HONORS STATISTICS
Mrs. Garrett Block 1 & 2 & 4
Monday November 25, 2013
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Daily Agenda
1. Welcome to class
2. Please find folder and take
your seat.
3. Review homework OTL C5#6 4. Review worksheets for test
5. Boxplot Quiz
6. Collect folders
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GRADED
GRADED
Histogram Q3 ___
GRADED
GRADED
GRADED
Histogram Q1 ___
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GRADED
Monday GRADED
Thursday
GRADED
10
GRADED
Histogram Q2 ___
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GRADED
Thursday
Today
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OPTIONAL MC Practice for Test 5 on Producing Data
Answers listed after question 20
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Answers to the 1­20 MC
These are my quick answers to the questions.... please question any that you do not agree with tomorrow before the test is distributed.
1. B
2. C
3. B
4. D
5. C
6. D
7. E
8. D
9. C
10. B
11. B
12. C
13. B
14. B
15. D
16. B
17. E
18. C
19. B
20. C
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Frequency
Gym class sit-ups
0­4 5­9 10­14 15­19 20­24 25­29
Number of sit-ups
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18 28 29 31 37 40 42 46 56 58
37+40 = 77/2 = 38.5
38.5
variation
bias
increases the validity of the results
makes the result more statistically
significant.
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BONUS OPPORTUNITY 5 points
November 26 TUESDAY
1) Create "lurking variable" situations (up to 5)
2) Identify clearly the x,y and z variables
3) Draw the proper diagram for x,y and z
4) Identify the proper association name
Common Response or Confounding
5) Be very clear about your association
Be creative and unique
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Honors Statistics
Test Review
Directions: Indicate whether the sentence or statement is true (T) or false (F).
If you choose false can you explain why the statement is false?
F
_____ 1.
T
_____ 2.
F
_____ 3.
By definition a simple random sample of size n is any sample that is selected in a manner to guarantee every individual in the population has an equal chance of selection.
Blocking is a technique that can be used to filter out the effects of extraneous
factors.
Response bias can occur when responses are not actually obtained from all
individuals selected for inclusion in the sample.
F
Increasing sample size will generally reduce bias in a sample.
T
A placebo is identical in appearance to the treatment of interest, but contains no active ingredients.
_____ 4.
_____ 5.
F
_____ 6.
F
_____ 7.
T
_____ 8. T
_____ 9.
F
In a well designed experiment, the factors are confounded whenever possible.
Random assignment to treatments will guarantee groups that are exactly alike for experimental purposes.
A control group provides a baseline for comparison to a treatment group.
Random assignment of volunteers should result in comparable experimental groups.
If the subjects as well as the person measuring the response are aware of the _____ 10.
treatment assigned to the subject, only single­blinding is being used.
F
_____ 11.
T
F
_____ 13.
_____ 12. F
_____ 14.
T
_____ 15.
The tendency for samples to differ from the corresponding population due to
the systematic exclusion of some part of the population is known as nonresponse bias.
The three key concepts in experimental design are control, randomization and replication.
A study is an observational study if the investigator observes how a response variable behaves when the researcher manipulates one or more factors.
An observational study can result in data that provides evidence for a cause­and­effect relationship.
The method of control wherein an extraneous variable is held constant is
called blocking.
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Honors Statistics
Experimental Design
Name:________________________________
High blood pressure adds to the workload of the heart and arteries and may increase the risk of heart attacks. If not treated, this condition can also lead to heart failure, kidney failure, or stroke. Angiotensin­converting enzyme (ACE) inhibitors are used to treat high blood pressure. It is well known that men and women may react differently to common cardiovascular drug treatments. Most studies of heart drugs involved only a very small percent of women, because it was simply assumed that the drug would work the same in both sexes. We want to conduct an experiment to see if ACE inhibitors are less effective in women than in men.
(a)
What sort of experimental design would you choose for this study, and why?
The best choice is a randomized blocked comparative experimental design.
Blocks should be formed for subject gender because men and women are known to react differently to these drugs. 17
(b)
Assume that 600 men and 500 women suffering from high blood pressure are available for the study. Outline in a diagram the design of the experiment. Be sure to indicate how many subjects are assigned to the various treatment groups.
Block 1:
600 men
1100 men and women with high blood pressure
(measure blood
pressure)
Block 2:
500 women
Group 1:
300 men
Treatment 1:
ACE inhibitor
Group 2:
300 men
Treatment 2:
received placebo
Group 1:
250 women
Treatment 1:
ACE inhibitor
Group 2:
250 women
Treatment 2:
received placebo
measure blood pressure
measure blood pressure
Random
Assignment
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(c)
Use line 134 of the random digits table (below) to select the first 3 men for the study, and use line 142 to select the first 3 women for the study.
300
600
MEN N = ______ n = _____
500
250
Women N = _______ n = _______
use 3 digit numbers from 001 to 600
LABEL: use 3 digit numbers from 001 to 500
LABEL: TABLE: start line 134 pick 3 digits
TABLE: start line 142 pick 3 digits
134 142
27816 78416 18329 21337 35213 37741 04312 68508
72829 50232 97892 63408 77919 44575 24870 04178
STOPPING PROCEDURE:
continue until 300 DIFFERENT 3 digit numbers
from 001 to 600 are selected
IDENTIFY SAMPLE:
278 167 841 618 329
STOPPING PROCEDURE:
continue until 250 DIFFERENT 3 digit numbers
from 001 to 500 are selected
IDENTIFY SAMPLE:
728 295 023 297
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Tonight's Homework: OTL C5 #6
Study for your test
TEST review worksheets
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This article describes a matched pairs experiment. There are two different treatments and each subject received both treatments. Explanatory variable was the type of treatment. The treatment is either breakfast, aspirin and alcohol or alcohol alone. The response variable is blood alcohol level.
The experimental design is a matched­pairs experiment.
It is a poorly designed experiment because only volunteers are used in the experiment. Also, there was no random assignment of treatments. All subject received both treatments which helps with control but did they all receive them in the same order? There are only 5 subjects so replication of results is an issue.
In statistics when the word "significantly" is used it refers to a result that happened that we did not expect
to occur. (The result beat the"chance" or the odds that it should happen.)
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This is wording of question bias.
Using the words "preserve their constitutional right" is powerful and people always wish to protect their legal rights.
If other words were used to ask the question, such as "should Americans limit the number and/or type of guns that a person can own". I believe the poll results would not be as strong
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This bias is undercoverage.
There are two reasons for choosing undercoverage. First only people who are 50+ are asked for their opinion. Second, only members of AARP are asked for their opinion. I believe that lower income people may not belong to this organization.
Wording of question is also an option. The question is worded confusingly and so people may not know how to respond. It also tells people that they will not be affected
by the proposal. (eventually our tax money is used for these programs)
People may feel that they are unsympathetic if they vote no for this legislation designed to help low income people and people with high health care costs.
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Using an SRS is a great start. However Joe needs to make a big attempt to contact the 13 people who did not respond because they were selected randomly and they could have similar reasons for their nonresponse. Getting 13 more people will not include the potentially similar opinions and result in bias of the experiment results.
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This method of assignment to treatment groups basically is blocking the experiment. If there is no reason to suspect that men and women will react to the treatment based on their gender then blocking should not be used.
Both men and women should be expected to be in the "real" treatment group or in the "control" treatment group.
Randomly flip a coin (or choose a random digit) and separate the 100 subjects into treatment 1 and treatment 2, disregard gender.
If gender is a potential confounding variable, then first
separate the people into gender groups (men and women)
then random separate the men into treatment 1 and treatment 2 groups. Likewise separate the women into treatment 1 and treatment 2 groups.
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The explanatory variable is type of pill the subject received.
The response variable is (pre vs post) learning and memory test results.
Double blind means that the subjects taking the pill and the "nurse" or person distributing the pill do not know which pill is being distributed and swallowed.
A experiment that has more subjects is potentially providing more evidence for a "working" product. Example half of 30 people (15) that increase memory and learning skills is not as astounding as half or 300 or 150 people with test results demonstrating an increase in memory and learning skills. The second result would happen less likely by chance if there is no effect from the ginko.
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I will block on genetics. I believe that a family history of Alzheimer disease would be a confounding variable in the results of the experiment.
240 healthy people over 60 years old
Block 1:
120 people with family history of Alzheimer Disease
Block 2:
120 people with no family history of disease
Group 1:
60 people
Treatment 1:
received ginko
Group 2:
60 people
Treatment 2:
received placebo
Group 1:
60 people
Treatment 1:
received ginko
Group 2:
60 people
Treatment 2:
received placebo
measure memory and learning capacity
measure memory and learning capacity
Random
Assignment
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Sample is ____________________________________
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)
use 3 digits between 001 and 120
3
continue until 60 different 3 digit numbers from 001 to 120 are selected
005, 118, 007, 067, 114
Sample is ____________________________________
454 677 170 977 558 000 953 286 329 485 822 269 005 652 711 388 899 307 460 227 400 118 584 848 767 525 739 559 294 007 699 719 148 160 779 573 977 729 759 335 684 173 501 315 529 727 658 508 957 067 502 114
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Your Choice:
1­ Design your own test review
2­ Do the bookwork below
3­ Do the Lurking Variable Bonus
4­ Start the Cookie Experiment write up
Test Review Homework: OTL C5 #7
pg 371: 5.46, 5.48 b only
pg:377: 5.60 a only
LABEL YOUR A­Skips ... none
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5.46 Pain relief study
(a) Why should Fizz not simply administer the
drug and record the patients' responses?
If a control group is not formed there will
be nothing to compare the new medication with.
The fact that the patients are in a study and
receive pain relief could then be attributed to
the "placebo effect".
(b) Outline the design of an experiment to compare the
drug's effectiveness with that of aspirin and a placebo.
60 patient
suffering from arthritis
Group 1:
20 subjects
Treatment 1:
received new
pain medication
Group 2:
20 subjects
Treatment 2:
received aspirin
Group 3:
20 subjects
Treatment 3:
received placebo
compare
pain relief
Random
Assignment
(c) Should the patients be told with drug they are receiving?
How would this knowledge probably affect their reactions?
The patients must not be told which pain medication they are
receiving. If a person knows they are receiving the placebo,
they will most likely not experience any pain relief. There will
be no "placebo effect". No chance for the person's mind to
do the pain relief.
(d) If patients are not told which treatment they are receiving, the
experiment is single­blind. Should this experiment be double­blind?
All experiments should be double­blind if it is possible to do so.
A double­blind experiment adds credibility to the results. Those
administering the medication cannot inadvertently bias the results
because they will not know which person is receiving the new pain relief medication.
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5.48 Carbon dioxide and tree growth
(b) Areas within the forest differ in soil fertility? Describe a matched pairs design using three pairs of circles that will reduce the extra variation
due to different fertility.
Technically a matched pairs study should only be done
with both treatments on the same plot of land. This
design will be addressed next ...
Design 1
A matched pairs experiment on six plots of land will
first require that the researchers analyze each plot to
determine the soil fertility. Hopefully three of the plots
will match up with the other three in terms of soil fertility.
Label the "matching soil plots" 1 and 2, 3 and 4, 5 and 6
Use a coin to randomize. Let heads be treated and tails untreated.
Flip a coin to determine if plot 1 is CO2 treated or untreated.
Repeat this process for plots 3 and 5. Heads = yellow
A potential randomization could look like this ...
1
5
2
4
3
6
Design 2
A matched pairs experiment should be done on the exact same
plot of land. Split each plot in half and randomly choose which
side to treat with the CO2. I must assume that the apparatus
is able to pipe the extra CO2 to only half the circle.
Use a coin to randomly pick the treatment for the left
side of each circle. Use a coin and let heads be treated
and tails untreated.
A potential randomization could look like this ...
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5.60 Acculturation rating
(a) Briefly describe a matched pairs design for this study. In particular, how will you use randomization in your design?
Group 1:
11 men
Treatment 1:
First ­ BI
Second ­ ARSMA
22 Mexican
Americans
calculate
correlation between tests
Group 2:
11 men
Treatment 2:
First ­ ARSMA
Second ­ BI
Random
Assignment
Randomization will be used to determine which test the men will take first.
To randomize flip a coin heads treatment 1 and tails treatment 2 until one treatment group is totally filled up (the rest go to the other treatment group)
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