TYPES OF DATA - Full of my life with mathematics only€¦ · TYPES OF DATA 4 Quantitative Data ... a “countable” number. ... EXAMPLE: the number of bedrooms in a house, or the

TYPES OF DATA

IS STATISTICS 100% CORRECT?

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Secondary Data Compilation

Observation

Experimentation

Print or Electronic

Survey

Primary

Data Collection

DATA SOURSES

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3

Data

Categorical

Numerical

Discrete Continuous

Examples:

Marital Status

Political Party

Eye Color

(Defined categories) Examples:

Number of Children

Defects per hour

(Counted items)

Examples:

Weight

Voltage

(Measured characteristics)

TYPES OF DATA

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Quantitative Data (Numerical) consists of

numbers representing counts or

measurements.

Qualitative Data (Categorical) can be

separated into different categories that are

distinguished by some nonnumeric

characteristic.

DEFINITIONS

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Discrete Data result when the number of

possible values is either a finite number or

a “countable” number.

Continuous Data result from infinitely

many possible values that correspond to

some continuous scale that covers a range

of values without gaps.

DEFINITIONS

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A variable - a characteristic of a population or a sample, e.g.

Examination marks

Stock price

The waiting time for medical services

Data - Observed values of variables

WHAT IS A VARIABLE?

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EXAMPLE

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Data - Observed values of variables

46 49 46 48 45 49 46 45 47 43

45 46 44 47 44 45 49 46 42 47

46 44 42 45 46 46 42 45 41 47

48 43 43 49 40 44 46 43 45 44

41 47 43 47 48 42 44 48 48 45

Scores on a Test

TYPES OF VARIABLES

A. Qualitative or Attribute variable - the characteristic being studied is nonnumeric.

EXAMPLES: Gender, religious affiliation, type of automobile owned, state of birth, eye color are examples.

B. Quantitative variable - information is reported numerically.

EXAMPLES: balance in your checking account, minutes remaining in class, or number of children in a family.

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QUANTITAIVE VARIABLES –

Classifications

Quantitative variables can be classified as either discrete or continuous.

A. Discrete variables: can only assume certain values and there are usually “gaps” between values.

EXAMPLE: the number of bedrooms in a house, or the number of hammers sold at the local

Home Depot (1,2,3,…,etc).

B. Continuous variable can assume any value within a specified range.

EXAMPLE: The pressure in a tire, the weight of a pork chop, or the height of students in a

class.

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SUMMARY: TYPES OF VARIABLES

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Scales of Measurement

1. Nominal Scale

Categorical/qualitative observations

Use number to represent the categories.

Example: Single=1, Married=2

2. Ordinal Scale

Ordered categorical observations

Value are in order

Example: Poor-1 Fair-2 Good-3

3. Interval Scale

Numerical/quantitative observations

Numerical bring the meaning of value.

Example: marks, temperature, IQ

4. Ratio Scale

Numerical/quantitative observations

Have absolute zero value

Example: weight, height, income

SCALES OF MEASUREMENT

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SCALES OF MEASUREMENT

Nominal level – data that is classified into categories and cannot be arranged in any particular order.

EXAMPLES: eye color, gender, religious affiliation.

Ordinal level – involves data arranged in some order, but the differences between data values cannot be determined or are meaningless.

EXAMPLE: During a taste test of 4 soft drinks, Mellow Yellow was ranked number 1, Sprite number 2, Seven-up number 3, and Orange Crush number 4.

Interval level – similar to the ordinal level, with the additional property that meaningful amounts of differences between data values can be determined. There is no natural zero point.

EXAMPLE: Temperature on the Fahrenheit scale.

Ratio level – the interval level with an inherent zero starting point. Differences and ratios are meaningful for this level of measurement.

EXAMPLES: Monthly income of surgeons, or distance traveled by manufacturer’s representatives per month.

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Nominal Scale is characterized by data

that consists of names, labels, or

categories only.

Ordinal Scale data can be arranged in

some order, but differences between data

values either cannot be determined or are

meaningless.

DEFINITIONS

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Interval Scale is like the ordinal scale, with additional property that the difference between any two data values is meaningful. However, data at this level do not have a natural zero starting point.

Ratio Scale is similar to the interval scale with additional property that there is an absolute zero (where zero indicates that none of the quantity is present). In this scale ratios are meaningful.

DEFINITIONS

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SUMMARY: SCALES OF

MEASUREMENT

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Ratio/Interval data

Age - income 55 75000

42 68000

. .

. . Weight

gain +10

+5 . .

Nominal

Person Marital status Ahmad married

Siva single

Ah Keong single . . . . Computer Brand

1 IBM

2 Dell

3 IBM . . . .

EXAMPLES

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Ratio/Interval data

Age - income 55 75000

42 68000

. .

. . Weight

gain +10

+5 . .

Nominal

With nominal data,

all we can do is,

calculate the proportion

of data that falls into

each category.

IBM Dell Compaq Other Total

25 11 8 6 50

50% 22% 16% 12%

EXAMPLES

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Knowing the type of data is necessary to properly select the

suitable technique to be used when analyzing data.

Type of analysis allowed for each type of data

Ratio/Interval data – arithmetic calculations/Average

67,74,71,83,93,55,48,82,68,62

Average=70.3

Nominal data – counting the number of observation/

frequency in each category

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

Data record: 1,2,2,2,4,1,2,2,1,3

Average=2.0; Does this mean average person is

married????

TYPES of DATA TYPES of

ANALYSIS

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Solution of Nominal data Category Code Frequency

Single 1 3

Married 2 5

Divorced 3 2

Widowed 4 4

Ordinal data - computations based on an ordering process

TYPES of DATA TYPES of

ANALYSIS

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Ratio/Interval*

Values are real numbers

All calculations are valid

Data may be treated as ordinal or nominal

Example : Examination Marks

Ordinal

Value must represent the ranked order of the data

Calculation based on an ordering process are valid

Data may be treated as nominal but not as interval

Nominal

Value are the arbitrary numbers that represent categories.

Only calculation based on the frequencies of occurrence are valid.

Data may not be treated as ordinal or interval

*Higher-level data type may be treated as lower-level ones.

HIERARCHY OF DATA

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This is often a preferred source of data due to low cost and convenience.

Published data is found as printed material, tapes, disks, and on the Internet.

Data published by the organization that has collected it is called PRIMARY DATA

For example: Data published by the US

Bureau of Census.

– Data published by an organization different than the

organization that has collected it is called

SECONDARY DATA.

For example: •The Statistical abstracts of the United States,

compiles data from primary sources

• Compustat, sells variety of financial data tapes

compiled from primary sources

PUBLISHED DATA

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Observational study is one in which measurements

representing a variable of interest are observed and

recorded, without controlling any factor that might

influence their values.

Experimental study is one in which measurements

representing a variable of interest are observed and

recorded, while controlling factors that might influence

their values.

When published data is unavailable, one

needs to conduct a study to generate the

data.

OBSERVATIONAL or

EXPERIMENTAL

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Statistical

Studies

Do you

make observations

only, or do you modify the

subjects?

Experiment Observational

When

observations

are made?

Retrospective

study

Prospective

study

Cross-sectional

study

Past

At

one

point

Future Design:

1. Control effects of variables

2. Use replication

3. Use randomization

STATISTICAL STUDIES

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IS STATISTICS 100% CORRECT?

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Voluntary Response Sample (or self-

selected sample) is one in which the

respondents themselves decide whether to

be included in the sample.

Voluntary response sample might not be

representative of the intended population.

DEFINITIONS

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Surveys solicit information from people.

Surveys can be made by means of

personal interview

telephone interview

self-administered questionnaire

SURVEYS

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A good questionnaire must be well designed:

• Keep the questionnaire as short as possible.

• Ask short,simple, and clearly worded questions.

• Start with demographic questions to help

respondents get started comfortably.

• Use dichotomous and multiple choice questions.

• Use open-ended questions cautiously.

• Avoid using leading-questions.

• Pretest a questionnaire on a small number of people.

• Think about the way you intend to use the

collected data when preparing the questionnaire.

QUESTIONNAIRE

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IS STATISTICS 100% CORRECT?

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