Introduction to Statistics for Built Environment

Course Code: AED 1222

Compiled byDEPARTMENT OF ARCHITECTURE AND ENVIRONMENTAL DESIGN (AED)

CENTRE FOR FOUNDATION STUDIES (CFS)INTERNATIONAL ISLAMIC UNIVERSITY MALAYSIA

Statistical DataData collection is one of the most critical steps in carrying out a statistical study.The quality of data gathered determines the quality of the study.

Sources of Statistical DataSources of Statistical Data

Data that are madeavailable by othersData that are madeavailable by others

Data resulting froman experiment

Data resulting froman experiment

Data collected in anobservational studyData collected in anobservational study

Secondary Source Data Primary Source DataExamples:

Survey, Questionaire, Observation

Examples:

Reports, Books, Catalogue, Brochure

Types of DataStatistical data may be classified into the two main categories of

DATADATA

Qualitative (Categorical/Attribute) data, that refers only to name classifications

Qualitative (Categorical/Attribute) data, that refers only to name classifications

Quantitative (Numerical) data that represent counts or measurements

Quantitative (Numerical) data that represent counts or measurements

Discrete (Counted items)Discrete

(Counted items)Continuous

(Measured characteristics)Continuous

(Measured characteristics)

Examples:

Marital Status Political Party Eye Color (Defined categories)

Examples:

Number of Children Defects per hour

Examples:

Weight Voltage

Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.

Qualitative Data/Variables

Qualitative Data : Labels or names used to identify an attribute of each element.

Eye color: dark brown, black, grey…

Exam results: pass or fail.

Socio-economic status: low, middle, high…

Race: Malay, Chinese, Indian…

For example…

It is represented in the form of separate distinct categories.

Quantitative Data /Variables

Quantitative Data indicate either “how many” or “how much”.

Data is in the form of counts or measurements.

Data are always numeric.

Some examples of quantitative variables are height, weight, and shoe size.

Qualitative data

Quantitative data

Quantitative data

Qualitative data

Quantitative data

Qualitative data

Quantitative data

Quantitative data

Qualitative data

Discrete & Continuous variables

Quantitative variables can be classified as DISCRETE or CONTINUOUS

1. A discrete variable is a Variable with possible scores of discrete points on the scale.

For example…1.The number of children in a household.A household could have 3 children or 6 children, but not 4.53 children. 2.The number of rooms in a house.A house could have 3 rooms or 5 rooms, but not 3.67 rooms.

Why discrete?Because discrete variables can only be integers or whole numbers

Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.

Discrete Data

• Discrete data: possible values are countable

Example: An advertiser asks 200 customers how many days per week they read the daily newspaper.

Number of days read

Frequency

0 44

1 24

2 18

3 16

4 20

5 22

6 26

7 30

Total 200

Discrete vs. continuous variables cont…

2. A continuous variable is where the scale is continuous and NOT made up of discrete steps, and measurements can take on any value.

For example: time taken to respond to a question.The response time could be 1.64 seconds, or it could be 1.64237123922121 seconds.

Another example could be the weight of a person or an object.A scale might show the weight of the person as 50.5 Kg but a more accurate scale could show a weight of 50.538 Kg

Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.

Continuous Data

• Continuous Data: may take on any value in some interval

Example: A manufacturer of insulation randomly selects 20 days and records the daily high temperature

24.5, 35.7, 17.3, 21.4, 24.5, 37.8, 26.6, 46.7, 58.2, 30.4, 32.6, 13.5, 12.7, 38.3, 41.2, 43.7, 44.9, 27.6, 53.8, 27.0

(Temperature is a continuous variable because it could be measured to any degree of precision desired)

13

“Number of correct answers on a 100 point multiple-choice test”.

(discrete)

14

“Marital status of 50 residents in a neighborhood”.

(discrete)

15

“Goal scores of each football team in the FIFA World Cup 2010”.

(discrete)

Sem. I, Session 2008/9AED 1122

Introduction to Mathematics & STATISTICS for Built Environment

16(continuous)

“Time taken to reach the class“.

17

“Height of tsunami waves in different affected countries”.

(continuous)

Measurement of variables

VARIABLES

Interval Interval Nominal Nominal

Ordinal Ordinal Ratio Ratio

The "levels of measurement", or scales of measure are expressions that typically refer to the theory of scale types developed by the psychologist Stanley Smith Stevens .

Stevens claimed that all measurement in science was conducted using four different types of scales that he called "nominal", "ordinal", "interval" and "ratio".

The nominal scale

• Nominal measurement consists of assigning items to groups or categories.

• No quantitative information is conveyed in nominal data.

• No ordering of the items is implied.

• Nominal scales are used to measure QUALITATIVE variables only.

• For example… rocks can be generally categorized as igneous, sedimentary and metamorphic

• Other example… Religious preference, race, and gender.

Nominal variable: • All energy sources (Petroleum, Natural Gas, Coal, Nuclear Electric & Renewable Energy)

Nominal variable: • 10 poorest countries in the world

The Ordinal Scale

Ordinal measurements are ordered in the sense that higher numbers represent higher values.

The intervals between the numbers are not necessarily equal.

Allow us to rank order the items in terms of “which has less?” and “which has more?”

Cannot say “how much more?”

Examples:- A Likert Scale use names with an order such as: "bad", "medium", and "good"; or "very satisfied", "satisfied", "neutral", "unsatisfied", "very unsatisfied." Other examples.. Socio economic status of families, Level of education, Gold Silver and Bronze at the Olympics.

Interval is a scale in which a certain distance along the scale means the same thing no matter where on the scale you are, but where "0" on the scale does not represent the absence of the thing being measured.

The Interval Scale

Allows us not only to rank order the items that are measured, but also to quantify and compare the sizes of differences between them.

For example… temperature, as measured in degrees Fahrenheit or Celsius, constitutes an interval scale. Equal differences on this scale represent equal differences in temperature, but a temperature of 30 degrees is not twice as warm as one of 15 degrees.

The Ratio Scale

Ratio is very similar to interval variables; in addition to all the properties of interval variables, it features an identifiable absolute zero "0" point.

Another example is the Kelvin temperature. Not only can we say that a temperature of 200 degrees is higher than one of 100 degrees, we can correctly state that it is twice as high.

Interval scales do not have the ratio property.

Typical examples of ratio scales are measures of time or space.

Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.

Data Measurement Levels

Ratio/Interval Data

Ordinal Data

Nominal Data

Highest Level

Complete Analysis

Higher Level

Mid-level Analysis

Lowest Level

Basic Analysis

Categorical Codes ID Numbers Category Names

Rankings Ordered Categories

Measurements

A practical example

Student Mark out of 100%

Mark relative to 40% pass mark Position Result

Ahmed 56 16 6 Pass

Ali 48 8 7 Pass

Comara 65 25 3 Pass

Dawod 73 33 2 Pass

Elias 62 22 4 Pass

Fatima 35 -5 10 Fail

Sayyed 20 -20 9 Fail

Hana 38 -2 8 Fail

Nurul 58 18 5 Pass

Zaleha 82 42 1 Pass

Ratio Interval Ordinal Nominal

Independent & dependant variables

• Independent variables:– manipulated by the experimenter.– the subjects/factors.

• Dependant variables:– measured from the subjects.– dependant upon the subjects/factors.

In general the independent variable is manipulated by the experimenter and its effects on the dependent variable are measured.

For example…

An experimenter/researcher might want to compare the effectiveness of four different types of antidepressants.

In this case, the independent variable (being manipulated) is the "type of antidepressant used".

The experiment seeks to determine the effect of the independent variable (the type of medicine) on relief from depression.

Therefore, in this example, relief from depression is the dependent variable.

Independent Dependent

Independent

Dependent

Independent

Independent