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Year 8AC9M8ST02

Random and Non-Random Sampling

Analyse and report on the distribution of data from primary and secondary sources using random and non-random sampling techniques to select and study samples. Compare variations in distributions and proportions obtained from random samples of the same size drawn from a population and recognise the effect of sample size on this variation.

A sample stands in for a population. Whether it can be trusted depends entirely on how it was chosen, and on how big it is.

Builds onYr 8 · How Data Is Collected

Method

Random means everyone has an equal chance
This is what makes a sample representative.
Convenience sampling is not random
Asking your friends is fast and biased.
Self-selected samples are the worst
Only people who care strongly respond.
Bigger samples vary less
Two samples of 10 can look wildly different. Two of 1000 rarely do.
Sample size does not fix bias
A biased method stays biased at any size.

Worked example

e.g. You survey 20 students at the school gym about weekly exercise. What is wrong?\text{You survey 20 students at the school gym about weekly exercise. What is wrong?}
  1. Identify the population you want to describe.all students at the school\text{all students at the school}
  2. Identify who could actually be selected.only students who go to the gym\text{only students who go to the gym}
  3. Name the problem.selection bias\text{selection bias}
  4. Explain the direction of the error.it will overstate exercise levels\text{it will overstate exercise levels}
  5. Say what a fair method would look like.draw names at random from the whole roll\text{draw names at random from the whole roll}
  6. Note that 200 gym-goers would not fix it.size does not cure bias\text{size does not cure bias}

Practice

Say who could not be chosen. That usually names the bias.

1
An online poll about internet use. What is wrong?\text{An online poll about internet use. What is wrong?}
AnswerOnly people online can answer.\text{Only people online can answer.}
2
Names drawn from a hat containing every student. Random?\text{Names drawn from a hat containing every student. Random?}
AnswerYes.\text{Yes.}
3
Two samples of 10 differ a lot. Is that surprising?\text{Two samples of 10 differ a lot. Is that surprising?}
AnswerNo. Small samples vary greatly.\text{No. Small samples vary greatly.}
4
Does raising a biased sample from 50 to 500 help?\text{Does raising a biased sample from 50 to 500 help?}
AnswerNo. The bias remains.\text{No. The bias remains.}
5
A radio station asks listeners to phone in. Problem?\text{A radio station asks listeners to phone in. Problem?}
AnswerSelf-selected — only strong opinions respond.\text{Self-selected — only strong opinions respond.}
6
What effect does a larger random sample have?\text{What effect does a larger random sample have?}
AnswerLess variation between samples.\text{Less variation between samples.}
Next step
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