday, Jan 31 - 230-320 (in Lab)
• Thursday, Feb 14 - 230-320 (in Lab)
• Thursday, Mar 7 - 230-320 (in Lab)
• Thursday, Mar 21 - 230-320 (in Lab)
• Thursday, Apr 4 - 230-320 (in Lab)

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Due Dates computer assignments

1. Tuesday, Jan 29
2. Tuesday, Feb 12
3. Thursday, Mar 12
4. Tuesday, Mar 26

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Comments

• All tests will be Open Book
• You are allowed to take in
• Textbooks
• Notes
• Calculator (no computers are allowed)
• Practice assignments with solutions will be
  posted before each test. These are not compulsory.

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Text

• Introduction To Probability Statistics/Student
  Minitab 14/Ewa Loe Access/Ebook (Required)
  Mendenhall (2010 Ed. 02).

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• The lectures will be given in Power Point

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To download lectures

• Go to the stats 244 web site
• Through PAWS or
• by going to the website of the department of
  Mathematics and Statistics -gt people -gt faculty
  -gt W.H. Laverty -gt Stats 244-gt Lectures.
• Then
• select the lecture
• Right click and choose Save as

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To print lectures

1. Open the lecture using MS Powerpoint
2. Select the menu item File -gt Print

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• The following dialogue box appear

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• In the Print what box, select handouts

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• Set Slides per page to 6 or 3.

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6 slides per page will result in the least amount
of paper being printed
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3 slides per page leaves room for notes.
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Course Outline
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Introduction

• Populations, samples
• Variables
• Data Collection
• Chapter 1

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Exploratory Statistics Organizing and displaying Data Numerical measures of Central Tendency and Variability Describing Bivariate Data Chapter 2 Chapter 3
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Probability Theory Concepts of Probability Random variables and their distributions Binomial distribution, Normal distribution Chapter 4 Chapter 5 Chapter 6
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Inferential Statistics Estimation, Hypotheses testing Comparing Samples Analyzing count data Regression and Correlation Non-parametric Statistics Chapters 7 - 13
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Introduction
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• The circular process of research

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What is Statistics?

• It is the major mathematical tool of scientific
  inference (research) with an interest in
  drawing conclusion from data.
• Data that is to some extent corrupted by some
  component of random variation (random noise)

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• Random variation or (random noise) can be defined
  to be the variation in the data that is not
  accounted for by factors considered in the
  analysis.

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Example

• Suppose we are collecting data on
• Blood Pressure
• Height
• Weight
• Age

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• Suppose we are interested in how
• Blood Pressure
• is influenced by the following factors
• Height
• Weight
• Age

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• Blood Pressure will not be perfectly predictable
  from
• Height
• Weight
• Age
• There will departures (random variation) from a
  perfect prediction because of other factors the
  could affect Blood pressure
• (diet, exercise, hereditary factors)

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Another Example

• In this example we are interested in the use of

1. antidepressants,
2. mood stabilizing medication,
3. anxiety medication,
4. stimulants and
5. sleeping pills.

The data were collected for n 16383 cases
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• In addition we are interested in how the use
  these medications is affected by

• Age
• 20-29, 30-39,40-49, 50-59, 60-69, 70

• Gender
• Male, female

• Education
• lt Secondary,
• Secondary Grad.,
• some Post-Sec.,
• Post-Sec. Grad.

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• Income
• Low, Low Mid, Up Mid, High

• Role
• parent, partner , worker
• parent, partner
• parent, worker
• partner, worker
• worker only
• parent only
• partner only
• no roles

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Some questions of interest

1. How are the dependent variables (antidepressant
   use, mood stabilizing medication use, anxiety
   medication use, stimulants use, sleeping pill
   use) interrelated?
2. How are the dependent variables (drug use)
   related to the independent variables (age,
   gender, income, education and role)?

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• Again the relationships will not be perfect
• Because of the effects of other factors
  (variables) that have not been considered in the
  experiment
• If the data is recollected, the patterns observed
  at the second collection will not be exactly the
  same as that observed at the first collection

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The data appears in the following Excel file

• Drug data

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In Statistics

• Questions
• About some scientific, sociological, medical or
  economic phenomena
• Data
• The purpose of the data is to find answers to the
  questions
• Answers
• Because of the random variation in the data (the
  noise). Conclusions based on the data will be
  subject to error.

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• The circular process of research

In what part of this process does statistics play
a role?
Questions arise about a phenomenon
A decision is made to collect data
Conclusion are drawn from the analysis
Experimental Design
A decision is made as how to collect the data
The data is summarized and analyzed
The data is collected
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• Statistical Theory is interested in
• The design of the data collection procedures.
  (Experimental designs, Survey designs). The
  experiment can be totally lost if it is not
  designed correctly.
• The techniques for analyzing the data.

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In any statistical analysis it is important to
assess the magnitude of the error made by the
conclusions of the analysis.
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Consider the following statement

• You can prove anything with Statistics.

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In fact

• One is unable to prove anything with Statistics.

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At the end of any statistical analysis there
always is a possibility of an error in any of the
decisions that it makes.
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The success of a research project does not depend
on the its conclusions
The success of a research project depends on the
accuracy of its conclusions
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If one is testing the effectiveness of a drug
There is two possible conclusions
1. The drug is effective
2. The drug is not effective
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The success of a this project does not depend on
the its conclusions
The success depends on the accuracy of its
conclusions
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For this reason
It is extremely important in any study to assess
the accuracy of its conclusions
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End Lecture 1
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Some definitions

• important to Statistics

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A population

• this is the complete collection of subjects
  (objects) that are of interest in the study.
• There may be (and frequently are) more than one
  in which case a major objective is that of
  comparison.

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A case (elementary sampling unit)

• This is an individual unit (subject) of the
  population.

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A variable

• a measurement or type of measurement that is made
  on each individual case in the population.

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Types of variables

• Some variables may be measured on a numerical
  scale while others are measured on a categorical
  scale.
• The nature of the variables has a great influence
  on which analysis will be used. .

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• For Variables measured on a numerical scale the
  measurements will be numbers.
• Ex Age, Weight, Systolic Blood Pressure
• For Variables measured on a categorical scale the
  measurements will be categories.
• Ex Sex, Religion, Heart Disease

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Note

• Sometimes variables can be measured on both a
  numerical scale and a categorical scale.
• In fact, variables measured on a numerical scale
  can always be converted to measurements on a
  categorical scale.

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Example

• The following variables were evaluated for a
  study of individuals receiving head injuries in
  Saskatchewan.

• Cause of the injury (categorical)
• Motor vehicle accident
• Fall
• Violence
• other

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• Time of year (date) (numerical or categorical)
• summer
• fall
• winter
• spring

• Sex on injured individual (categorical)
• male
• female

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• Age (numerical or categorical)
• lt 10
• 10-19
• 20 - 29
• 30 - 49
• 50 65
• 65

• Mortality (categorical)
• Died from injury
• alive

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Types of variables

• In addition some variables are labeled as
  dependent variables and some variables are
  labeled as independent variables.

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• This usually depends on the objectives of the
  analysis.
• Dependent variables are output or response
  variables while the independent variables are the
  input variables or factors.

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• Usually one is interested in determining
  equations that describe how the dependent
  variables are affected by the independent
  variables

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Example

• Suppose we are collecting data on
• Blood Pressure
• Height
• Weight
• Age

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• Suppose we are interested in how
• Blood Pressure
• is influenced by the following factors
• Height
• Weight
• Age

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• Then
• Blood Pressure
• is the dependent variable
• and
• Height
• Weight
• Age
• Are the independent variables

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Example Head Injury study

• Suppose we are interested in how
• Mortality
• is influenced by the following factors
• Cause of head injury
• Time of year
• Sex
• Age

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• Then
• Mortality
• is the dependent variable
• and
• Cause of head injury
• Time of year
• Sex
• Age
• Are the independent variables

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dependent
Response variable
independent
predictor variable
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A sample

• Is a subset of the population

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In statistics

• One draws conclusions about the population based
  on data collected from a sample

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Reasons

• Cost

It is less costly to collect data from a sample
then the entire population
Accuracy
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Accuracy
Data from a sample sometimes leads to more
accurate conclusions then data from the entire
population
Costs saved from using a sample can be directed
to obtaining more accurate observations on each
case in the population
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Types of Samples

• different types of samples are determined by how
  the sample is selected.

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Convenience Samples

• In a convenience sample the subjects that are
  most convenient to the researcher are selected as
  objects in the sample.
• This is not a very good procedure for inferential
  Statistical Analysis but is useful for
  exploratory preliminary work.

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Quota samples

• In quota samples subjects are chosen conveniently
  until quotas are met for different subgroups of
  the population.
• This also is useful for exploratory preliminary
  work.

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Random Samples

• Random samples of a given size are selected in
  such that all possible samples of that size have
  the same probability of being selected.

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• Convenience Samples and Quota samples are useful
  for preliminary studies. It is however difficult
  to assess the accuracy of estimates based on this
  type of sampling scheme.
• Sometimes however one has to be satisfied with a
  convenience sample and assume that it is
  equivalent to a random sampling procedure

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Some other definitions
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A population statistic (parameter)

• Any quantity computed from the values of
  variables for the entire population.

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A sample statistic

• Any quantity computed from the values of
  variables for the cases in the sample.

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• Since only cases from the sample are observed
• only sample statistics are computed
• These are used to make inferences about
  population statistics
• It is important to be able to assess the accuracy
  of these inferences

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