ACCA Applied Knowledge · Management Accounting

Sampling methods: formula sheet

Full chapter guide

Key formulas

Sampling fraction: Sampling fraction = sample size ÷ population size; Shows what share of the population is in the sample. Useful when a question asks you to compare sizes.
Sampling error: Sampling error = sample statistic − true population value; Usually unknown in practice. It arises from chance, and tends to fall as sample size rises.
Frame check rule: Frame should be complete, accurate, up to date, no duplicates, and match the population; If any of these fail, bias is likely.
Census vs sample rule: Use a census when the population is small or every item must be checked; use a sample when cost, time or destructive testing matter; A rule of thumb, not a fixed law.
Sampling interval (systematic): k = population size ÷ sample size; Round down to a whole number if needed. Choose a random start between 1 and k, then add k each time.
Proportionate stratified sample: Stratum sample = (stratum size ÷ population size) × total sample size; Round to whole items and check that the strata samples add up to the total sample size.
Simple random selection rule: Chance of selecting each item = sample size ÷ population size; Applies when all items have an equal chance. Ignore repeated numbers if sampling without replacement.
Random vs non-random: Random: every item has a known chance of selection. Non-random: selection by judgement or convenience; Only random methods let you measure sampling error with statistics.
Quota sampling: Quota for a group = group share of population × total sample size; Example: 40% of the population and a sample of 200 gives a quota of 80.
Cluster sampling: Select clusters, then study items within the selected clusters; Saves cost when the population is spread out; the clusters should be typical.
Convenience sampling: Select the items easiest to reach; Cheapest and quickest, highest risk of bias.
Systematic sampling interval: Interval = population size ÷ sample size; Choose a random start within the first interval, then take every nth item. Risky if the list has a repeating pattern that matches the interval.
Stratified sample size per group: Group sample = (group size ÷ population size) × total sample; This is proportionate stratification. It keeps each group's share the same as in the population.
Random versus non-random rule: Random = known chance, measurable error, needs frame. Non-random = cheaper, faster, bias likely.; Use this as your first filter in any scenario question.

Quick revision

The population is the whole group you want information about.
The sampling frame is the list of items from which the sample is drawn.
Sampling saves time and cost and is needed when testing destroys the item.
Random sampling gives every item a known chance of selection.
Simple random sampling needs a full sampling frame, such as a numbered list.
Systematic sampling picks every nth item after a random start.
Stratified sampling splits the population into groups and samples each group.
Cluster sampling selects whole groups, which cuts cost but can be less representative.
Quota sampling fills set numbers per category, but selection is not random.
Judgemental sampling relies on a person's view, so it can be biased.
Convenience sampling is quick and cheap but is the most likely to be unrepresentative.
Non-random methods do not let you measure sampling error reliably.

Common mistakes

Treating the population and the sampling frame as the same thing. Fix: The population is who you want to know about. The frame is the actual list you can pick from. Check how well they match.
Saying a bigger sample removes bias. Fix: A bigger sample tends to reduce sampling error only. If the frame or method is flawed, bias stays.
Treating stratified and cluster sampling as the same. Fix: Stratified samples from every group. Cluster samples only from some groups chosen at random.
Using a fixed start such as item 1 in systematic sampling. Fix: Choose the start at random from 1 to k, otherwise the sample is not truly random.
Confusing quota sampling with stratified random sampling. Fix: In stratified sampling items are picked at random within each group. In quota sampling the interviewer picks freely until the quota is full, so it is non-random.
Saying cluster sampling studies a few items from every group. Fix: Cluster sampling selects some groups and studies items within those groups only. Stratified sampling uses every group.
Treating quota and stratified sampling as the same thing. Fix: Stratified picks items within each group at random. Quota lets the interviewer choose who fills the quota. So quota is non-random and may be biased.
Saying random sampling is always the best choice. Fix: If there is no sampling frame, or time and money are tight, a non-random method may be the sensible answer.

Exam tips

Read the scenario for clues: destructive testing, tight deadlines and large populations all point to sampling.
Keep the definitions separate: population is the target group, frame is the list, sample is the part selected.
If an option says a larger sample removes bias, treat it with suspicion.
In multiple response questions, select exactly the number asked and check each option against the definitions.
For number entry, compute sample size ÷ population size and convert to a percentage only if asked.
Learn one clue phrase for each method, so you can match a scenario to it in seconds.
In number entry questions on sampling, calculate carefully and check that the total equals the sample size.
When asked for an advantage or a weakness, tie it to a specific feature such as frame needed, pattern risk, cost or group representation.