Exercises statistics

Quantitative Data Analysis & Statistical Analyses – Chapter 14&16

Applied Research Methods in Social Sciences – Faculty of Political Sciences - University Babeș-Bolyai Cluj

Beca Marușa

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Homework 2

TABLE OF CONTENTS

Chapter 14 ..................................................................................................................................................... 1

Answer ex 1 ............................................................................................................................................... 1

Answer ex 2 ............................................................................................................................................... 2

Answer ex 3 ............................................................................................................................................... 2

Answer ex 4 ............................................................................................................................................... 4

Chapter 16 ..................................................................................................................................................... 6

Answer ex 4 ............................................................................................................................................... 6

List of tables .................................................................................................................................................. 7

Chapter 14 1. How might the various majors at your college be classified into categories? Create a

coding system that would allow you to categorize them according to some meaningful

variable. Then create a different coding system, using a different variable.

Answer ex 1 Major category:

1 - Arts and Humanities

2 - Business

3 - Health and Medicine

4 - Multi-/Interdisciplinary Studies

5 - Public and Social Services

6 - Science, Math, and Technology

7 - Social Sciences

8 - Trades and Personal Services

Career category:

1 - Arts, Entertainment, and Sports

2 - Business

3 - Health and Medicine

4 - Media and Social Sciences

5 - Public and Social Services

6 - Science, Math, and Technology

7 - Trades and Personal Services

2. How many ways could you be described in numerical terms? What are some of your

intrinsically numerical attributes? Could you express some of your qualitative attributes

in quantitative terms?



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Answer ex 2 I can be described in numerical terms two ways: intrinsically and extrinsically.

Intrinsic is any property that my character has internally, as opposed to an extrinsic that my

character has from using some item.

My intrinsically numerical attributes are: height, weight, age, speed.

My qualitative attributes:

gender – female (1), male (0)

type of temperament – choleric (1), sanguine (0), melancholic (2), phlegmatic (3)

colour of eyes – brown (1), black (0), blue (2), green (3)

race – white (0), yellow (1), black (2)

type of personality – introvert (0), extrovert (1)

3. How would you construct and interpret a contingency table from the following

information: 150 Democrats favor raising the minimum wage and 50 oppose it; 100

Republicans favor raising the minimum wage and 300 oppose it?

Answer ex 3 Politicians’ attitude towards raising minimum wage:

Table 1 Attitude of politicians toward raising minimum wage (numbers)

Attitude/Political

orientation Democrats Republicans Grand Total

Favor 150 100 250

Oppose 50 300 350

Grand Total 200 400 600

From the table above we can see that there were 600 participants of whom 200 Democrats (one

third) that participate at the study and 400 Republicans (two thirds).

Table 2 Attitude of politicians toward raising minimum wage (total percentage)

Attitude/Political


Favor 25% 17% 42%

Oppose 8% 50% 58%

Grand Total 33% 67% 100%

From the table above we can see that of the total of participants (600 people) we can observe that

42% (250) we in favor of raising minimum wage and 58% (350) was against it. 50% of

Republicans (300 people) oppose to the raising minimum wage and 25% (150) of Democrats are

in favor of raising minimum wage.



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Table 3 Attitude of politicians toward raising minimum wage (percentage down)

Attitude/Political


Favor 75% 25% 42%

Oppose 25% 75% 58%

Grand Total 100% 100% 100%

75% of Democrats (150) are in favor of raising minimum wage of all 200 interviewed Democrats

and 25% (50) are against. 25% (100) of Republicans are in favor of raising minimum wage of

400 Republicans and 75% (300) are against.

Table 4 Attitude of politicians toward raising minimum wage (percentage across)

Attitude/Political


Favor 60% 40% 100%

Oppose 14% 86% 100%

Grand Total 34% 66% 100%

Of all 250 politicians interviewed who were in favor of raising minimum wage 60% (150) were

Democrats and only 40% (100) were Republicans. Of all 350 politicians interviewed who were

against raising minimum wage 14% (50) were Democrats and 86% (300) were Republicans.

4. Using the hypothetical data in the following table, how would you construct and interpret

tables showing the following?

a. The bivariate relationship between age and attitude toward abortion

b. The bivariate relationship between political orientation and attitude toward

abortion

c. The multivariate relationship linking age, political orientation and attitude toward

abortion

Table 5 The multivariate relationship between age, political orientation and attitude toward abortion

Age Political orientation Attitude toward abortion Frequency

Young Liberal Favor 90

Young Liberal Oppose 10

Young Conservative Favor 60

Young Conservative Oppose 40

Old Liberal Favor 60

Old Liberal Oppose 40



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Old Conservative Favor 20

Old Conservative Oppose 80

Answer ex 4 a. The bivariate relationship between age and attitude toward abortion

Table 6 The bivariate relationship between age and attitude toward abortion (numbers)

Attitude/Age Old Young Total

Favor 80 150 230

Oppose 120 50 170

Total 200 200 400

From table 6 we can observe that there were half (200) old people participating at the research

and half (200) young people.

Table 7 The bivariate relationship between age and attitude toward abortion (total percentage)


Favor 20% 37.5% 57.5%

Oppose 30% 12.5% 42.5%

Total 50% 50% 100%

Of all participants (400) 57.5% (230) are in favor of abortion and 42.5% (170) are against.

Table 8 The bivariate relationship between age and attitude toward abortion (percentage across)


Favor 35% 65% 100%

Oppose 71% 29% 100%

Of all participants that are in favor of abortion (230) the majority i.e. 65% (150) were young and

only 35% (80) were old. Of all participants that are against abortion (170) the majority i.e. 71%

(120) were old and only 29% (50) were young.

Table 9 The bivariate relationship between age and attitude toward abortion (percentage down)

Attitude/Age Old Young

Favor 40% 75%

Oppose 60% 25%

Total 100% 100%



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60% (120) of old people oppose abortion of all 200 and only 40% (80) are in favor. 75% (150) of

young people are in favor of abotion and only 25% (50) are against it.

b. The bivariate relationship between political orientation and attitude toward abortion

Table 10 The bivariate relationship between political orientation and attitude toward abortion (numbers)

Attitude/Political

orientation Conservative Liberal Total

Favor 80 150 230

Oppose 120 50 170

Total 200 200 400

From table 10 we can observe that there were half (200) conservative people participating at the

research and half (200) liberals.

Table 11 The bivariate relationship between political orientation and attitude toward abortion (percentage across)

Attitude/Political

orientation Conservative Liberal Total

Favor 35% 65% 100%

Oppose 71% 29% 100%

Of all participants that are in favor of abortion (230) the majority i.e. 65% (150) were liberal and

only 35% (80) were conservative. Of all participants that are against abortion (170) the majority

i.e. 71% (120) were conservative and only 29% (50) were liberal.

Table 12 The bivariate relationship between political orientation and attitude toward abortion (percentage down)

Attitude/Political

orientation Conservative Liberal

Favor 40% 75%

Oppose 60% 25%

Total 100% 100%

60% (120) of conservative people oppose abortion of all 200 and only 40% (80) are in favor.

75% (150) of liberal people are in favor of abotion and only 25% (50) are against it.

c. The multivariate relationship linking age, political orientation and attitude toward

abortion


(percentage across)



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Attitude/Age,

Political

orientation

Conservative Conservative

Total

Liberal Liberal

Total

Grand

Total Old Young Old Young

Favor 9% 26% 35% 26% 39% 65% 100%

Oppose 47% 24% 71% 24% 6% 29% 100%

From table 13 we can observe that the young liberals (39%, i.e. 90) represent the highest

percentage of people that are in favor of abortion. The least in favor of abortion are the old

conservatives (9%, i.e. 20). Only 6% (10) of young liberals oppose abortion and a percentage of

47% (80) of old conservatives are against it.


(percentage down)

Attitude/Age,

Political orientation

Conservative Conservative

Total

Liberal Liberal

Total Old Young Old Young

Favor 20% 60% 40% 60% 90% 75%

Oppose 80% 40% 60% 40% 10% 25%

Grand Total 100% 100% 100% 100% 100% 100%

From the table above we can see that 90% (90) of young liberals are in favor of abortion whereas

80% (80) of old conservatives are against it.

Chapter 16

4. Find a study that reports the statistical significance of its findings and critique the clarity

with which it is reported.

Answer ex 4

In the article Identification of dietary patterns using factor analysis in an epidemiological

study in São Paulo written by Dirce Maria Lobo Marchioni and others, the authors tried to

identify patterns of food intake in a group of individuals living in São Paulo, and to develop

objective dietary measurements for epidemiological purposes. The method used was exploratory

factor analysis of data in a case-control study in seven teaching hospitals in São Paulo. The

participants were 517 patients (260 oral cancer cases and 257 controls) admitted to the study

hospitals between November 1998 and March 2001. The weekly intake frequencies for dairy

products, cereals, meat, processed meat, vegetables, pulses, fruits and sweets were assessed by

means of a semi-quantitative food frequency questionnaire. Dietary patterns were identified by



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factor analysis, based on the intake of the eight food groups, using principal component analysis

as an extraction method followed by varimax rotation.

Factor analysis identified three patterns that accounted for 55% of the total variability within the

sample. The first pattern ("prudent") was characterized by vegetable, fruit and meat intake; the

second ("traditional") by cereals (mainly rice) and pulses (mainly beans); and the third ("snacks")

by dairy products and processed meat. The study identified food intake patterns through an a

posteriori approach. Such analysis may be useful for nutritional intervention programs and, after

computing scores for each individual according to the patterns identified, for establishing a

relationship between diet and other epidemiological measurements of interest.

List of tables Table 1 Attitude of politicians toward raising minimum wage (numbers) ................................................... 2

Table 2 Attitude of politicians toward raising minimum wage (total percentage) ........................................ 2

Table 3 Attitude of politicians toward raising minimum wage (percentage down) ...................................... 3

Table 4 Attitude of politicians toward raising minimum wage (percentage across) ..................................... 3

Table 5 The multivariate relationship between age, political orientation and attitude toward abortion ....... 3

Table 6 The bivariate relationship between age and attitude toward abortion (numbers) ............................ 4

Table 7 The bivariate relationship between age and attitude toward abortion (total percentage) ................. 4

Table 8 The bivariate relationship between age and attitude toward abortion (percentage across) .............. 4

Table 9 The bivariate relationship between age and attitude toward abortion (percentage down) ............... 4

Table 10 The bivariate relationship between political orientation and attitude toward abortion (numbers) 5

Table 11 The bivariate relationship between political orientation and attitude toward abortion (percentage

across) ........................................................................................................................................................... 5

Table 12 The bivariate relationship between political orientation and attitude toward abortion (percentage

down) ............................................................................................................................................................ 5


(percentage across) ........................................................................................................................................ 5


(percentage down) ......................................................................................................................................... 6

Data & Analytics

Exercises statistics