basic statistics introduction to statistics .pptx

Copyright © 2020 Pearson Education Ltd.
A LWAY S L E A R N I N G Slide 1
Defining and Collecting
Data
Chapter 1

Objectives
In this chapter you learn:
 To understand issues that arise when defining
variables.
 How to define variables.
 To understand the different measurement scales.
 How to collect data.
 To identify different ways to collect a sample.
 To understand the issues involved in data
preparation.
 To understand the types of survey errors.

Classifying Variables By Type
 Categorical (qualitative) variables take categories
as their values such as “yes”, “no”, or “blue”,
“brown”, “green”.
 Numerical (quantitative) variables have values that
represent a counted or measured quantity.
 Discrete variables arise from a counting process.
 Continuous variables arise from a measuring process.
DCOVA

Examples of Types of Variables
DCOVA
Question Responses Variable Type
Do you have a Facebook
profile? Yes or No Categorical
How many text messages
have you sent in the past
three days?
---------------
Numerical
(discrete)
How long did the mobile
app update take to
download?
---------------
Numerical
(continuous)

Types of Variables
DCOVA
Variables
Categorical Numerical
Discrete Continuous
Examples:
 Marital Status
 Political Party
 Eye Color
(Defined Categories)
Examples:
 Number of Children
 Defects per hour
(Counted items)
Examples:
 Weight
 Voltage
(Measured
characteristics)
Nominal Ordinal
Examples: Ratings
 Good, Better,
Best
 Low, Med, High
(Ordered Categories)

Measurement Scales
A nominal scale classifies data into distinct
categories in which no ranking is implied.
Categorical Variables Categories
Do you have a
Facebook profile?
Type of investment
Cellular Provider
Yes, No
AT&T, Sprint, Verizon,
Other, None
Growth, Value, Other
DCOVA

Measurement Scales (con’t.)
An ordinal scale classifies data into distinct
categories in which ranking is implied.
Categorical Variable Ordered Categories
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
Standard & Poor’s bond ratings AAA, AA, A, BBB, BB, B, CCC, CC,
C, DDD, DD, D
Student Grades A, B, C, D, F
DCOVA

Measurement Scales (con’t.)
 An interval scale is an ordered scale in which the
difference between measurements is a meaningful
quantity but the measurements do not have a true
zero point.
 A ratio scale is an ordered scale in which the
difference between the measurements is a
meaningful quantity and the measurements have a
true zero point.
DCOVA

Interval and Ratio Scales
DCOVA

Data Is Collected From Either A
Population or A Sample
POPULATION
A population contains all of the items or
individuals of interest that you seek to study.
SAMPLE
A sample contains only a portion of a
population of interest.
DCOVA

Population vs. Sample
All the items or individuals
about which you want to draw
conclusion(s).
A portion of the population
of items or individuals.
Population Sample
DCOVA
A Population of Size 40 A Sample of Size 4

Collecting Data Via Sampling Is Used
When Doing So Is
 Less time consuming than selecting every item
in the population.
 Less costly than selecting every item in the
population.
 Less cumbersome and more practical than
analyzing the entire population.
DCOVA

Parameter or Statistic?
 A population parameter summarizes the value
of a specific variable for a population.
 A sample statistic summarizes the value of a
specific variable for sample data.
DCOVA

Sources Of Data Arise From
The Following Activities
 Capturing data generated by ongoing business
activities.
 Distributing data compiled by an organization or
individual.
 Compiling the responses from a survey.
 Conducting a designed experiment and
recording the outcomes.
 Conducting an observational study and
recording the results.
DCOVA

Examples of Data Collected From
Ongoing Business Activities
 A bank studies years of financial transactions to
help them identify patterns of fraud.
 Economists utilize data on searches done via
Google to help forecast future economic
conditions.
 Marketing companies use tracking data to
evaluate the effectiveness of a web site.
DCOVA

Examples Of Data Distributed
By An Organization or Individual
 Financial data on a company provided by
investment services.
 Industry or market data from market research
firms and trade associations.
 Stock prices, weather conditions, and sports
statistics in daily newspapers.
DCOVA

Examples of Survey Data
 A survey asking people which laundry detergent
has the best stain-removing abilities.
 Political polls of registered voters during
political campaigns.
 People being surveyed to determine their
satisfaction with a recent product or service
experience.
DCOVA

Examples of Data From A
Designed Experiment
 Consumer testing of different versions of a
product to help determine which product should
be pursued further.
 Material testing to determine which supplier’s
material should be used in a product.
 Market testing on alternative product
promotions to determine which promotion to
use more broadly.
DCOVA

Examples of Data Collected
From Observational Studies
 Market researchers utilizing focus groups to
elicit unstructured responses to open-ended
questions.
 Measuring the time it takes for customers to be
served in a fast food establishment.
 Measuring the volume of traffic through an
intersection to determine if some form of
advertising at the intersection is justified.
DCOVA

Observational Studies & Designed
Experiments Have A Common Objective
 Both are attempting to quantify the effect that a
process change (called a treatment) has on a
variable of interest.
 In an observational study, there is no direct
control over which items receive the treatment.
 In a designed experiment, there is direct control
over which items receive the treatment.
DCOVA

Sources of Data
 Primary Sources: The data collector is the one
using the data for analysis:
 Data from a political survey.
 Data collected from an experiment.
 Observed data.
 Secondary Sources: The person performing
data analysis is not the data collector:
 Analyzing census data.
 Examining data from print journals or data published
on the internet.
DCOVA

A Sampling Process Begins With A
Sampling Frame
 The sampling frame is a listing of items that
make up the population.
 Frames are data sources such as population
lists, directories, or maps.
 Inaccurate or biased results can result if a
frame excludes certain groups or portions of the
population.
 Using different frames to generate data can
lead to dissimilar conclusions.
DCOVA

Types of Samples
Samples
Non Probability
Samples
Judgment
Probability Samples
Simple
Random
Systematic
Stratified
Cluster
Convenience
DCOVA

Types of Samples:
Nonprobability Sample
 In a nonprobability sample, items included are
chosen without regard to their probability of
occurrence.
 In convenience sampling, items are selected based
only on the fact that they are easy, inexpensive, or
convenient to sample.
 In a judgment sample, you get the opinions of pre-
selected experts in the subject matter.
DCOVA

Types of Samples:
Probability Sample
 In a probability sample, items in the
sample are chosen on the basis of known
probabilities.
Probability Samples
Simple
Random
Systematic Stratified Cluster
DCOVA

Probability Sample:
Simple Random Sample
 Every individual or item from the frame has an
equal chance of being selected.
 Selection may be with replacement (selected
individual is returned to frame for possible
reselection) or without replacement (selected
individual isn’t returned to the frame).
 Samples obtained from table of random
numbers or computer random number
generators.
DCOVA

Selecting a Simple Random Sample
Using A Random Number Table
Sampling Frame For
Population With 850
Items
Item Name Item #
Bev R. 001
Ulan X. 002
. .
. .
. .
. .
Joann P. 849
Paul F. 850
Portion Of A Random Number Table
49280 88924 35779 00283 81163 07275
11100 02340 12860 74697 96644 89439
09893 23997 20048 49420 88872 08401
The First 5 Items in a simple
random sample
Item # 492
Item # 808
Item # 892 -- does not exist so ignore
Item # 435
Item # 779
Item # 002
DCOVA

 Decide on sample size: n
 Divide frame of N individuals into groups of k
individuals: k=N/n
 Randomly select one individual from the 1st
group
 Select every kth
individual thereafter
Probability Sample:
Systematic Sample
N = 40
n = 4
k = 10
First Group
DCOVA

Probability Sample:
Stratified Sample
 Divide population into two or more subgroups (called
strata) according to some common characteristic.
 A simple random sample is selected from each subgroup,
with sample sizes proportional to strata sizes.
 Samples from subgroups are combined into one.
 This is a common technique when sampling population of
voters, stratifying across racial or socio-economic lines.
DCOVA

Probability Sample
Cluster Sample
 Population is divided into several “clusters,” each representative of
the population.
 A simple random sample of clusters is selected.
 All items in the selected clusters can be used, or items can be
chosen from a cluster using another probability sampling technique.
 A common application of cluster sampling involves election exit polls,
where certain election districts are selected and sampled.
Population
divided into
16 clusters. Randomly selected
clusters for sample
DCOVA

Probability Sample:
Comparing Sampling Methods
 Simple random sample and Systematic sample:
 Simple to use.
 May not be a good representation of the population’s
underlying characteristics.
 Stratified sample:
 Ensures representation of individuals across the
entire population.
 Cluster sample:
 More cost effective.
 Less efficient (need larger sample to acquire the
same level of precision).
DCOVA

Data Cleaning Is An Important Data
Preprocessing Task Prior To Analysis
Data cleaning corrects irregularities in the data:
 Invalid variable values, including:
 Non-numerical data for numerical variable.
 Invalid categorical values for a categorical variable.
 Numeric values outside a defined range.
 Coding errors, including:
 Inconsistent categorical values.
 Inconsistent case for categorical values.
 Extraneous characters.
 Data integration errors, including:
 Redundant columns.
 Duplicated rows.
 Differing column lengths.
 Different units of measure or scale for numerical variables.
DCOVA

Data Cleaning Cannot Be A Fully
Automated Process
 Excel, JMP, and Minitab have functionality to
lessen the burden of data cleaning.
 The software guides in the book explain this
functionality.
 When performing data cleaning, always
preserve a copy of the original data for later
reference.
DCOVA

Cleaning Invalid Variable Values
Can Be Semi-Automated
 Invalid variable values can be identified by
simple scanning techniques, for example:
 Non-numeric entries for numerical variables.
 Values for categorical variables that don’t match a
pre-defined category.
 Values for a numeric variable outside a pre-defined
explicit range.
 Features exist in Excel, JMP, or Minitab to
assist in this task.
DCOVA

Examples Of Coding Errors
Copy-and-paste or data import can result in poor
recording or entry of data.
Categorical variable: Gender, Correct coding: F or M
 Correctable error: Female.
 Invalid data: New York.
 Correctable or software tolerated: m.
 Extraneous and nonprintable characters:
 Leading or trailing space(s): _F or F_.
 Other nonprintable characters may also be leading or trailing
DCOVA

Data Integration Errors From Combining
Two Different Computerized Data Sources
 Data integration errors often requires time-
consuming manual effort.
 Some examples:
 Variable names or definitions may differ.
 Duplicated rows (observations) may also occur.
 Different units of measurement (or scale) may not be
obvious without human interpretation.
DCOVA

Data Can Be Formatted and / or
Encoded In More Than One Way
 Some electronic formats are more readily
usable than others.
 Different encodings can impact the precision of
numerical variables and can also impact data
compatibility.
 As you identify and choose sources of data you
need to consider / deal with these issues.
DCOVA

Stacked vs Unstacked Data
 For unstacked data you create separate
numerical variables for different groups (i.e.
genders, locations, etc.)
 For stacked data you create a single column for
the variable of interest and create additional
columns for the potential grouping variables.
DCOVA

After Collection It Is Often Helpful To
Recode Some Variables
 Recoding a variable can either supplement or replace
the original variable.
 Recoding a categorical variable involves redefining
categories.
 Recoding a numerical variable involves changing this
variable into a categorical variable.
 When recoding be sure that the new categories are
mutually exclusive (categories do not overlap) and
collectively exhaustive (categories cover all possible
values).
DCOVA

Evaluating Survey Worthiness
 What is the purpose of the survey?
 Is the survey based on a probability sample?
 Coverage error – appropriate frame?
 Nonresponse error – follow up.
 Measurement error – good questions elicit good
responses.
 Sampling error – always exists.
DCOVA

Types of Survey Errors
 Coverage error or selection bias:
 Exists if some groups are excluded from the frame and have
no chance of being selected.
 Nonresponse error or bias:
 People who do not respond may be different from those who
do respond.
 Sampling error:
 Variation from sample to sample will always exist.
 Measurement error:
 Due to weaknesses in question design and / or respondent
error.
DCOVA

Types of Survey Errors
 Coverage error
 Nonresponse error
 Sampling error
 Measurement error
Excluded from
frame
Follow up on
nonresponses
Random
differences from
sample to sample
Bad or leading
question
(continued)
DCOVA

Ethical Issues About Surveys
 Coverage error and nonresponse error can be
leveraged by survey designers to purposely
bias survey results.
 Sampling error can be an ethical issue if the
findings are purposely not reported with the
associated margin of error.
 Measurement error can be an ethical issue:
 Survey sponsor chooses leading questions.
 Interviewer purposely leads respondents in a
particular direction.
 Respondent(s) willfully provide false information.
DCOVA

Chapter Summary
In this chapter we have discussed:
 Understanding issues that arise when defining
variables.
 How to define variables.
 Understanding the different measurement scales.
 How to collect data.
 Identifying different ways to collect a sample.
 Understanding the issues involved in data
preparation.
 Understanding the types of survey errors.

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