Math 299
Exam 1
Review

This exam will cover topics from Chapter 1 and the part of Section 2.1 that we've covered. It will be a take-home exam. You many use class notes/materials, Maple, Excel, Statcrunch, and any of the applets used in class.You will receive the exam on Friday, September 23. It will be due in my office at 4:00PM on Tuesday, September 27. Collaboration of any kind is not permitted. Any instance of such should be reported to me. Appropriate disciplinary action will be taken.

From section 1.1 you should know:
How to construct a two-way table
How to calculate (appropriate) conditional proportions and compare them
How to construct a segmented bar graph (by hand) and describe what it reveals
How to calculate baseline risk, odds, relative risk, and odds ratios
How to decide which calculation is being asked for in the context of the problem
How to interpret the results of the calculations
How to identify observational units
How to define variables appropriately
The distinction between variables and the outcomes or levels of the variable
How to determine whether a variable is quantitative or categorical
How to identify the explanatory variable and the response variable

From section 1.2 you should know:
How to distinguish between a retrospective design (select units according to the response variable) and a prospective design (select units according to the explanatory variable).
Not to generalize P(response) for a retrospective design
Not to generalize P(explanatory) fro a prospective design
It is always ok to calculate odds ratio
Some of the limitations in the type of conclusions that can be drawn from different designs
That we cannot draw cause-and-effect conclusions from an observational study
That the difference in proportions does not take into account the magnitude of the baseline risk
Small differences in proportions “seem” much larger when the baseline risk is small
That relative risk and odds ratio will be similar when the proportion of successes is small in both groups
Odds ratio = (relative risk)(1-prop success group 2)/(1-prop success group 1)
Odds ratio can be used as an approximation to the relative risk in this case
When there is no difference in the proportion of successes in the two groups, the odds ratio and relative risk both equal one and the variables are said to be independent.
The advantages to blinding and double-blinding in a study

From section 1.3 you should know:
How to identify a potential confounding variable in observational studies
Be sure to comment on how there is a differential effect among the explanatory variable groups
Determine whether or not Simpson’s Paradox is present in a three-way table
The conditions that lead to Simpson’s Paradox
How to explain Simpson’s Paradox to someone not in a statistics class
How to calculate a “weighted” overall proportion

From section 1.4 you should know:
How to distinguish between an observational study and an experiment
The advantages of using a placebo treatment
The purposes/goals/merits of randomization
How to carry out a randomization using Excel or Statcrunch
When we are allowed to draw cause-and-effect conclusions (perhaps just about the observational units in the study)
The basic idea of blocking (what it gains for you)

From section 1.5 you should know:
The reasoning of “statistical significance”
Not to use the word “significance” anymore when don’t really mean it
What a p-value measures
How to make conclusions based on a p-value
How to interpret a results from a randomization simulation
How to carry out a randomization simulation
Including how to approximate the p-value based on the simulation results

From section 1.6 you should know:
How to interpret “probability” as a long-run relative frequency
How to list elements of a sample space
How to decide if outcomes are equally likely
How to calculate a probability of an event consisting of equally likely outcomes
How to calculate hypergeometric probabilities (by hand)
How to identify whether hypergeometric probabilities apply to a given situation

From section 1.7 you should know:
How to carry out Fisher’s Exact Test and interpret the results
To remember to think about the scope of conclusions that can be drawn based on the study design

From section 2.1 you should know:
How to describe what is meant by the terms shape, center, and spread in relation to the distribution of a variable
How to compute the five number summary (by hand) for a "small" set of data
How to determine whether an observation is an outlier based upon the 1.5xIQR rule
How to compute and interpret the z-score for an observation

Notes to keep in mind:
Part of your grade will be based on communication.  Be precise in your statements and use of terminology.  Avoid unclear statements, especially don’t use the word “it”!
Show the work of any calculations you do by hand.
Report use of any "tools" used for computation.