ISDS361 Notes - Chapter 1

8/14/2019 ISDS361 Notes - Chapter 1

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Graphical Descriptive

Techniques

Chapter 2

Learning Objectives

Understand different types of data:

Nominal

Ordinal

Learn how to describe a set of Nominal data.

Learn how to describe the relationships between

.

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Populations & Samples

Population Sample

Subset

3

The graphical & tabular methods presented here apply to bothentire populations and samples drawn from populations.

Definitions

Variable: some characteristic of a population or

sample.

.g. s u en gra es.

Typically denoted with a capital letter: X, Y, Z

Values: range of possible values for a variable.

E.g. student grades (0..100)

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Data: observed values of a variable.

E.g. student grades: {67, 74, 71, 83, 93, 55, 48}

Variable: what you want to measure

Values Example: Gas range: 2.90 5.00

Data: actual gas prices


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Types of Data & Information

Interval Data

e.g. heights, weights, prices, etc.

e.g. Marital status:

Single = 1, Married = 2, Divorced = 3, Widowed = 4

Ordinal Data

e.g. College course rating system:

oor = 1 fair = 2 ood = 3 ver ood = 4 excellent = 5

5

, , , ,

We can say things like:

excellent > poor or fair < very good

Interval : nominal/quantitative > arithmetic (if you can apply, then interval)

Ex: avg price, avg qty, age, distance traveled

Nominal & Ordinal: both qualitative/categorical

Nominal Ex: single x single married; cant say one is better than other; gender, race

Ordinal Data: order matters (different from nominal)

Grades

Hierarchy of Data & Types of CalculationsInterval

- Values are real numbers.

- All calculations are valid.

- Data ma be treated as ordinal or nominal .

Ordinal- Values must represent the ranked order of the data.

- Calculations based on a ranking process are valid.

- Data may be treated as nominal but not as interval.

Nominal

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- a ues are t e ar trary num ers t at represent categor es.

- Only calculations based on the count/frequencies of occurrence are valid.

- Data may not be treated as ordinal or interval.Interval : nominal/quantitative > arithmetic (if you can apply, then interval)

Ex: avg price, avg qty, age, distance traveled

Nominal & Ordinal: both qualitative/categorical

Ex: single x single married; cant say one is better than other; gender, race

Ordinal Data: order matters (different from nominal)

Grades


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Your Turn

In-class team exercises (pages 17-18)

.

2.3

2.4

2.5

2.6

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Graphical & Tabular Techniques forNominal Data The only allowable calculation on nominal data is to

.

We can summarize the data in a table that presents

the categories and their counts called a frequency

distribution.

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A relative frequency distribut ion lists the

categories and the proportion with which each occurs.

Tabular description = Table

Frequency Distribution: Looks at counts only (own versus rent)

Relative Frequency Distribution: Proportion / percentage (% of rent vs % buying)


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Work Status in the General Social Survey 2008

Survey respondents were asked the following:

Last week were you working full time, part time, going

, ,

were:

1. Working full time

2. Working part time

3. Temporarily not working

4. Unemployed, laid off

5. Retired

Generally, variable has a short name

Variable = Work Status

Values: 1-8

9

6. School

7. Keeping house

8. Other

The responses were recorded using the codes 1, 2, 3, 4, 5, 6, 7, and 8.

Work Status in the General Social Survey 2008

2023 responses.

ur as s o cons ruc a requency an re a ve

frequency distribution for these data and

graphically summarize the data by producing a bar

chart and a pie chart.

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Survey Data (150 observations) 1 1 1 1 2 4 3 5 1 3 1 3 7 5 1

1 5 2 1 5 1 3 3 3 1 1 5 3 1 55 1 1 3 3 5 5 6 3 5 3 5 5 5 1

1 2 1 1 5 5 3 2 1 6 1 1 4 5 1

3 3 1 3 5 3 3 7 3 7 2 1 5 7

3 6 2 6 3 6 6 6 5 6 1 1 6 3

7 1 1 1 5 1 3 1 3 7 7 2 1 1

2 5 3 1 1 3 1 1 7 5 3 2 1 1

6 5 7 1 3 2 1 3 1 1 7 5 5 6

1 4 6 1 3 1 1 5 5 5 5 1 5 5

6 1 3 3 1 3 7 1 1 1 2 4 1 1

3 3 7 5 5 1 1 3 5 1 5 4 5 3

4 1 4 5 3 1 5 3 3 3 1 1 5 3

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5 6 4 3 5 6 4 6 5 5 5 5 3 1

2 3 2 7 5 1 6 6 2 3 3 3 1 1

5 1 4 6 3 5 1 1 2 1 5 6 1 1

5 1 3 5 1 1 1 3 7 3 1 6 3 1

2 2 5 1 3 5 5 2 3 1 1 3 6 1

1 1 1 7 3 1 5 3 3 3 5 3 1 7

Frequency & Relative Frequency Distributions

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Frequency Distribution: =countif(A1:A2023,1) = 1003 (BAR CHARTS)

Relative frequency Distribution with Pivot tables (PIE CHARTS)


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Nominal Data (Frequency)

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Bar Charts are often used to display frequencies.

Frequency Distribution: =countif(A1:A2023,1) = 1003 (BAR CHARTS)

Nominal Data (Relative Frequency)

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Pie Charts show relative frequencies.

Relative frequency Distribution with Pivot tables (PIE CHARTS)


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Nominal Data

Its all the same information,(based on the same data).

Just different resentation.

15Frequency Distribut ion: =countif(A1:A2023,1) = 1003 (BAR CHARTS)

Relative frequency Distribu tion with Pivot tables (PIE CHARTS)

Your Turn

In-class team exercises using MS. Excel (pages 29-

31 :

2.21

2.28

2.32

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Describing the Relationship between Two

Nominal Variables

Newspaper Readership Survey

In a major North American city there are four competing

newspapers: the Post, Globe, Sun, and Star.

To help design advertising campaigns, the advertising

managers of the newspapers need to know which

segments of the newspaper market are reading their

papers.

A survey was conducted to analyze the relationship

between newspapers and occupation.

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Newspaper Readership Survey

A sample of newspaper readers was asked to

report which newspaper they read:

Globe (1)

Post (2)

Star (3)

Sun (4)

The readers were also asked to indicate whether

- , -worker (2), or professional (3)

How many possible combinations of these two

variables are there?

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Cross-classification table of Frequencies

As a first step we need to produce a cross-classification table, which lists the frequency of each

combination of the values of the two variables.

Newspaper Blue Collar White Collar Professional Total

Globe 27 29 33 89

Post 18 43 51 112

Star 38 21 22 81

Sun 37 15 20 72

Total 120 108 126 354

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By counting the number of t imes each of the 12 possible combinations occurs, we can produce the

following cross-tabulation (cross-classification)

Relative Frequencies

If occupation and newspaper are related, thenthere will be notable differences in newspapers

. An easy way to see this is to covert the frequencies in

each column to relative frequencies.

Newspaper Blue Collar White Collar Professional

Globe 27/120 =0.23 29/108 = 0.27 33/126 = 0.26

Post 18/120 = 0.15 43/108 = 0.40 51/126 = 0.40

Star 38/120 = 0.32 21/108 = 0.19 22/126 = 0.17

Sun 37/120 = 0.31 15/108 = 0.14 20/126 = 0.16

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Interpretation

The relative frequencies in columns 2 and 3 are similar, but there arelarge differences between columns 1 and 2 and between columns 1and 3.

Newspaper Blue Collar White Collar Professional

Globe 27/120 =0.23 29/108 = 0.27 33/126 = 0.26

Post 18/120 = 0.15 43/108 = 0.40 51/126 = 0.40

Star 38/120 = 0.32 21/108 = 0.19 22/126 = 0.17

Sun 37/120 = 0.31 15/108 = 0.14 20/126 = 0.16

similar

This tells us that blue collar workers tend to read different newspapersfrom both white collar workers and professionals and that white collarand professionals are quite similar in their newspaper choice.

dissimilar

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Graphing the Relationship between 2Nominal Variables

Post

60

G&M G&M

G&M

Post

Post

Star

Star Star

Sun

Sun

Sun

0

10

20

30

40

50

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Bluecollar Whitecollar ProfessionalOccupation

Use the data from the cross-classification table to create bar charts


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Interpretation

If the two variables are unrelated, the patterns exhibitedin the bar charts should be approximately the same.

If some relationship exists, then some bar charts will differ from

others.

The graphs tell us the same story as did the table.

The shapes of the bar charts for occupations 2 and 3 (White-

collar and Professional) are very similar.

Both differ considerably from the bar chart for occupation 1 (Blue-

collar).

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Your Turn

In-class team exercises using MS. Excel (pages 39-

40 :

2.44

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Homework

Pages 41-42:

.

2.52

2.54

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ISDS361 Notes - Chapter 1

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Transcript of ISDS361 Notes - Chapter 1