Variables
Video Discussion of What Variables Are (2:43)
Link to transcript of the video
'Population'
A population is simply a group of people with some common characteristic, such as age, race, gender, or place of residence. A "target population" is a population for which you would like to make some conclusions. Examples:
 residents of Mumbai
 members of Blue Cross/Blue Shield (a U.S. health insurance organization)
 postmenopausal women in Massachusetts
 coal miners in Pennsylvania
 male physicians in the United States
 members of the BUSPH intramural softball team
Fixed versus Dynamic Populations
 Fixed population: In a fixed population membership is relatively permanent and perhaps defined by some event. Once a person experiences the defining event they remain part of that population as long as they are alive. Examples of relatively fixed populations might include:
survivors of the atomic blasts in Japan,
veterans of the Vietnam war or the Gulf Wars
members of the U.S. military who sustained a head wound while stationed in Iraq
residents of New Orleans who lost their homes during hurricane Katrina.
all babies born in Tanzania in 2012
Enrollment in an epidemiological study can also be the defining event for a person to enter a fixed population:
Persons who completed and returned a questionnaire in response to an invitation to join the Black Women's Health Study, and who were found to be eligible by study staff
Residents of Boston public housing who met eligibility criteria, completed informed consent and a baseline survey, and had one meeting with a community health worker to discuss smoking cessation
 Dynamic population: In a dynamic population, membership is defined by current status, so membership is not necessarily permanent. A person is a member of the population as long as they meet the definition of the population, and they cease to be a members of the population when they no longer meet the definition. Note that a person can be a member, leave, and then become a member again. Examples of a dynamic population include:
residents of any town or, state, or country
members of a health insurance plan
women who have given birth within the past 12 months
It can be a bit challenging at times to distinguish between fixed and dynamic populations, because the same description (e.g., resident of Boston) can be interpreted as an event or a current state. There are two helpful solutions to help clear up this confusion:
 Ask for a clearer description. For example, compare "ever lived in Boston for at least one day" and "currently lives in Boston ". The first describes a fixed population, the second a dynamic one.
 Think about why you are interested in the population. If we are interested in a question that is only relevant while the person lives in Boston, such as risk of accidents while riding a bicycle, then the population is dynamic, because once a person moves out of Boston there is no reason to follow them. On the other hand, if we are interested in a question that remains relevant even after a person leaves the city (e.g., does exposure to pollution lead to later development of disease), then you would want a fixed population.
Ratios, Proportions, and Rates
Ratio: A ratio is just a number that is obtained by dividing one number by another. A ratio doesn't necessarily imply any particular relationship between the numerator and the denominator. For example, if there were 100 women in this class and 20 men, the ratio of women to men would be 100/20 or 5 women for each man. This is just a simple ratio that indicates how many times larger one quantity is compared to the other.
Proportion: A type of ratio that relates a part to a whole; often expressed as a percentage (%). For example, if there are 120 women in a class of 130 students, then the proportion of women is 120/130 = 92%.
Rate: A type of ratio in which the denominator also takes into account another dimension, usually time. For example, speed is measured in miles/hour; it can be calculated by dividing the number of miles traveled by the number of hours that it took. Water flow might be quantified in gallons/minute; one might measure the number of gallons released during a period of time and divide by the number of minutes it took in order to calculate the average rate. An example of a rate that doesn't involve time is motor vehicle deaths, which are often reported as deaths/vehiclemiles. This is one way in which the relative safety of different types of transportation (automobiles, buses, trains, airplanes) can be compared.
While the term "rate" is used very broadly among the general population (birth malformation rate, autopsy rate, smoking rate, smoking rate, tax rate), in reality all these measures are proportions. For example, the smoking "rate" among adults is actually the number of adults in a population who smoke divided by the total number of adults in the population—in other words, a proportion because the numerator is a subset of the whole. One way to tell a proportion from a true rate is that a rate can never be expressed as a percentage, while a proportion should always be able to be expressed as a percentage.
Counts of Diseased People
Counting the people with disease is an important basic measure of disease frequency that is essential to detecting trends or the sudden occurrence of a problem, such as an epidemic. Simple counts of the number of diseased people are also important to public health planners and policy makers for assessing the need for resources in a population.
Table  New AIDS Cases by Year
Year 
Total AIDS Cases in City A 

2001 
0 
2002 
1 
2003 
5 
2004 
22 
2005 
75 
The count of AIDS cases shown here for City A would likely stimulate discussion among public officials & health providers, but count data alone don't allow us to fully understand the problem. We don't know if all of the cases were long time residents who developed AIDS while living in City A. Some may have moved into town after they developed AIDS. We also don't know whether any of the cases moved away or died.
A second limitation of just counting the number of existing cases is that it doesn't allow us to make fair comparisons of the frequency of HIV in different cities, since they don't take into account the total number of residents.
When measuring disease frequency, proportions and rates are very helpful when comparing groups, because they relate the number of people with disease to the size of the population in which they occur. Prevalence and incidence are the two fundamental measures of disease frequency.
Suppose, for example, that City A had 75 HIV+ residents, while City B had 35. This would suggest a larger problem in City A.
Table  Existing Cases of HIV+ in Cities A and B

Existing Cases 

City A 
75 
City B 
35 
However, suppose City A was substantially larger, with 30,000 residents, compared to only 7,000 in City B. To be fair, one would need to take this into account by dividing the number of cases in each city by the respective population size.
Table  HIV+ Cases, Population Size, and Prevalence in Cities A and B

Existing Cases 
Population Size 
Prevalence 

City A 
75 
30,000 
0.0025 
City B 
35 
7,000 
0.0050 
In essence, the resulting decimal fractions indicate the frequency of HIV per person in each city, and we can now see that City B actually has a higher prevalence of HIV+ residents than City A, in fact twice as high (0.005 vs. 0.0025). However, the frequency of HIV per individual is not a very intuitive or useful concept. However, if we multiply each of the results x 10,000, we have the frequency per 10,000 population. Obviously, neither city has exactly 10,000 residents, but by converting the decimal fractions to this standard population size, we can now have a more understandable description of the prevalence of HIV+ residents in each city.

Existing Cases 
Population Size 
Prevalence (as a decimal fraction) 
Prevaence (per 10,000 population) 

City A 
75 
30,000 
0.0025 
25 per 10,000 
City B 
35 
7,000 
0.0050 
50 per 10,000 