Sampling Techniques (WJEC GCSE Maths & Numeracy (Double Award)): Revision Note

Sampling Techniques

What are populations and samples?

• The population refers to the whole set of things which you are interested in

  • e.g. if a vet wanted to know how long a typical French bulldog sleeps for in a day

    • then the population would be all the French bulldogs in the world

  • Be careful - the word 'population' can mean different things in different contexts

    • e.g. 'the population of the UK' is usually used to refer to everyone in the UK

    • But if you're studying UK dentists then the 'population' for your study would be restricted to all the dentists in the UK

• A sample refers to a subset of the population which is used to collect data from

  • e.g. out of all the French bulldogs in the world (the population)

    • a vet might take a sample of French bulldogs from different cities and record how long they sleep in a day

• There are several different types of sampling you need to know

What is random sampling?

• In random sampling every member of the population has an equal probability of being selected for the sample

• To select a simple random sample of members of the population

  • Uniquely number every member of the population

  • Then randomly select  different numbers using a random number generator (or other form of random selection)

What is systematic sampling?

• In systematic sampling a sample is formed by choosing members of a population at regular intervals using a list

  • e.g. to select 1/10 of the students in a school as a sample

    • Start with a list of all students

    • Select one student at random as a 'starting point'

    • Then also select every 10th student on the list after that starting point

    • (If necessary, wrap back around to the start of the list when you get to the end)

What is stratified sampling?

• In stratified sampling the population is divided into separate groups (called strata) and then a random sample is taken from each group

  • The proportion of a sample that belongs to a group is equal to the proportion of the population as a whole that belongs to that group

    • e.g. if 1/20 of the population belongs to a particular group

    • then 1/20 of the sample should come from that group

    • i.e.

  • A population could be split into groups by age ranges, gender, occupation, etc.

What are the advantages and disadvantages of different sampling techniques?

• In general

  • Sampling techniques can be improved by taking a larger sample

  • You want to minimise the bias within a sample

    • This occurs when the sample is not representative of the population

    • The best way to avoid bias (when possible) is to use a random method

  • Sometimes the 'best' method would cost too much or take too much time

    • So you need to choose the 'best method you can afford (or have the time for)'

  • A sample only gives information about the members in the sample

    • A different sample from the same population could lead to different conclusions about the population!

• Random sampling

  • This is the best sampling method for avoiding bias

    • Although it is possible that members of some groups in the population will not be represented in the sample

    • To avoid this stratified sampling can be used instead

  • It is most useful when you have a small population or want a small sample

    • e.g. children in a class

  • This cannot be used if it is not possible to number or list all the members of the population

    • e.g. the fish in a lake

• Stratified sampling

  • This should be used when the population can be split into obvious groups

  • Useful when there are very different groups of members within a population

  • The sample will be representative of the population structure

    • Members of every group are guaranteed to be included in the sample

  • The members selected from each group are chosen randomly

    • This helps to avoid bias

  • This cannot be used

    • if the population cannot be split into groups

    • or if the groups overlap

• Systematic sampling

  • This is useful when you want a sample from a large population

  • You need access to a list of the population

    • If the order of the list is random then the sample will also be random

  • This cannot be used if it is not possible to number or list all the members of the population

    • e.g. penguins in Antarctica

  • Be careful of periodic (i.e. regularly recurring) patterns in the list

    • e.g. a list of names where the names are grouped by 5-person teams with the team captain appearing first

    • If you selected every 5th name in the list you would end up with either all captains or no captains in your sample