1. PROBLEM SET ONE: QUESTION 10:
NOTE: IN ADDITION TO HANDING IN A HARD COPY, PLEASE EMAIL
COPIES OF YOUR WORK TO: kcobb@stanford.edu
The final part of your homework is to write a brief explanation of a simple statistical
concept and to find one or two INTERESTING examples in the medical literature of
medical studies where the statistic or concept was applied (to access Stanford’s Lane
Medical Library, where many examples are available to you online, goto:
http://lane.stanford.edu/index.html).
You will be contributing content for a web-based easy-to-use program (something like
“TurboTax for study design”) that is being developed to help medical researchers design
studies (for more information on the project, goto: http://clio.stanford.edu). The program
leads the user from a specific hypothesis (eg., Does studying statistics at Stanford
(exposure) lead to an increase in gray hairs (outcome)?) to an appropriate study design
(as we’ve learned in class, the main options are: case-control, cohort, or randomized
clinical trial), and through data collection, sample size calculations, and data analysis.
Our class has been solicited to write “learning modules” for statistical concepts that occur
in the Sample Size Calculations section. Users can click on learning modules to get more
information about a statistical topic if they are unfamiliar with it. Each person in our
class will receive 1 of 13 topics we have been given to cover, so there will be some
duplication. Feel free to swap topics amongst yourselves.
This will give you a chance to explore the medical literature and to think about how
statistics are applied to medical studies. Please be BRIEF and write in the ACTIVE
VOICE. These should be as lively and entertaining (while still being accurate, of course)
as possible!
Instructions:
We want you to provide 5 short elements:
(1) A definition/statement of the problem or issue (see below for an example)
(2) An explanation of your statistical topic
(3) 1 or 2 examples of a medical study where the topic is applied (and how it is
applied). Please cite specific, real studies if possible.
(4) Expansion/amplificaiton – if there’s something more you want to add
(5) Web resource/s: if you can find any Web resources to refer naïve statisticians to…
Here is an example:
WHAT YOU ARE GIVEN:
Your learning module topic: Types of data
Where the user is coming from: The user has defined a study design (cohort study) and
hypothesis, including exposure and outcome variables.

2. Trigger Question (This is the last thing the user sees before accessing your learning
module): Will you compare your exposure groups based on a binary, categorical (other
than binary), or a continuous measure of the outcome?
Learning Module Objective: Your job is to help the user to determine whether she will
compare the exposure groups in her cohort study using a binary, continuous, or
categorical (>2 groups) measure of her outcome variable.
For example, if you are comparing statistics students with humanities students with
regards to the amount of gray hair that they accumulate during the winter term, you could
either measure gray hair as binary (grew at least one gray hair/grew no gray hairs);
categorical (grew a little or no gray hair vs. grew a moderate amount vs. grew a lot of
gray hair); or continuous (the number of gray hairs the student grew during the term).
The form of the outcome variable will determine the eventual statistical analysis.
WHAT YOU MIGHT WRITE (this example is a little long; try to keep it to 1 page
MAXIMUM):
Definition/statement of the problem:
A comparison between exposed and unexposed groups can be based on different types of
measurement scales. There are 3 basic classes of measures: Binary, categorical,
continuous.
Explanation of the concepts:
1) Binary measures compare 2 or more groups according to presence or absence of an
outcome (yes or no). This measure is commonly used to compare the frequency
(proportion) of events in 2 or more groups. The odds ratio and the relative risk are
examples of compound binary measures.
Example: I hypothesize that palm pilots (exposure) cause brain rot (outcome) in medical
students. For this study I will use a binary measure to classify subjects according to
whether they own a palm pilot or not (yes/no). Brain rot will also be classified with a
binary measure. We will observe students in a class for five minutes on a random day.
Those who are sleeping will be deemed to have brain rot and those who are not will be
deemed rot-free.
2.) Categorical measures compare 2 or more groups according to 2 or more
classifications, such as “No outcome” “Early Stage,” “Advanced Stage”. This type of
scale, which has a natural ranking and is sometimes referred to as “ordinal,” is commonly
used in studies seeking to establish a dose-response relationship between an exposure and
an outcome. Another type of categorical scale is a nominal scale. An example would be
classification of subjects according to type of primary cancer (outcome). There is no
natural ranking to the categories. The objective is to compare frequency of outcomes in
these subgroups without implying a hierarchy of outcome.
Example: Same study, but I would like to know whether palm pilot use is related to
severity of brain rot. I will use an ordinal measure of outcome for the in-class diagnosis:

3. alert, nodding, comatose-- and compare the frequency of these outcomes in palm pilot
owners and non-owners.
3.) The third type of scale is continuous, or sometimes referred to as “interval.” A
continuous measure has some important properties: it usually has a natural 0 and the
distances between units on the scale are equal. Some examples are age, systolic blood
pressure, body temperature, or a score on a test. This type of measure is often used to
compare mean or median values between exposed and unexposed groups.
Example. Same study, but because I cannot find enough alert or nodding subjects, I plan
to compare the mean Glasgow Coma score in Palm owners and non-owners.
Expansion/Amplification.
The type of measurement scale used to compare groups depends on the type of data that
can be collected and the objectives of the analysis. Binary and categorical measures are
relatively easy to obtain and have the advantage of making more definitive statements
about an association. Their disadvantage is that they usually require many more subjects
than continuous measures to analyze. Continuous measures may be more difficult to
obtain, and they may be more difficult to interpret, but they offer more information for a
relatively smaller sample size.
For further reading: [some stat web site]