MDM4U - Collecting Samples

Chapter 5.2,5.3

Why Sampling?

sampling is done because a census is too expensive or time consuming

the challenge is being confident that the sample represents the population accurately

convenience sampling occurs when you simply take data from the most convenient place (for example collecting data by walking around the hallways at school)

convenience sampling is not representative

Random Sampling

representative samples involve random sampling random events are events that are considered to

occur by chance random numbers are described as numbers that

occur without pattern random numbers can be generated using a

calculator, computer or random number table random choice is used as a method of selecting

members of a population without introducing bias

1) Simple Random Sampling

this sample requires that all selections be equally likely and that all combinations of selections be equally likely

the sample is likely to be representative of the population

but if it isn’t, this is due to chance example: put entire population’s names in a

hat and draw them

2) Systematic Random Sampling you decide to sample a fixed percent of the

population using some random starting point and you select every nth individual

n in this case is determined by calculating the sampling interval (population size ÷ sample size)

example: you decide to sample 10% of 800 people. n = 800 ÷ 80 = 10, so generate a random number between 1 and 10, start at this number and sample each 10th person

3) Stratified Random Sampling the population is divided into groups called

strata (which could be MSIPs or grades) a simple random sample is taken of each of

these with the size of the sample determined by the size of the strata

example: sample CPHS students by MSIP, with samples randomly drawn from each MSIP (the number drawn is relative to the size of the MSIP)

4) Cluster Random Sampling

the population is ordered in terms of groups (like MSIPs or schools)

groups are randomly chosen for sampling and then all members of the chosen groups are surveyed

example: student attitudes could be measured by randomly choosing schools from across Ontario, and then surveying all students in those

5) Multistage Random Sampling groups are randomly chosen from a

population, subgroups from these groups are randomly chosen and then individuals in these subgroups are then randomly chosen to be surveyed

example: to understand student attitudes a school might randomly choose one period, randomly choose MSIPs during that period then randomly choose students from within those MSIPs

6) Convenience Sampling

groups are chosen from the population that are easy to access, results in unreliable results

example: going to the park and asking for opinions on new pet by-laws

example: asking students in a grade 12 math class if they plan on going to university

7) Voluntary Sampling

groups are given the choice of participating or not, usually only receive responses from those that are heavily in favour or heavily against

example: a store sending a customer satisfaction email to it’s customers

Example: do students ND want a longer lunch? (sample 200 of 800 students) Simple Random Sampling

Create a numbered, alphabetic list of students, have a computer generate 200 names and interview those students

Systematic Random Sampling sampling interval n = 800 ÷ 200 = 4 generate a random number between 1 and 4 start with that number on the list and interview

each 4th person after that

Example: do students at ND want a longer lunch? Stratified Random Sampling

group students by grade and have a computer generate a random group of names from each grade to interview

the number of students interviewed from each grade is probably not equal, rather it is proportional to the size of the group

if there were 180 grade 10’s, 180 ÷ 800 = 0.225 800 × 0.225 = 45 so we would need to interview 45

grade 10s

Example: do students at ND want a shorter lunch? Cluster Random Sampling

randomly choose enough homeroom classes to sample 200 students

say there are 25 per homeroom, we would need 8 classes, since 8 x 25 = 200

interview every student in each of these rooms

Example: do TCDSB high school students want a shorter lunch? Multi Stage Random Sampling

Randomly select 4 high schools in the TCDSB Randomly choose 5 homeroom classes randomly choose 10 students from those classes interview every student in those classes 200 students total

Example: do ND high school students want a shorter lunch? Convenience

Ask students in this data class for their opinion

Voluntary Ask students in ND to fill out a SurveyMonkey

survey to get their opinion. No one is forced to participate

Sample Size

the size of the sample will have an effect on the reliability of the results

the larger the better factors:

variability in the population (the more variation, the larger the sample required to capture that variation)

degree of precision required for the survey the sampling method chosen

Techniques for Experimental Studies Experimental studies are different from

studies where a population is sampled as it exists

in experimental studies some treatment is applied to some part of the population

however, the effect of the treatment can only be known in comparison to some part of the population that has not received the treatment

Vocabulary treatment group

the part of the experimental group that receives the treatment

control group the part of the experimental group that does not

receive the treatment

Vocabulary

placebo a treatment that has no value given to the control

group to reduce bias in the experiment no one knows whether they are receiving the

treatment or not (why?) double-blind test

in this case, neither the subjects or the researchers doing the testing know who has received the treatment (why?)

Class Activity

How would we take a sample of the students in this class using the following methods:

a) 40% Simple Random Sampling b) 20% Systematic Random Sampling? c) 40% Stratified Random Sampling? d) 50% Cluster Random Sampling?

Homework

p. 219 #2, 5