INTRODUCTION TO STATISTICS

LECTURE – 1 part 2

GE 608

Experimental Methods and AnalysisOct 18, 2015

Muharrum 13, 1437

MEASUREMENT

• Measurement may be defined as the assignment of numbers to objects (شيء) or events (أحداث ) according to a set of rules.

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Levels of Measurement

1. Nominal ( فقط سم level of measurement ( باإل

2. Ordinal (ترتيبي ) level of measurement

3. Interval (الفاصلة ) level of measurement

4. Ratio (نسبة ) level of measurement

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Levels of Measurement

1. Nominal ( فقط سم level of measurement ( باإل

• Qualitative data only

• Categorized using names, labels, or qualities

• No mathematical computations can be made

2. Ordinal (ترتيبي ) level of measurement

• Qualitative or quantitative data

• Data can be arranged in order

• Differences between data entries is not meaningful

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Example: Classifying Data by Level

Two data sets are shown. Which data set consists of data at the nominal ( فقط سم level? Which data set ( باإلconsists of data at the ordinal (ترتيبي ) level? (Source: Nielsen Media Research)

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Solution: Classifying Data by Level

Ordinal (ترتيبي ) level (lists the ranks of five TV programs. Data can be ordered. Difference between ranks is not meaningful.)

Nominal ( سم باإلlevel ( فقط

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MEASUREMENT SCALES

• Nominal Scale ( فقط سم Contains only : ( باإلqualitative data. Data at this level are categorized using names, labels, or qualities. (e.g., gender, perception)

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MEASUREMENT SCALES

• Ordinal Scale (ترتيبي ) : data are qualitative or quantitative. Data on this scale can be arranged in order but difference between data entries are not meaningful. (e.g., Education, Income)

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Levels of Measurement

3. Interval (الفاصلة ) level of measurement

• Quantitative data

• Data can be ordered

• Differences between data entries are meaningful

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• Zero represents a position on a scale (not an inherent zero – zero does not imply “none”) e.g. temperature

Levels of Measurement

4. Ratio (نسبة ) level of measurement

• Similar to interval level

• Zero entry is an inherent zero (implies “none”)

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• A ratio of two data values can be formed

• One data value can be meaningfully expressed as a multiple of another

Example: Classifying Data by Level

Two data sets are shown. Which data set consists of data at the interval level (الفاصلة ) ? Which data set consists of data at the ratio level (نسبة ) ? (Source: Major League Baseball)

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Solution: Classifying Data by Level

Interval level (Quantitative data.

Can find a difference between two dates,

but a ratio does not make sense.)

Ratio level (Can find differences and write ratios.)

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Summary of Four Levels of Measurement

Level ofMeasurement

Put data in

categories

Arrangedata inorder

Subtractdata

values

Determine if one data value is a

multiple of another

1. Nominal سم ) باإل ( فقط

Yes No No No

2. Ordinal ( ترتيبي)

Yes Yes No No

3. Interval ( الفاصلة)

Yes Yes Yes No

4. Ratio ( نسبة)

Yes Yes Yes Yes14

For example:Names of TV channels: CNN, BBC

Summary of Four Levels of Measurement

Level ofMeasurement

Put data in

categories

Arrangedata inorder

Subtractdata

values

Determine if one data value is a

multiple of another

1. Nominal سم ) باإل ( فقط

Yes No No No

2. Ordinal ( ترتيبي)

Yes Yes No No

3. Interval ( الفاصلة)

Yes Yes Yes No

4. Ratio ( نسبة)

Yes Yes Yes Yes15

For example: Top 3 TV programs:1. Arab Idol, 2. AlJazeera News 3. Arab News

Summary of Four Levels of Measurement

Level ofMeasurement

Put data in

categories

Arrangedata inorder

Subtractdata

values

Determine if one data value is a

multiple of another

1. Nominal سم ) باإل ( فقط

Yes No No No

2. Ordinal ( ترتيبي)

Yes Yes No No

3. Interval ( الفاصلة)

Yes Yes Yes No

4. Ratio ( نسبة)

Yes Yes Yes Yes16

For Example: Temperature

Summary of Four Levels of Measurement

Level ofMeasurement

Put data in

categories

Arrangedata inorder

Subtractdata

values

Determine if one data value is a

multiple of another

1. Nominal سم ) باإل ( فقط

Yes No No No

2. Ordinal ( ترتيبي)

Yes Yes No No

3. Interval ( الفاصلة)

Yes Yes Yes No

4. Ratio ( نسبة)

Yes Yes Yes Yes17

For Example: Goals scored by different football teams

Summary of Four Levels of Measurement

Level ofMeasurement

Put data in

categories

Arrangedata inorder

Subtractdata

values

Determine if one data value is a

multiple of another

1. Nominal سم ) باإل ( فقط

Yes No No No

2. Ordinal ( ترتيبي)

Yes Yes No No

3. Interval ( الفاصلة)

Yes Yes Yes No

4. Ratio ( نسبة)

Yes Yes Yes Yes18

Lecture-1 Summary

• Introduction to Statistics Definitions• Statistics, Data

Data sets• Population, Sample, Parameters, Statistic

Branches of statistics• Descriptive, Inferential

• Data classification Types of data• Qualitative, Quantitative

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Lect 2 - Summary

• Data classification Distinguished between qualitative data and quantitative

data Classified data with respect to the four levels of

measurement:

• Nominal

• Ordinal

• Interval

• Ratio

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