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1-1

The Field

of Statistics

As

a

field of study,

statistics

is

set of

procedures

for

gathering,

measuring, classifying

coding, computing,

analyzing, and summarizing

systematically

acquired

numerical information

o

Scientific applications

of statistics: A

tool for testing scientillc

theo

ries

r

Practical applications of

statistics:

Used by marketing advertisers,

government policy makers,

public

health

officials, insurance

underwriters, educators,

survey firms,

stock investors and

analysts, and odds

makers.

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1-2

The

Statistical

Imagination

An appreciation of

how usual or unusual

an eveng circumstance, or

behavior

is in relation to a larger set of similar

events, and an

appreciation of an event's causes and consequences

.

It is

a balanced

way of observing the

world

.

It

involves the ability to think through

a

problem

and

maintain a

sense of

proportion

when

weighing

evidence

aga-lnst

preconceived

notions

.

It helps

us

to understand

that most

events

are

predictable

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How

the

Statistical

Imagination

Is Linked

to

the Sociological Imagination

Social

reality

is

normative:

interpretation

depends on the

plece'

time,

and

culture

in

which

it

is observed,

Social

norm:

a shared

idea

of

the

behayior that

is

appropriate

or

inappropriate

in

a

given

situation in

a

given

culture.

Statistical

norm:

an average

rate

of occurrence of

a

phenomenon

(often

a

measurement

of

a

social

norm).

Social

values: shared

ideas among the members

of

a

society

about

the

way things

ought

to be.

Statistical

ideal:

a

socially desired rate

of

occurrence

of a

phenomenon

(often reflects

social values).

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Data:

Statistical error:

Tools

for Proportional Thinking

Systematically

acquired

information

that is

organized

following

the

procedures

of science

and statistics

Known degrees of imprecision

in the

procedures

used to

gather

and

process

information

Two Purposes of Statistics

Descriptive

statistics:

Used

to

tell

us

how

many

observations

were

recorded

and how frequently

each score

or

category

of observations

occurred

in the data

Inferential

statistics:

Used

to show cause and effect relationships

and

to

test hypotheses and

scientific

theories

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WIIAT

IS SCIENCE?

.

Science

is a systematic

method

ofexplainiog

empirical

phenomena

'

Empirical

means observable and measurable

'

Phenomena are

facts, happenstances,

events, or

circumstances

Purpose

of

Science

The

purpose

ofscientific

investigation is to explain

things.

These

explanations

take

the

form

of theory:

Scientific theory:

A

set

of

interrelated, logically

organized statements

that

explain

a

phenomenon

ofspecial interest,

and

that

have

been

corroborated

through

observation

and

analysis

The

Limitations of

Science

.

Restricted

to examining

empirical

phenomena

a

Many

sound,

factuatly

based

scientific arguments lack

political

or

taxpayer

suPPort

r

Ethical

dilemrnas

often

arise

from scientilic

research

and

create

resistance

to

its

aPPlication

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DATA AND VARIABLES

Yariables:

Measurable

phenomena

that vary or

change

over

time, or that

differ from

place

to

place

or from

individual

to

individual

Study

sutrjects:

The

people

or

objects

under

scientific observation

Variatiotr: How much the measurements

ofa variable

differ

among study subjects

Constants:

Characteristics of study

subjects

that

do not

vary

A Hypothesis

A

prediction

about the

relationship

between two

variables,

asserting that

changes

in

lh€

metsure

of an

independent

variable

will

correspond

to

 

changes

in

the

measure of

a

dependent

variable.

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Independent

and

Dependent

Variables

Dependent

variable:

The

variable whose variation we

wish

to explain

Independent

variables:

The

predictor

variables

that

are

related

to,

or

predict

variation

in, the dependent

variable

Relationships

B€tween

Independent

and Dependent

Variables

Independent

Variable

Dependent

Variable

Cause

Predictor

Stimulus

.-r

Effect

-)

Outcome

--)

Response

Intervention

(action

taken) -r

Result

Correlation:

change

in

-)

Associated change

in

another

one

variable

variable

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1-8

THE

RESEARCH PROCESS

.

Involves organizing

ideas

into

a theory,

making

empirical

predictions

that support

the

theory, and

then

gathering data

to

test these

predictions

.

Cumulative

process

-

a

continual

process

of accumulation

of

knowledge

.

Eight

steps:

1.

Definelstate

the

issue

of

focus

2.

Review

the

past

researchlliterature

3.

Develop

the

hYPothesis(es)

4.

Ghoose

the

method*

5.

Gollectthe

data*

6.

TesUAnalYze

7.

WriteudPublish

resulb

8.

J

ustifi

cationlfalsifi

cation

'

=

may

be

reYersed

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Mathematical

Proportions

Division

problems

that

weigh a

part (the

numerator)

against

a

whole

(the

denominator).

Mathematical

proportions

are

a

way to

quantify:

.

Proportional

thinking'

placing

an

observation

into a

larger

context

o

A sense

of

proportion, to see

things

objectively,

make

fair

judgements

about

events

and behavior,

and give the

correct

amount

of

attention

to

things

that

really

matter

Calculating

Proportions and Percentages

Start

with

a

fraction:

# in

a

category

#

in

total

group

Divide

the fraction

to

obtain

a

proportion

(in

decimal

form).

The

quotient

will

always

have values between

0

and

1:

p

[oftotal

group

in

a

categoryl

=

#inacategory

=

quotient

#

in

total

group

For

ease

of

interpretation, transform

the

proportion into

a percentage,

which

means

per

hundred.

Multiply the

proportion

by

100.

The

quotient

will

always

have values

between

O / and 100 / t

70

[oftotal

group ir

a

categoryl

-p

(100)

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Simple

Rules

for

Transforming Fractions,

Proportions, and

Percentages

To change

a fraction

into a

proportion:

Divide

the numerator by the denominator to obtain the

 decimalized

quotient

To change

a

proportion into

a

percentage:

Multiply

the

proportion

by

100

(simply

move

the

decimal

point

two

places

to the

right)

To

transform

a

percentage

into a

proportion:

Divide

the

percentage

by 100

(simply

move

the

decimal

point

two

places

to the

left

and

drop

the percentage

symbol)

To express

a

proportion

as a

fraction:

Observe

the decimal

places,

and express

the fraction

accordingly.

For example,

.378

is 378 thousandths:

.37s = 178

1,000

(See page 567

for

a

review of decimal

place

locations.)

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