Chapter 1 introduction to statistics

Chapter 1
Introduction to Statistics
Larson/Farber 4th ed. 1

Chapter Outline
• 1.1 An Overview of Statistics
• 1.2 Data Classification
• 1.3 Experimental Design

Section 1.1
An Overview of Statistics

Section 1.1 Objectives
• Define statistics
• Distinguish between a population and a sample
• Distinguish between a parameter and a statistic
• Distinguish between descriptive statistics and inferential statistics

What is Data?
Data
Consist of information coming from observations, counts, measurements,
or responses.
• “People who eat three daily servings of whole grains
have been shown to reduce their risk of…stroke by
37%.” (Source: Whole Grains Council)
• “Seventy percent of the 1500 IT students playing
DOTA 2 and CSGO.”

What is Statistics?
Statistics
Applied mathematics that deals
with collection, organization,
presentation, analysis, and
interpretation of numerical data
in order to make decisions.

Data Sets
Population
The collection of all outcomes,
responses, measurements, or
counts that are of interest.
Sample
A subset of the population.

Most agreed or strongly agreed (60%) that
they like interactive videogames and only 18%
disagreed or strongly disagreed. The rest
weren't sure (22%).
In June 2007, A survey asked Smart Girls what they
thought about Interactive Video Games. There were 147
respondents, 97% of who are girls, and most are between
10 and 14 years old. Almost 40% are the oldest in their
family and 30% are the youngest. Middle child and only
child came out about even with 20 saying they are the
middle child and 19 saying they are an only child.
Example: Identifying Data Sets

Example: Identifying Data Sets
In a recent survey, 4501 adults in the Philippines were asked if they
think global warming is a problem that requires immediate
government action. Nine hundred thirty-nine of the adults said yes.
Identify the population and the sample. Describe the data set.
(Adapted from: Pew Research Center)

Solution: Identifying Data Sets
• The population consists of the responses of
all adults in the PHL.
• The sample consists of the responses of the
1526 adults in the PHL in the survey.
• The sample is a subset of the responses of all
adults in the PHL.
• The data set consists of 824 yes’s and 702
no’s.
Responses of adults in
the PHL (population)
Responses of
adults in survey
(sample)

Parameter and Statistic
Parameter
A number that describes a population
characteristic.
Average age of all people in the United States
Statistic
A number that describes a sample
characteristic.
Average age of people from a sample
of three states

Example: Distinguish Parameter and Statistic
Decide whether the numerical value describes a
population parameter or a sample statistic.
1. A recent survey of a sample of NBAs
reported that the average salary for an
NBA is more than Php82,000. (Source:
The Wall Street Journal)
Solution:
Sample statistic (the average of Php82,000 is
based on a subset of the population)

Example: Distinguish Parameter and Statistic
Decide whether the numerical value describes a
population parameter or a sample statistic.
2. Starting salaries for the 667 IT
graduates from Holy Angel University
increased 8.5% from the previous year.
Solution:
Population parameter (the percent increase of
8.5% is based on all 667 graduates’ starting
salaries)

Branches of Statistics
Descriptive Statistics
Involves organizing,
summarizing, and
displaying data.
e.g. Tables, charts,
averages
Inferential Statistics
Involves using sample
data to draw
conclusions about a
population.

Example:
A teacher arranges the scores obtained by his students in a graph
A researcher may wish to find out whether
exposure to pollution may reduce life span
Descriptive
Inferential

Example: Descriptive and Inferential Statistics
Decide which part of the study represents the descriptive branch of
statistics. What conclusions might be drawn from the study using
inferential statistics?
A large sample of men, aged 48,
was studied for 18 years. For
unmarried men, approximately
70% were alive at age 65. For
married men, 90% were alive at
age 65. (Source: The Journal of
Family Issues)

Solution: Descriptive and Inferential Statistics
Descriptive statistics involves statements such as “For unmarried men,
approximately 70% were alive at age 65” and “For married men, 90%
were alive at 65.”
A possible inference drawn from the study is that being married is
associated with a longer life for men.

Section 1.1 Summary
• Defined statistics
• Distinguished between a population and a sample
• Distinguished between a parameter and a statistic
• Distinguished between descriptive statistics and inferential statistics

Section 1.2
Data Classification

Types of Data According to Sources
1. Primary data. They refer to information which is directly
gathered from respondents or which is based on direct or
firsthand experience.
Example: diary
2. Secondary data. They refer to information which is taken from
published or unpublished data gathered by other individuals or
agencies.
Example: magazine, books

Types of Variables
Qualitative Variable
Consists of attributes, labels, or nonnumerical entries.
Major Place of birth Eye color

Types of Variavles
Quantitative variables
Numerical measurements or counts.
Age Weight of a letter Temperature

• Distinguish between qualitative data and quantitative data
• Classify data with respect to the four levels of measurement

Example: Classifying Data by Type
The base prices of several vehicles are shown in the table. Which data are
qualitative data and which are quantitative data? (Source Ford Motor
Company)

Solution: Classifying Data by Type
Quantitative Data
(Base prices of
vehicles models are
numerical entries)
Qualitative Data
(Names of vehicle
models are
nonnumerical entries)

Classification of quantitative variables
1. Continuous data
- numerical responses that arise from a
measurement process.
Ex. 1.234 in, 2.8 cm
2. Discrete data
-these are numerical responses that arise
from a counting process.
Ex. Number of children in a community

Levels of Measurement
1. Nominal level of measurement
• Qualitative data only
• Categorized using names, labels, or qualities
• No mathematical computations can be made
2. Ordinal level of measurement
• Qualitative or quantitative data
• Data can be arranged in order
• Differences between data entries is not meaningful

Example: Classifying Data by Level
Two data sets are shown. Which data set consists of data at the nominal
level? Which data set consists of data at the ordinal level? (Source: Nielsen
Media Research)

Solution: Classifying Data by Level
Ordinal level (lists the rank of five
TV programs. Data can be ordered.
Difference between ranks is not
meaningful.)
Nominal level (lists the
call letters of each network
affiliate. Call letters are
names of network
affiliates.)

3. Interval level of measurement
•Quantitative data
•Data can ordered
•Differences between data entries is meaningful
•Zero represents a position on a scale (not an inherent
zero – zero does not imply “none”)

Example: Classifying Data by Level
Two data sets are shown. Which data set consists of data at the interval
level? Which data set consists of data at the ratio level? (Source: Major
League Baseball)

4. Ratio level of measurement
•Similar to interval level
•Zero entry is an inherent zero (implies “none”)
•A ratio of two data values can be formed
•One data value can be expressed as a multiple of
another

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.)

Summary of Four Levels of Measurement
Level of
Measuremen
t
Put data
in
categories
Arrange
data in
order
Subtract
data
values
Determine if one
data value is a
multiple of
another
Nominal Yes No No No
Ordinal Yes Yes No No
Interval Yes Yes Yes No
Ratio Yes Yes Yes Yes

Section 1.2 Summary
• Distinguished between qualitative data and quantitative data
• Classified data with respect to the four levels of measurement

• Discuss how to design a statistical study
• Discuss data collection techniques
• Discuss sampling techniques

Methods of Collecting Data
• 1. Interview Method
• A. Direct method- the researcher personally interview the
respondent.
• B. Indirect method- the researcher uses a telephone to
interview the respondent.
2. Questionnaire Method
is a list of well-planned questions written on paper, which
can be either personally administered or mailed by the
researcher to the respondents.
3. Observation Method
the researcher observes the subject of the study which may
be an individual, a group, or any unit of interest.

Methods of Collecting Data
• 4. Registration Method
• Examples of data gathered using this method are those
obtained from National Statistics Office(NSO), Land
Transportation, Department of Education, and other
government agencies.
5. Mechanical Devices
The devices that can be used when gathering data for social
and educational researches are the camera, projector, tape
recorder, etc. In chemical, biological and medical
researches, the common devices are x-ray machine, CT
scan, microscope, etc. In astronomy and atmospheric
researches, the telescope, barometer, radar machine,
computer, etc.

Example: Methods of Data Collection
A study of how fourth grade students solve a puzzle.
Solution:
Observational study (observe and
measure certain characteristics of
part of a population)

Example: Methods of Data Collection
A study of U.S. residents’ approval rating of the U.S. president.
Solution:
Interview(Ask “Do you approve
of the way the president is
handling his job?”)

Sampling Techniques
Probability Sampling
it is a sampling technique in which every individual in a
population has an equal chance of being selected to be a member of the
sample.
1. Random Sampling
selects a sample using the concept of the lottery method.
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Other Sampling Techniques
2. Systematic Sample
• Choose a starting value at random. Then choose every kth member
of the population.
• In the West Ridge County example you could assign
a different number to each household, randomly
choose a starting number, then select every 100th
household.

3.Stratified Sample selects a sample when the population is segmented
into groups or sections called stratifications or strata.
• To collect a stratified sample of the number of people
who live in Angeles City households, you could
divide the households into socioeconomic levels and
then randomly select households from each level.

Example: Identifying Sampling Techniques
You are doing a study to determine the opinion of students at your school
regarding computer games research. Identify the sampling technique
used.
1. You divide the student population with respect to
majors and randomly select and question some
students in each major.
Solution:
Stratified sampling (the students are divided into
strata (majors) and a sample is selected from each
major)

Example: Identifying Sampling Techniques
2. You assign each student a number and generate
random numbers. You then question each student
whose number is randomly selected.
Solution:
Simple random sample (each sample of the same size
has an equal chance of being selected and each
student has an equal chance of being selected.)

Sampling Techniques
2. Non-Probability Sampling
1. Purposive Sampling
select the sample respondents based on certain
criteria laid down by the researcher.
2. Quota Sampling
samples are selected using quota system.
3. Convenience Sampling
the researcher picks his sample respondents from
the population that he finds convenient to interview
due to their availability or accesability.

Other Sampling Techniques
4. Cluster Sample
• Divide the population into groups (clusters) and
select all of the members in one or more, but not
all, of the clusters.
• In Pampanga example you could divide the
households into clusters according to zip codes, then
select all the households in one or more, but not all,
zip codes.

Chapter 1 introduction to statistics

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