Chapter 4 Sampling Methods

population

in a statistical study; the entire group of individuals we want information about

census

collection of data from every individual in the population

sample

a subset of the individuals in the population from which we actually collect data

sample survey

a study that collects data from a sample in order to learn about the population from which the sample was collected

bias

shown when a statistical study would consistently underestimate or overestimate the value you want to know

convenience sample

• choosing individuals from the population who are easy to reach

• often produces unrepresentative data

• almost guaranteed to show bias

convenience sample examples

• going to the library to learn how much people in your town like to read books

• sharing a link on facebook

• surveying only your friends

• easy for experimenter

voluntary response sample

• consists of people who have chosen to respond

• over-represents people with strong opinions, especially negative opinions

• almost guaranteed to show bias

voluntary response sample examples

• american idol votes

• sharing a link on social media

• online ratings or reviews of products/services

simple random sample

• SRS

• gathering a representative sample from a population where every group of size n has the same chance of being chosen

• each selection is independent

how to choose an SRS

put all names on equal size slips of paper, place in a hat, and draw out a sample

steps for choosing SRS

1. label each individual with a distinct numerical value with a the same number of digits

2. randomize, either using technology or a list of random digit (RNG = random # generator)

3. select the sample that corresponds to the selected integers

sampling with replacement

an individual can be selected more than once

sampling without replacement

an individual from the population can only be selected once

systematic sample

the elements of the population are put into a list, and then every nth element in the list is chosen

systematic sample examples

in a school of 2000, all students would be put into a list and every 100th student would be chosen

stratified sample

• the population is divided into different subgroups, or strata, then are randomly selected proportionally

• layers

• chose from every group

stratified sample examples

students are divided up by grade subgroups (9th, 10th, 11th, 12th). A proportionate number of students from each grade are randomly chosen

cluster sample

• divide population area into sections of those that are close to each other

• randomly choose some of those clusters and include all members from those selected clusters

• clusters may not be representative of population

cluster sample examples

• acity is divided into subpopulations by zip code. Two zip codes are randomly chosen

• 5 classrooms on the math hallway are chosen for an FHS survey; everyone in those classes is included in the sample

multi-stage sample

combines two or more sampling methods

undercoverage bias

occurs when some members of the population are less likely to be chosen or cannot be chosen in the sample

voluntary response bias

• occurs when using a voluntary response sample

• not representative of population

non-response bias

• occurs when an individual chosen for the sample cannot be contacted or refuses to cooperate

• occurs after sample is taken

response bias

• occurs when there is a systematic pattern of inaccurate answers to a survey question

• can be caused by the behavior of the respondent or the behavior of the interview

• untruthful answers, poorly worded questions