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Midterm

STAB22 Midterm: STAB22- Midterm Study Guide


Department
Statistics
Course Code
STAB22H3
Professor
Mahinda Samarakoon
Study Guide
Midterm

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STAB22-Midterm Review Study Guide
Ch.1 Introduction to Statistics:
What is Statistics?
A way of reasoning
A collection of tools and methods to help us understand the world
All about variation
Who, What, Where, When, Why and How
Who: individual cases, objects that are described by a set of data
oE.g. people, animals, things
What: the variables
oCategorical variables – characteristics, can’t be measured or
counted
E.g. hair color, eye color, area code, zip code
oQuantitative variables - #s, units, can be measured or
counted)
E.g. age
Where: the place in which the variables take place
When: the time in which the variables take place
Why: the purpose of the data
Ordinal Scales/Variables:
Falls between nominal and interval scales
Have natural ordering of values but undefined interval distances
between the values
oE.g. Social class: upper class, middle class, lower class
Nominal Variables:
A variable whose values are used only to name categories
oE.g. Province, Country names
Also referred to as categorical or qualitative variables
Identifier variables:
A categorical variable that records an unique value for each case, used
to name or identify it
oE.g. Student ID number
Ch.2 Displaying and describing categorical data:
Bar chart:
May be used to display the distribution of a categorical variable,
showing the counts for each category next to each other for easy
comparison

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Pie Chart:
Shows the whole group of cases as a circle
Slice the circle into pieces who size is proportional to the fraction of the
whole in each category

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Contingency tables:
Two or more categorical variables
Shows how individuals are distributed along each variables, contingent
on the value of other variable
Ex:
Gender Smoker Non-Smoker Total
Male 72 44 116
Female 34 53 87
Total 106 97 203
Relative Frequency Contingency Table:
% Value for cell x = (Count value in cell x / Total number surveyed) x
100
Gender Smoker Non-Smoker
Male (72/203) x 100% =
35.47%
(44/203) x 100% =
21.67%
Female (34/203) x 100% =
16.75%
(53/203) x 100% =
26.11%
Marginal Distribution:
In the margins of a contingency table, the frequency distribution of one
of the variables
Either counts or percentages
Ex:
Gender Smoker Non-Smoker Total
Male (72/203) x 100%
= 35.47%
(44/203) x 100%
= 21.67%
(116/203) x 100% =
57.14%
Female (34/203) x 100%
= 16.75%
(53/203) x 100%
= 26.11%
(87/203) x 100% =
42.86%
Total (106/203) x 100%
= 52.22%
(97/203) x 100%
= 47.78%
(203/203) x 100% =
100%
Marginal Distribution:
oGender: 57.14% and 42.86%
oSmoker Status: 52.22% and 47.78%
Conditional Distribution:
Show the distribution of one variable for just those cases that satisfy
condition on another variable
Ex:
Gender Smoker Non-Smoker Total
Male 72 44 116
Female 34 53 87
Total 106 97 203
Gender:
o(72/116) x 100% = 62.07%
o(44/116) x 100% = 37.93 %
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