Transcript Sample - Rice University

Chapter 3 Goals
After completing this chapter, you should be
able to:



Describe key data collection methods
Know key definitions:
Population vs. Sample
Primary vs. Secondary data types
Qualitative vs. Qualitative data
Time Series vs. Cross-Sectional data
Explain the difference between descriptive and
inferential statistics

Describe different sampling methods & Experiments
Chap 1-1
Tools of Business Statistics

Descriptive statistics


Collecting, presenting, and describing data
Inferential statistics

Drawing conclusions and/or making decisions
concerning a population based only on
sample data
Chap 1-2
Descriptive Statistics

Collect data

e.g. Survey, Observation,
Experiments

Present data


e.g. Charts and graphs
Characterize data

e.g. Sample mean =
x
i
n
Chap 1-3
Data Sources
Primary
Secondary
Data Collection
Data Compilation
Print or Electronic
Observation
Survey
Experimentation
Chap 1-4
Survey Design Steps

Define the issue

what are the purpose and objectives of the survey?

Define the population of interest

Formulate survey questions

make questions clear and unambiguous

use universally-accepted definitions

limit the number of questions
Chap 1-5
Survey Design Steps
(continued)

Pre-test the survey

pilot test with a small group of participants

assess clarity and length

Determine the sample size and sampling
method

Select Sample and administer the survey
Chap 1-6
Types of Questions

Closed-end Questions


Select from a short list of defined choices
Example: Major: __business __liberal arts
__science __other
Open-end Questions

Respondents are free to respond with any value, words, or
statement
Example: What did you like best about this course?

Demographic Questions

Questions about the respondents’ personal characteristics
Example: Gender: __Female __ Male
Chap 1-7
Populations and Samples

A Population is the set of all items or individuals
of interest


Examples:
All likely voters in the next election
All parts produced today
All sales receipts for November
A Sample is a subset of the population

Examples:
1000 voters selected at random for interview
A few parts selected for destructive testing
Every 100th receipt selected for audit
Chap 1-8
Population vs. Sample
Population
a b
Sample
cd
b
ef gh i jk l m n
o p q rs t u v w
x y
z
c
gi
o
n
r
u
y
Chap 1-9
Why Sample?

Less time consuming than a census

Less costly to administer than a census

It is possible to obtain statistical results of a
sufficiently high precision based on samples.
Chap 1-10
Sampling Techniques
Samples
Non-Probability
Samples
Judgement
Convenience
Probability Samples
Simple
Random
Systematic
Stratified
Cluster
Chap 1-11
Statistical Sampling

Items of the sample are chosen based on
known or calculable probabilities
Probability Samples
Simple
Stratified
Systematic
Cluster
Random
Chap 1-12
Simple Random Samples

Every individual or item from the population has
an equal chance of being selected

Selection may be with replacement or without
replacement

Samples can be obtained from a table of
random numbers or computer random number
generators
Chap 1-13
Stratified Samples

Population divided into subgroups (called strata)
according to some common characteristic

Simple random sample selected from each
subgroup

Samples from subgroups are combined into one
Population
Divided
into 4
strata
Sample
Chap 1-14
Systematic Samples

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
N = 64
n=8
First Group
k=8
Chap 1-15
Cluster Samples


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
Population
divided into
16 clusters.
Randomly selected
clusters for sample
Chap 1-16
Data Types
Data
Qualitative
(Categorical)
Quantitative
(Numerical)
Examples:



Marital Status
Political Party
Eye Color
(Defined categories)
Discrete
Examples:


Number of Children
Defects per hour
(Counted items)
Continuous
Examples:


Weight
Voltage
(Measured
characteristics)
Chap 1-17
Data Types

Time Series Data


Ordered data values observed over time
Cross Section Data

Data values observed at a fixed point in time
Chap 1-18
Data Types
Sales (in $1000’s)
2003
2004
2005
2006
Atlanta
435
460
475
490
Boston
320
345
375
395
Cleveland
405
390
410
395
Denver
260
270
285
280
Time
Series
Data
Cross Section
Data
Chap 1-19
Data Measurement Levels
Measurements
Ratio/Interval Data
Rankings
Ordered Categories
Categorical Codes
ID Numbers
Category Names
Ordinal Data
Nominal Data
Highest Level
Complete Analysis
Higher Level
Mid-level Analysis
Lowest Level
Basic Analysis
Chap 1-20
Randomization of Subjects

Randomization: the use of chance to divide
experimental units into groups
Chap 1-21
Experiment Vocabulary

Experimental units


Subjects

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Specific experimental condition applied to the units
Factors

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Experimental units that are human
Treatment
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Individuals on which the experiment is done
Explanatory variables in an experiment
Level

Specific value of a factor
Chap 1-22
Example of an Experiment


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Does regularly taking aspirin help protect people
against heart attacks?
Subjects: 21,996 male physicians
Factors
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
Treatments
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Aspirin (2 levels: yes and no)
Beta carotene (2 levels: yes and no)
Combination of the 2 factor levels (4 total)
Conclusion

Aspirin does reduce heart attacks, but beta carotene has no
effect.
Chap 1-23
Chap 1-24
Block designs

Random assignment of units to treatments is carried out separately
within each block (Group of experimental units or subjects that are
known before the experiment to be similar in some way that is
expected to affect the response to the treatments)
Chap 1-25
Inferential Statistics

Making statements about a population by
examining sample results
Sample statistics
(known)
Population parameters
Inference
Sample
(unknown, but can
be estimated from
sample evidence)
Population
Chap 1-26
Key Definitions

A population is the entire collection of things
under consideration


A parameter is a summary measure computed to
describe a characteristic of the population
A sample is a portion of the population
selected for analysis

A statistic is a summary measure computed to
describe a characteristic of the sample
Chap 1-27
Statistical Inference Terms

A parameter is a number that describes the
population.


Fixed number which we don’t know in practice
A statistic is a number that describes a sample.



Value is known when we have taken a sample
It can change from sample to sample
Often used to estimate an unknown parameter
Chap 1-28
Statistical Significance


An observed effect (i.e., a statistic) so large that
it would rarely occur by chance is called
statistically significant.
The difference in the responses (another
statistic) is so large that it is unlikely to happen
just because of chance variation.
Chap 1-29
Inferential Statistics
Drawing conclusions and/or making decisions
concerning a population based on sample results.

Estimation


e.g.: Estimate the population mean
weight using the sample mean
weight
Hypothesis Testing

e.g.: Use sample evidence to test
the claim that the population mean
weight is 120 pounds
Chap 1-30
Sampling variability

Sampling variability


Value of a statistic varies in repeated random
sampling
If the variation when we take repeat samples from
the same population is too great, we can’t trust the
results of any one sample.
Chap 1-31
Sampling Distribution

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Calculate the statistic of interest T(X) for a sample (this
may be the only estimate we may get for a parameter)
Somehow get another sample, recalculate T. It will be
different each time since X is random.
Plot histogram of T. This is the sampling distribution of
T.
A distribution for T obtained from a fixed number of trials
is only an approximation to the sampling distribution,
just as a in the case for a sample of X.
Chap 1-32
Remember!

Population size doesn’t matter


The variability of a statistic from a random sample
does not depend on the size of the population, as
long as the population is at least 100 times larger
than the sample.
We are only estimating the parameters of the
population, we are not really doing much with
the population itself (that’s simulation, or
empirical distribution modeling).
Chap 1-33
Sampling Distribution of p̂
Chap 1-34
Bias and Variability

Unbiased and Sample Variance ( N   )
Chap 1-35
Chapter Summary

Reviewed key data collection methods

Introduced key definitions:
Population vs. Sample
Primary vs. Secondary data types
Qualitative vs. Qualitative data
Time Series vs. Cross-Sectional data

Examined descriptive vs. inferential statistics

Described different sampling techniques

Reviewed data types and measurement levels

Introduced concept of sampling distribution
Chap 1-36