# Census and bias

### Census and bias

#### Lessons

Census:
A census is the procedure of conducting experiments to figure out information about members of a given population.
Doesn’t necessarily have to be human!

Explanatory Variables and Response Variables:
A response variable is the outcome of the experiment. This is typically the sort of outcome the experiment is concerned with finding. Think of it as the “response” of the experiment.

The explanatory variable is the variable that affects the response variable. Think of it as the “explanation” to the response variable.

There may be many explanatory variables in an experiment; typically it is better to find the single most relevant explanatory variable.

2 errors in conducting a census:
Sampling error and bias

Bias:
Poorly implemented sampling techniques can lead a wide variety of Bias. A Bias is when the selection of a sample results in an unfair proportion of the sample having a tendency to favour certain outcomes.
i.e. Trying to decide what proportion of the population likes ice cream, but only asking kids

Sources of Bias:
There are many different ways in which a sample could result in bias, here are only a few of the most common sources of bias:

Response Bias:
In general people will not want to have unpopular opinions, so they may respond untruthfully when being face to face with an interviewer or if they were not anonymous for the survey. A good way to solve this issue is to ensure that all participants of a survey remain anonymous.
e.g. Doctors asking patients if they are following their orders (people will be tempted to lie to the doctor to maintain image or not incur the doctors wrath)

Selection Bias:
When selecting people for a survey make sure that your selection process doesn’t favour any of the population that has a specific preference for an outcome in your experiment. When collecting samples think about how you are gathering your data and make sure that it is fully randomized.
e.g. When polling the amount of families in an area it would be a selection bias to poll all the people entering a toy store (as more families will shop at a toy store).

Non-response Bias:
Sometimes individuals chosen for the sample in a census may be unwilling or unable to participate. A non-response bias is the bias that results when there are very low response rates and it becomes unclear what part of the population is participating in this survey.
e.g. If a mail survey was conducted asking people about what sorts of car they drive it is likely that few people would respond and it would be hard to know what proportion of the population this represents.

Voluntary Response Bias:
If individuals offer to participate in a survey they may have very strong feelings one way or the other about a specific matter.
e.g. A radio DJ asks his listeners to call in if they think Segway scooters are stupid and should be outlawed. This may encourage a small proportion of the population who hates Segway scooters to call in.

So basically make sure to choose your sample well using a good sampling technique and make sure there is no bias!
• Introduction
a)
What is a census? And what are some variables in a census?

b)
What is bias?

• 1.
Determining Response Variables and Explanatory Variables
Classify the response variables and the explanatory variables from the following experiments:
a)
A census is done on amount of money people make and how long they spent in school.

b)
A study is concerned with looking at what sports athletes do and how far they can throw a Frisbee.

c)
An experiment correlates the amount of sunlight and the amount of food produced by a crop.

• 2.
Classifying Bias
For each of the following experiments below determine the sort of bias may be present , and provide a solution to overcoming the bias:
a)
A university (UBC) wishes to figure out how many students like its new online homework submitting system (Connect). So UBC sends emails out to all the students currently enrolled asking them to submit a survey asking them how much they like Connect. (In all likelihood few people will respond).

b)
A study is done by the U.S. Census board trying to figure out the proportion of the population that plays PS4 games. So they send a representative out to a Best Buy to ask the customers of the store whether they play PS4 or not.

c)
Emily believes that everybody loves Adele, so on Facebook she tells her friends to comment on a post about how much they love Adele. Since all her response are positive she concludes that nearly 100% of the population must love Adele

d)
Dr. Anstee is a professor of mathematics at UBC. He loves mathematics and wants to know how many of his students share his love for math. So in his office hours he asks all of his student’s one at a time how much they truly love math.