Notesale: Turn your study into money

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Chapter 1
Data collection
1
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In addition, statistics is about providing a measure of confidence in any conclusions
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➢ Individual: A person/object of the population that is being studied
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• Population: every student at the school
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The second possibility is to pick 50 students and check the
scenario
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A parameter is a numerical summary of population
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9%
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Suppose we pick a sample of 250 students and from this sample, we found 84
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This
value represents a statistic
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(We will study these in Chapters 2 to 4
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(We will study these in Chapters 5 to 11
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Identify the research objective
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Collect the data needed to answer questions
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Describe the data
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Perform inference
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)

Distinguish between Qualitative and Quantitative Variables
Variables are the characteristics of the individuals within the population
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➢ Individuals:
➢ Variables:

Tomatoes
Weight, Color, age, size (approx
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Qualitative (categorical) variables
Allow for classification based on characteristics
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Example 4:

Classify each of the following variables as qualitative or quantitative:

a) Nationality:
b) Number of children:
c) Level of education:
d) Annual household income:
e) Daily intake of whole grains in grams:

Distinguish between Discrete and Continuous Variables
Discrete variables
Have either a finite or countable number of possible values
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)

Quantitative

Continuous variables

Variables

Have an infinite number of possible values that are not countable
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(If you measure to get the value of a quantitative variable, it is continuous
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For example,

variable: gender

data: male, female

➢ Qualitative data: Observations corresponding to a qualitative variable
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o Discrete data
o Continuous data
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1
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Note: If the convenience is used to obtain a sample, the results of the survey are meaningless
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It is convenient to survey the students in your class
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We will discuss four basic sample techniques in this chapter
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•
•
•
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Simple random sampling (SRS)
Stratified sampling
Systematic sampling
Cluster sampling
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Such a sample is called a
simple random sample
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Example 2: Suppose a study group consists of 5 students:
Bob (B)

Mike (M)

Jan (J)

Sean (S)

Lucy (L)

2 of the students must go to the board to demonstrate a HW problem
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Solution:

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How to use a table of random numbers to obtain a simple random sample?

Procedure:
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(say there are N individuals)
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3
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(This is done by closing our eyes and placing the pencil on it to
accomplish the goal of being random
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Then we read and write down the numbers until we obtain a sample of desired size
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If your N has k digits, then we read k digit numbers from the table
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We can read the numbers from left to right or downwards
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You may ignore if a number is repeated
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Example 3: Obtain a SRS of size 4 from the following population using the above table of random
numbers
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Bob

frank

Heidi

Mike

Luke

Peter

Alice

Elsa

Kate

Sean

Greg

Nate

Jake

Olive

Walter

Carla

Ian

Tom

Dean

Ryan

Zack

Young

Vinci

Xu

Solution:

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Technology
We can use excel to obtain a simple random sample for Example 3
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2
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4
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Go to “Data analysis” under the “Data” tab
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Click inside the input range box and highlight the cells 1 to 24 in column A
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)
5
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6
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7
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1
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Example 1: A market researcher selects 500 drivers under 30 years of age and 500 drivers
above 30 years of age
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The
first individual selected correspond to a random number between 1 and k
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He decides to survey every 7-th customer
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He then surveys the 5-th
customer exiting the store and every 7-th customer thereafter until he has a sample of 40
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Example 3: A sociologist wants to gather data regarding household income with the city of
Boston
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Note: Stratified versus Cluster sampling
•
•

In stratified sampling, we divide the population into groups and obtain a simple random
sample from each group
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Convenient Sample: is one in which the individuals in the sample are easily obtained
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1
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For example, a sample of customers at a shopping mall will almost surely over-represent the
middle-class and retired people and under-represent the poor
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Three sources of bias
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Non-response bias
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Sampling bias means that the technique used to obtain the individuals to be in the sample tends
to favor one part of the population over another
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2
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Non-response can be improved through call-backs or rewards/incentives
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Response bias exists when the answers on a survey do not reflect the true feelings of the
respondent
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(A good interviewer can obtain a truthful answer to “Have you ever
cheated on your taxes?”)
b) Misrepresented answers
c) Words used in survey questions
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Example 1:

Determine the type of bias in each of the following can occur:

i
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ii
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One question on this survey is “How much sleep do you get?”

iii
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iv
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Of the 1000
households selected, 24 responded
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Such
errors could also be present in a complete census of the population
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This
type of error occurs because a sample gives incomplete information about a population

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