Statistics: Chapter One

Chapter 1
Introduction
Chap 1-1
Statistics 1

Learning Objectives
Chap 1-2
In this chapter you learn:
 Definition of Statistics & Identify variables in a statistics.
 Types of Statistics
 Distinguish b/w quantitative & qualitative variables.
 Determine the 4 levels of measurement.
 Identify populations & samples.
 Distinguish different types of Sampling

Introduction to Statistics?
Chap 1-3
Decision making is an important aspect of our lives. We make
decisions based on the information we have.
Statistical methods help us examine information. Moreover, statistics
can be used for making decisions when we are faced with
uncertainties.
Statistical methods enable us to look at information from a small
collection of people or items and make inferences about a larger
collection of people or items.

What is statistics?
Chap 1-4
 Statistics is the study of how to collect, organize, analyse,
present and interpret numerical information from data.
The definition implies the knowledge of different stages of Statistical study.
 Stage 1: Collection of data – data collection relates to problem under
investigation
 Stage 2: Organization of data – Figures collected by researcher or
investigator need to be organized by tabulating and classifying
 Stage 3: Data presentation – data is presented in the form of graphs,
diagrams, tables
 Stage 4: Analyzing of data – data analysis is done using average,
dispersion, correlation, regression
 Stages 5: Interpretation of data – conclusion are drawn on the base which
decision are made

Types of Statistics
 Statistics
 is the study of how to collect, organize, analyse, present and
interpret numerical information from data.
Descriptive Statistics
Is a methods of collecting,
organizing, summarizing, and
describing data from samples or
populations.
Inferential Statistics
Is a methods consists of generalizing from
samples to populations, performing
estimations and hypothesis tests,
determining relationships among
variables, and making predictions.
Chap 1-5

Descriptive Statistics
 Collect data
 e.g., Survey
 Present data
 e.g., Tables and graphs
 Characterize data
 e.g., Sample mean =
n
Xi
Chap 1-6

 Estimation
 e.g., Estimate the population
mean weight using the sample
mean weight
 Hypothesis testing
 e.g., Test the claim that the
population mean weight is 120
pounds
Drawing conclusions about a large group of
individuals based on a subset of the large group.
Chap 1-7

 Generalizing from samples to
populations
Chap 1-8

Individuals vs Variables
Chap 1-9
The general prerequisite for statistical decision making is the gathering of
data. First, we need to identify the individuals or objects to be included
in the study and the characteristics of the individuals that are of interest.
 An Individuals: are the people or objects included in the study
(Number of students taking a Statistics 1 course).
 A variable: is a characteristic of the individual to be measured or
observed (age, weight, marital status, gender, income)

Chap 1-10
Variables can be classified as qualitative or quantitative. Qualitative
variables are variables that can be placed into distinct categories,
according to some characteristic or attribute.
Example:
o If subjects are classified according to gender (male or female), then
the variable gender is qualitative.
o If subject are classified according to marital status (married, single
or divorced), then the variable marital status is qualitative variable.
o Other example of qualitative variables are: nationality, eye color,
political parts etc.
Variables & Types of Data

Chap 1-11
Quantitative variables have values that represent quantities. These
variables have a value or numerical measurement for which operations
such as addition or averaging make sense.
Example:
o The variable age is numerical, and people can be ranked in order
according to the value of their ages.
o Other example of quantitative variables are heights, weights, GPA,
and body temperatures etc.
Variable and Types of Data

Chap 1-12
Quantitative variables can be further classified into two groups: Discrete
and Continuous variables.
 Discrete variables can be assigned values such as 0, 1, 2, 3 and are
said to be countable.
o Examples of discrete variables are the number of children in a family,
the number of students in a classroom, and the number of calls
received by a switchboard operator each day for a month.

Chap 1-13
Continuous variables can assume an infinite number of values between
any two specific values. They are obtained by measuring. They often
include fractions and decimals.
o Continuous variables, can assume an infinite number of values in an
interval between any two specific values.
o For example temperature, is a continuous variable, since the variable
can assume an infinite number of values between any two given
temperatures.
o Weight is also an another example of continuous variables

The classification of variables can be
summarized
Data
Qualitative Quantitative
Discrete
Chap 1-14
Continuous
Examples:
 Marital Status
 Political Party
 Eye Color
(Defined categories) Examples:
 Number of Children
 Call per hour
 Shoe size
(Counted items)
Examples:
 Weight
 Voltage
 Temperature
(Measured characteristics)

Example: Types of Variables
Chap 1-15
Question Response Data Type
Do you currently have a profile
on Facebook?
Yes No Qualitative
How many text messages have
you sent in the past week?
__________ Quantitative (discrete)
How long did it take to
download a video lesson?
______seconds Quantitative
(continuous)

Levels of Measurement
In addition to being classified as qualitative or quantitative, variables can
be classified by how they are categorized, counted, or measured.
For example, can the data be organized into specific categories, such as
area of residence (rural, suburban, or urban)? Can the data values be
ranked, such as first place, second place, etc.? Or are the values obtained
from measurement, such as heights, IQs, or temperature?
This type of classification — uses measurement scales
There are four level of measurement scales
o Nominal
o Ordinal
o Interval
o Ratio
Chap 1-16

Levels of Measurements
 Nominal Level of Measurement: Applies to data that consist of
names, labels, or categories. There are no implied criteria by which the
data can be ordered from smallest to largest.
 Examples:
o Classifying NGUC lecturers according to subject taught (English, BA,
Statistics or mathematics)
o Classifying Students in a class as male or female
o Marital status (single, married, divorced)
o industry type (manufacturing, financial, agriculture, etc.)
Chap 1-17

Example of Nominal Scales
Chap 1-18
Question Response
Do you currently have a
profile on Facebook?
Yes No
Types of investment Stock Bond Other None
Internet Email Provider Gmail Windows live Yahoo Others

 Ordinal Level of Measurement: Applies to data that can be arranged
in order. However, differences between data values either cannot be
determined or are meaningless.
 Examples:
o Ranking students in a class as first, second, third, fourth and so on
o Guest speaking my be ranked as superior
Ordinal scales can also use attribute labels such as “bad”, “medium”,
and “good”, or "strongly dissatisfied", "somewhat dissatisfied",
"neutral", or "somewhat satisfied", and "strongly satisfied”.
Chap 1-19

Example of Ordinal Scales
Chap 1-20
Question Response
Student class designation Freshman – Sophomore - Junior - Senior
Product satisfaction Very unsatisfied - Fairly unsatisfied -
Neutral - Fairly satisfied - Very satisfied
Faculty rank Professor - Associate Professor -
Assistant Professor - Instructor
Student grades A - B - C - D - F

Interval Level of Measurement: Applies to data that can be arranged in
order. In addition, differences between data values are meaningful.
 Examples:
o IQ test
o Temperature (There is a meaningful difference each unit, such as 72
and 73F)
One property is lacking in the interval scale: There is no true zero. For
example, IQ tests do not measure people who have no intelligence. For
temperature, 0F does not mean no heat at all.
Chap 1-21

Ratio Level of Measurement: Applies to data that can be arranged in
order. In addition, both differences between data values and ratios of data
values are meaningful. Data at the ratio level have a true zero.
Examples:
o Weight (one person can lift 200 pounds & another can lift 100 pounds,
then the ratio between them is 2 to 1)
o Height, area, and number of phone calls received are another examples
Ratio scales are those that have all the qualities of nominal, ordinal, and
interval scales, and in addition, also have a “true zero”
Chap 1-22

The classification of Quantitative & Qualitative
variables
Data
Quantitative
Chap 1-23
Ordinal
o Labels
Example:
Religion, Gender,
Ethnic, Blood type
Interval Ratio Nominal
Qualitative
o Can count & Rank
o Unequal interval
Example:
Education Level, Social Class
5 point likert scale
o Can count, Rank &
can take difference
o No true zero
Example:
Temp Fo, birth year,
o Most quantitative
variables are ratio
o Count, rank & ratio
o True zero

Data & Source of Data
DATA
Data are the different values associated with a variable.
INFORMATION
Data is transformed into a useful facts that can be used for a specific purpose
such decision making for a particular situation.
PRIMARY DATA
Data you have collected your own and used it. This data can be obtained by
direct observation, experiment, questionnaires or survey, etc.
SECONDARY DATA
Data that some else has collected and made available for other people to use it
Chap 1-24

Advantages Vs Disadvantages
Primary data
Chap 1-25
Advantages:
 Collected by the person,
institution or government
that uses it
Disadvantages:
 Can be very expensive
and time consuming
Secondary data
Advantages:
 Readily available
 Less expensive to collect
Disadvantages:
 No control how the data
was collected
 Less reliable

Primary data
Chap 1-26
Primary data collection methods
Direct Observation
or Focus Group
SurveyExperiments
Observing subjects in their
natural environment.
Example: Watching to see
if drivers stop at a stop sign
Treatments are applied
in controlled conditions
Example: Crop growth
from different plots
using different fertilizers
Subjects are asked to respond
questions or discuss attitudes
Example:
• Telephone survey
• Mailed questionnaire
• personal interview

Basic Vocabulary of Statistics
POPULATION
A population consists of all the items or individuals about which you want
to draw a conclusion.
SAMPLE
A sample is the portion of a population selected foranalysis.
PARAMETER
A parameter is a numerical measure that describes a characteristic of a
population.
STATISTIC
A statistic is a numerical measure that describes a characteristicof a sample.
Chap 1-27

Population vs. Sample
Population Sample
Measures used to describe the
population are called parameters
Measures computed from
sample data are called statistic
Chap 1-28

Sampling Techniques
In slide 27 we define population as all items or individuals under study
and sample as a subgroup of the population. However, the sampling
technique used can be either Probability sampling or Non-probability
sampling
Chap 1-29
Probability Sampling: is technique in which each member of population
has an equal chance of being selected. The main purpose of sampling is to
create a sample that is representative of the population it is being drawn
from hence it is very difficult to survey the whole population
Non-probability Sampling: is a sampling technique where the sample are
gathered in a process that does not give all the individuals in the population
equal chances of being selected.

Sampling Techniques
Probability sampling can be sub-divided into many different types;
1. Simple Random Sampling: each member of the population (N) has the
same probability (chance) of being selected for your sample (n).
Sometimes this is called a Lottery method.
Chap 1-30

Sampling Techniques
2. Stratified Sampling
Divide the entire population into distinct subgroups called strata. The
strata are based on a specific characteristic, such as age, income,
education level, and so on.
All members of a stratum share the specific characteristic. Draw random
samples from each stratum.
Example:
in the population of all undergraduate college students, some strata
might be freshmen, sophomores, juniors, or seniors. Other strata might
be Male or Female
Chap 1-31

Sampling Techniques
3. Systematic Sampling
Systematic Sampling technique involves numbering all members of the
population sequentially. Then, from a starting point selected at random,
include every kth member of the population in the sample.
Example:
If you select every 5the person to walk out of a supermarket to your
sample after randomly selected the person you start for the sampling,
you are performing Systematic Sampling.
Chap 1-32

Sampling Techniques
4. Cluster Sampling
Divide the entire population into pre-existing segments or clusters. The
clusters are often geographic. Make a random selection of clusters.
Include every member of each selected cluster in the sample.
Example:
In conducting a survey of schoolchildren in a large city, we could first
randomly select five schools and then include all the children from each
selected school.
Chap 1-33

Sampling Techniques
Chap 1-34
Non-probability sampling can be sub-divided into different types;
1. Snowball Sampling:
Snowball sampling is appropriate to use when the population you are
interested in hard-to-reach. These include populations such as drug
addicts, homeless people, individuals with AIDS/HIV,, and so forth.
2. Convenience Sampling:
Convenience sampling is a non-probability sampling method that selects
the item from the population based on accessibility and ease of selection.
This sampling technique, the subjects are chosen simply because they are
easy to recruit. It is easy, cheap and least time consuming data collection
technique but has many disadvantages.

Sampling Techniques
Chap 1-35
3. Multistage Sampling
Use a variety of sampling methods to create successively smaller groups
at each stage. The final sample consists of clusters.
Often a population is very large or geographically spread out. In such
cases, samples are constructed through a multistage sample design of
several stages, with the final stage consisting of clusters.
Example:
 The first stage, random number of districts are chosen in all regions
 This followed by random number of villages
 Then third stage may be households
 Then all ultimate units (house holds, for example) selected in the last step
are surveyed.

Classification of Sampling Techniques
Chap 1-36
Sampling
Non-probability
Sampling
Probability
Sampling
Cluster
Sampling
Systematic
Sampling
Stratified
Sampling
Simple
Random
Multistage
Sampling
Convenience
Sampling
Snowball
Sampling

Statistics: Chapter One

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