Misunderstanding samples and sampling
Generalising from a sample that is too small may lead to conclusions about a larger population that lack credibility. There is, however, no need to sample every element in a population to make credible, reliable conclusions. Recognising the variation between samples and establishing when samples are representative of a population ensures sampling methods are efficient and effective.
Students may have strong beliefs about what makes a fair sample. They often have difficulty understanding the characteristics of an unbiased sample, the naturally occurring variation within samples and the need for samples to be representative.
As a starting point, classroom discussions should focus on possible bias. This might relate to:
- survey questions
- sample size
- sampling methods.
Biased samples favour one way of thinking over another. Activities should challenge students’ notions of the nature of sampling and the purpose of a sample in relation to the questions asked. They should also consider the context of the data in order to appreciate how sampling can influence the claims made.
Bias in survey questions
The way survey questions are posed and the choices given for responses to survey questions have the potential to introduce bias into survey results.
Good survey questions
Teachers can help students to write good survey questions.
Writing survey questions
Students use an online tool to construct a survey and collect data for an investigation.
Bias from sample size
Bias is introduced when the sample size is not representative of the population from which it is taken.
How big a sample?
The larger the sample size the more likely it is that the sample results will reflect the results from the population.
Increasing sample size
This activity compares the distributions of smaller samples with larger samples to determine when a sample is representative of the larger population.
Bias in sampling methods
Samples need to be representative of the larger population. It is important to identify when bias may be introduced through various sampling methods.
Selecting sampling methods
Students need experience in using various sampling strategies to develop an appreciation of when a sample may be biased.
Sampling methods activity
This is a three-stage activity that includes establishing student prior learning, developing fluency, and determining changes in student thinking in relation to sampling methods.