BIOL 300 Chapter Notes - Chapter 5i, 9: Null Hypothesis, Estrous Cycle, Round-Off Error
May 31st, 2018 BIOL 300
Week 3 Reading
Interleaf 5: Making a plan
- Here are some guidelines to avoid a few common pitfalls
o Develop a clear statement of the research question
▪ This needs to be as specific as possible. What is the scientific hypothesis?
Is the question interesting? Has it already been addressed sufficiently in
the literature? Identify clear objectives for the experiment
o List the possible outcomes of your experiment
▪ Once you have a preliminary plan for the treatments you want to
compare, think of the outcomes you might obtain. Can you draw firm
conclusions no matter what the outcome? Do these conclusions answer
the question? If not, then modify your design
o Develop an experimental plan
▪ Write it down. Let it sit for a few days and then review it again
o Keep the design of your experiment as simple as possible
▪ Do you really need 12 different treatments, or will two suffice?
Simplifying the design will make it easier to keep track of your objectives,
and it will avoid the need for complex statistical analyses
o Check for common design problems
▪ Is there replication of treatments? Are these replicates truly
independent? Will your sampling method yield random samples? Can you
identify any confounding variables that will complicate the interpretation
of the results?
o Is the sample size large enough?
▪ Avoid getting to the end of an experiment before discovering that your
sample size is only large enough to demonstrate an unrealistically large
effect. Is the sample size sufficient to produce a confidence interval
narrow enough to permit conclusions, regardless of the size of the
treatment effect?
o Discuss the design with other people
▪ Many brains think better than one, and others will often see a problem
(and hopefully a solution) that was’t oious to ou. It is ette to get
that feedback before doing all the work than to be told after the fact,
he it’s too late to do athig aout it.
Chapter 9: Contingency analysis
- Contingency tables display how the frequencies of different values for ne variable
depend on the value of another variable when both are categorical
- Analysis of contingency data can be used to answer questions such as the following
o Do bright and drab butterflies differ in the probability of being eaten?
o How much more likely to drink are smokers than non-smokers?
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o Are heart attacks less likely among people who take aspirin daily?
- In experimental studies, contingency data can help us establish whether the probability
of living or dying differs between medical treatments. We can test hypotheses about
differences in the probabilities using a contingency test
- Contingency analysis allows us to determine whether, and to what degree, two (or
more) categorical variables are associated
o In other words, a contingency analysis helps us to decide whether the proportion
of individuals falling into different categories of a response variable is the same
for all groups
o Contingency analysis estimates and tests for an association between two or
more categorical variables
- At the heart of contingency analysis is the investigation of the independence of variables
o If two variables are independent, then the state of one variable tells us nothing
about the probability of the different values of the other variable
9.1 Associating two categorical variables
- An association between two
categorical variables implies that the
two variables are not independent
o For example, during the Titanic
disaster, women has a lower
probability of death than men.
Sex and death were not
independent. If death had been
independent of sex, then the
probability of death would have
been equal for both sexes, and
the resulting mosaic plot would
look like the one to the right
9.2 Estimating association in 2 x 2 tables: odds ratio
- The odds ratio measures the magnitude of association between two categorical
variables when each variable has only two categories
o One of the variables is the response variable – lets call its two categories
suess ad failue, hee suess just efes to the foal outoe of
interest
o The other variable is the explanatory variable, whose two categories identify the
two groups whose probability of success is being compares
o The odds ratio compares the proportion of successes and failures between the
two groups
- Consider a variable for which a single random trial yields one of two possible outcomes:
success or failure
o The probability of success and the probability of failure is . The odds of
success () are the probability of success divided by the probability of failure
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find more resources at oneclass.com
o If soeties itte as :, o the odds ae oe to oe, the oe
success occurs for every failure.
o If the odds are 10 (10:1), then 10 trials results in success for every one that
results in failure
- The estimate of the odds is calculated from a random sample of trials using the
observed proportion of successes () as follows
- Example: Take two aspirin and call me in the morning?
o Aspirin, the medicine commonly used to headache and fever, has been shown to
reduce the risk of stroke and heart attack in susceptible people. Observational
studies have suggested that aspirin may also reduce the risk of cancer. A large,
carefully designed experimental study was conducted to test this possibility. A
total of 39,876 women were randomly assigned one of two different treatments.
Of these, 19,934 women received 100 mg of aspirin every other day. The other
19,942 women received a placebo. The women did not know which treatment
they received. The women were monitored for 10 years. During the course of
the study, 1438 of the women on aspirin and 1427 of those receiving the placebo
were diagnosed with invasive cancer
o At a glance at the mosaic plot, we see that the cancer rates did not change
much, if at all, as a result of taking aspirin
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Here are some guidelines to avoid a few common pitfalls: develop a clear statement of the research question, this needs to be as specific as possible. Identify clear objectives for the experiment: list the possible outcomes of your experiment, once you have a preliminary plan for the treatments you want to compare, think of the outcomes you might obtain. If not, then modify your design: develop an experimental plan, write it down. Simplifying the design will make it easier to keep track of your objectives, and it will avoid the need for complex statistical analyses: check for common design problems. Is the sample size large enough: avoid getting to the end of an experiment before discovering that your sample size is only large enough to demonstrate an unrealistically large effect. It is (cid:271)ette(cid:396) to get that feedback before doing all the work than to be told after the fact, (cid:449)he(cid:374) it"s too late to do a(cid:374)(cid:455)thi(cid:374)g a(cid:271)out it.
