Vocabulary

Parameter -- an attribute that refers to the ENTIRE population

Statistic -- a value that refers to a subset or a sample of a population

Proportion -- a percentage; used for non-numerical data (e.g. polls that ask for a preference in something, or a yes-no question)

Mean -- the average

x̅ (“x-bar”) -- mean symbol for a statistic

μ (“mu") -- mean symbol for a parameter

p̂ (“p-hat”) -- proportion symbol for a statistic

P - proportion symbol for a parameter

Random Number Generator (RNG) -- generates random numbers from a computer

Sample - take a small proportion of a population

Census - take everything from a population (usually ineffective and time-consuming)

Surveying Methods and Bias

Simple Random Sample (SRS) - Randomly picks N objects from a population; ONLY sample where all combinations of N objects have an equal chance of being selected

Stratified Random Sample - Divide the population into homogeneous subgroups (meaning that everything in a subgroup has same characteristics) and take a SRS from each subgroup

Cluster Sampling - The population is ALREADY divided up into clusters (e.g. houses on the same block, classes, etc), take a SRS of all the clusters; from the chosen clusters, take CENSUS of the cluster (so survey everything inside of that cluster)

Systematic Sampling - Every Nth object is selected (e.g. every 10th person in a grocery line is surveyed)

Convenience Sample - typically not a good sampling strategy; exposed to bias; means that survey objects that are readily available

Nonresponse bias - some people refuse to participate in the survey

Response bias -- Something in a survey (e.g. wording) is designed to lead the subjects to an answer

Voluntary Response Bias -- People with typically strong opinions will respond to a survey (such as radio shows where people will call in--usually people who don't care won't respond

Key Tips

How to Answer Survey Design Questions

First, assign all the potential subjects from the population a number between 1 to N (where N represents the population size) with no repeating numbers. We want to select only x units from the population. Using a RNG, generate x numbers within the range of 1 to N (no repeating numbers allowed). The units whose numbers were generated get to be selected to participate in the survey.

Other Important Things

Stratified Random Sample is the only sampling method that is guaranteed to get a sample that is representative of a population.

Why? Let's say that the National Basketball Association (NBA) wants to get a survey of players' approval of a new rule. We'll say that this rule somehow benefits teams in large cities. If the NBA conducted a simple random sample of all the players, there is a chance that all the players would be from large cities--over-exaggerating the number of players who support the new rule. The NBA recognizes this and decided to do a stratified sample. The NBA would split the players into two strata (stratum (strata is plural) is another word for a homogeneous group), one stratum for large city players and another stratum for small city players. It would then take an equal percentage from both strata (let's say 10%). Now the sample would be much more representative as no subgroup is being oversampled or underrepresented.

Cluster sampling uses a census; a stratified random sample does not take a census.