1. Introduction to Statistical Methods
Stats 244.3
Introduction to Statistical Methods

2. Assignments, Labs, Term tests - 40%
Instructor:
W.H.Laverty
Office:
235 McLean Hall
Phone:
Lectures:
M T W Th F 11:00am - 12:20pm
AGRI 2E25
Lab: T W Th 12:30 - 1:20 AGRI 2E25
Evaluation:
Assignments, Labs, Term tests - 40%
Every Thursday – Term Test Final Examination - 60%

3. Text:
Moore – The Basic Practice of Statistics

4. The lectures will be given in Power Point

5. To download lectures Go to the stats 245 web site Then Through PAWS or
by going to the website of the department of Mathematics and Statistics -> people -> faculty -> W.H. Laverty -> Stats 244-> Lectures.
Then
select the lecture
Right click and choose Save as

6. To print lectures Open the lecture using MS Powerpoint
Select the menu item File -> Print
Stat 244.3

7. The following dialogue box appear

8. In the Print what box, select handouts

9. Set Slides per page to 6 or 3.

10. 6 slides per page will result in the least amount of paper being printed1 2 3 4 5 6

11. 3 slides per page leaves room for notes.1 2 3

12. Course Outline

13. Introduction
Populations, samples
Variables
Data Collection
Chapter 1

14. Exploratory Statistics
Organizing and displaying Data
Numerical measures of Central Tendency and Variability
Describing Bivariate Data
Chapter 2
Chapter 3

15. Probability Theory
Concepts of Probability
Random variables and their distributions
Binomial distribution, Normal distribution
Chapter 4
Chapter 5
Chapter 6

16. Inferential Statistics
Estimation, Hypotheses testing
Comparing Samples
Analyzing count data
Regression and Correlation
Non-parametric Statistics
Chapters

17. Introduction

18. The circular process of research:
Questions arise about a phenomenon
A decision is made to collect data
A decision is made as how to collect the data
The data is collected
The data is summarized and analyzed
Conclusion are drawn from the analysis

19. 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)

20. 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.

21. Suppose we are collecting data on Blood Pressure Height Weight Age
Example
Suppose we are collecting data on
Blood Pressure
Height
Weight
Age

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

23. 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)

24. Another Example In this example we are interested in the use of:
antidepressants,
mood stabilizing medication,
anxiety medication,
stimulants and
sleeping pills.
The data were collected for n = cases

25. 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
< Secondary,
Secondary Grad.,
some Post-Sec.,
Post-Sec. Grad.

26. Income Low, Low Mid, Up Mid, High Role parent, partner , worker
parent, worker
partner, worker
worker only
parent only
partner only
no roles

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

28. 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

29. The data appears in the following Excel file
Drug data

30. In Statistics Questions Data Answers
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.

31. The circular process of research:
In what part of this process does statistics play a role?
Questions arise about a phenomenon
Conclusion are drawn from the analysis
A decision is made to collect data
Statistics
Statistics
Experimental
Design
A decision is made as how to collect the data
The data is summarized and analyzed
The data is collected

32. 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.

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

34. Consider the following statement:
You can prove anything with Statistics.

35. One is unable to “prove” anything with Statistics.
In fact:
One is unable to “prove” anything with Statistics.

36. At the end of any statistical analysis there always is a possibility of an error in any of the decisions that it makes.

37. 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

38. 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:

39. The success of a this project does not depend on the its conclusions
The success depends on the accuracy of its conclusions

40. For this reason:
It is extremely important in any study to assess the accuracy of its conclusions

41. important to Statistics
Some definitions
important to Statistics

42. 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.

43. A case (elementary sampling unit):
This is an individual unit (subject) of the population.

44. A variable:
a measurement or type of measurement that is made on each individual case in the population.

45. 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. .

46. 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

47. 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.

48. 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

49. Time of year (date) (numerical or categorical)
summer
fall
winter
spring
Sex on injured individual (categorical)
male
female

50. Age (numerical or categorical)
< 10
10-19
50 – 65
65+
Mortality (categorical)
Died from injury
alive

51. Types of variables
In addition some variables are labeled as dependent variables and some variables are labeled as independent variables.

52. 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.

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

54. Suppose we are collecting data on Blood Pressure Height Weight Age
Example
Suppose we are collecting data on
Blood Pressure
Height
Weight
Age

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

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

57. 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

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

59. dependent
Response variable
independent
predictor variable

60. Announcement Assignment 1 is posted It is not to be handed in
A solution will be posted later

61. Samples

62. Is a subset of the population
A sample:
Is a subset of the population

63. In statistics:
One draws conclusions about the population based on data collected from a sample

64. Reasons:
Cost
It is less costly to collect data from a sample then the entire population
Accuracy

65. 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

66. Types of Samples
different types of samples are determined by how the sample is selected.

67. 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.

68. 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.

69. 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.

70. 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

71. Population
Case ×
Sample
Variables X Y Z

72. Some other definitions

73. A population statistic (parameter):
Any quantity computed from the values of variables for the entire population.

74. A sample statistic:
Any quantity computed from the values of variables for the cases in the sample.

75. 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

76. Organizing Data the next topic