Transcript Chapter 2

Experimental Design
Sections 1.2 & 1.3
Section 1.2 - Random Samples
• Samples are used to gain an understanding of “Total
Population”
• Def: Simple Random Sample (SRS) - is a subset of the
population that is selected in a way where each
member had an equal chance of being chosen.
• What does it mean to be “random”?
Using the Random Number Table
(Appendix 1)
• Gives a starting point for you to find
“matches” or select individuals.
Steps:
1. number all members of population sequentially.
2. determine starting point on random # table
(given).
3. looking at correct number of digits, find matches
which will produce the sample.
Example 1 - SRS
Pick an SRS of size 4 from the class starting on the
7th row, 3rd block
• Label students 01-25
• Looking at 2 digits at a time, start on the 7th row,
3rd block to locate matches
7th row:
82739 57890 20807 47511 81676 55300 94383 14893
8th row:
60940 72024 17868 24943 61790 90656 87964 18883
Example 2 - SRS
Pick an SRS of size 30 from a population of 500
cars starting on the 11th row, 1st block. List
only the first 5 matches.
Answer: 092,041,271,238,276
Example 3 - SRS
Pick 150 students from the Univ. of Florida which
has a population of 50,000 students starting on
the 1st row, 7th block. List the first 5 matches.
Answer: 42544, 47150, 01927, 27754, 42648
Other types of Sampling
(Summary on page 17)
1. Stratified - draw a certain number of
individuals from a population after it is
divided up into smaller groups (strata)
Lynchburg
College
Students
Fr.
So.
Jr.
Sample
(10 from each strata)
Sr.
Other types of Sampling
(Summary on page 17)
2. Systematic – arrange individuals in some
order, then select every kth element.
Ex. Elementary school – count up by 3’s: 1-2-3, 1-2-3,
1-2-3, … to form 3 groups.
 Downfall: if a machine produces something and
you check every 16th element, but there is a
mistake in every 17th element, big problem.
Other types of Sampling
(Summary on page 17)
3. Cluster – divide up demographic area into
sections, select a few sections, and then sample
every individual in that section.
Ex. Large city school children: select 5 schools
(clusters) and then sample all kids from those 5
schools.
 Sample is compose of 5 schools rather than an SRS of
2500 students.
Other types of Sampling
(Summary on page 17)
4. Multistage – start with a large group to
sample and then break down group based on
certain factors with final stage consisting of
clusters.
Ex. 60,000 households → then by race →
smaller groups (age, income, etc.) → clusters
→ interviews/surveys
Other types of Sampling
(Summary on page 17)
5. Convenience – use results/data that is
available, some information is better than no
information.
Ex. Ask your friends to complete a survey on
nuclear reactors, stratification layers in lakes, or
equilibrium points of a specific parasite that
infect dogs.
Types of errors
• Sampling errors: difference between
measurements from a sample compared to
what the population data should actually be.
• Nonsampling errors: result of poor sample
design, sloppy data collection, faulty
machines, bias, undercoverage, etc.
Section 1.3 – Intro. To Experimental
Design
• Guidelines for a Study
1.
2.
3.
4.
Identify individuals of interest
Specify variables to be studied
Sample or population? Size?
Create data collection plan and obtain
permissions.
5. Collect data
6. Analyze data using statistics
7. Conclusions and concerns
Good Practices / Terminology
• Treatment – Specific condition administered to
subjects (diet pill, music, etc.)
• Placebo – “dummy” treatment given to a test
group. Has no actual effect on subjects.
Placebo Effect – subject receives no actual treatment, but thinks he/she is
receiving treatment and responds favorably.
• Blind study – subjects do not know which
treatment they are receiving.
Double Blind – neither subjects nor persons performing study know
treatment groups.
Good Practices / Terminology
• Control Group – treatment group who is given
a placebo. Should not show any changes, but
if there is change, results could be used to
account for any lurking or confounding
variables.
Lurking Variable – variable that isn’t studied, but may have an influence
on other variables in the study.
ex. Diet pills and weight loss: Lurking variable could be exercise or nutrition.
Confounding Variable – Two variables whose effects can’t be
distinguished from each other.
ex. Study involving GPA: difficulty of courses, IQ, and available study time are
all confounding variables.
Good Practices / Terminology
• Matched Pairs Design
Test the time it takes for two groups to complete a maze with the treatment being a certain type of music.
Trial 1:
Trial 2:
with music
Group A
Group B
without music
Group B
Group A
Compare results and make conclusions using data
about each group with both treatments.
Good Practices / Terminology
• Replication – Perform an experiment on many
individuals to reduce the possibility of error or a
result occurring by chance.
• Census – data from the entire population is used
• Sample – data from part of the population is used
• Bias – Results skewed in some way due to
personal opinion / favoritism.
Usefulness of Data
• Situation 1
A uniformed police officer interviews a group of 20
college freshman. The officer asks each one his or
her name and then if he or she has used an illegal
drug in the last month.
In fear of getting in trouble – students may not
answer truthfully or refuse to participate.
Usefulness of Data
• Situation 2
Jessica saw some data showing that cities with more
low-income hosing have more homeless people.
Does building low-income hosing cause
homelessness?
Lurking / Confounding Variables such as the size
of the city.
Usefulness of Data
• Situation 3
A survey about food in the café was conducted by
placing forms for students to pick up as you got
your card scanned. A drop box was then placed in
the foyer outside the café.
 Voluntary response likely produced negative comments
 Nonresponse by losing document before it was turned in
 Fill out form before you ate, not accurate account of the quality
of the food
Usefulness of Data
• Situation 4
Extensive studies on coronary problems were
conducted using men over the age of 50.
Results may not help out other age groups or the
female gender
Types of Studies
Observational
Experiment
• Simply observe subjects
without any influence on
the variable being studied
• Researcher actually does
something (treatment) to
the subject being studied
Ex. A researcher stood by a
busy intersection to see if
the color of the car
someone drove related to
running red lights.
Ex. Subjects were assigned to
two groups. The first group
was given an herbal
supplement and the other a
placebo. After 6 months the
red blood cell counts were
compared.
Types of Experimental Designs
1. Completely Randomized – random process
(ie. random number table) is used to assign
each individual to one of the treatment
groups.
Ex. Laser heart treatment on 300 individuals
with heart pain problems.
Patients
w/heart
pain
problems
Random
Assignments
Group 1, 150 patients,
laser treatment
Group 2, 150 patients,
no treatment
Compare
pain relief
Types of Experimental Designs
2. Randomized Block Experiment – sort
individuals into blocks and then use random
process to assign individuals in the block to
one of the treatments.
Def: block – group of individuals that share a
common feature that may affect the
treatment.
Patients w/heart
pain problems
Men
Women
Random
Assignments
Random
Assignments
Group 1,
laser
treatment
Compare
pain relief
Group 2,
no
treatment
Group 1,
laser
treatment
Compare
pain relief
Group 2,
no
treatment
Data Collection
• By means of surveys
Sampling, census, observation, or experiments. Not
just questionnaires.
• Methods most commonly used
1. Surveys – quick and effective
2. Observational study – less permission needed
and don’t have to bother anyone to obtain data
3. Experiments – time consuming, but yield the
most meaningful and valid results.
Problems with Data Collection Surveys
•
•
•
•
Nonresponse / Small sample size
Truthfulness
Faulty recall – forgot details of an event
Hidden bias – wording leads subjects to respond a
certain way
• Vague wording – words with different meanings to
different persons are used (often, seldom, occasionally)
• Interview influence – tone of voice, body language,
attire, etc. influence results
• Voluntary response – Individuals with strong feelings
about a subject are more likely to respond in a positive
way, which is not reflective about the entire
population.
Problems with conclusions when using
a sample
• Inference about a population
– Results of a sample may not reflect the entire
population correctly
– Large sample sizes give more accurate results
Homework
• Section 1.2
Pg. 18 #’s: 6a, 7 starting at line 7, 8 starting at line 8,
9 starting at line 9, 10 starting at line 10, 13
starting at line 13.
• Section 1.3
Pg. 28 #’s: 5,7a,9
&
Pg. 32 #’s: 3a,6,7