Sampling methods

Question 1

What is cluster sampling?

Answer 1

Dividing the population into a large number of relatively small groups or clusters (such as all farms round villages). A simple random sample is taken to choose the clusters and every unit within a chosen cluster is surveyed. This works well if you want to reduce the cost of transport for interviewers as they do not need to go to as many places.

Cluster sampling often uses groups that already exist such as classes or geographic entities.

Question 2

What is convenience sampling?

Answer 2

This does not involve random sampling as the field staff collect data from any willing and available respondent. It is easier to carry out as you don’t need a sampling frame but you have no idea how representative your units are in relation to the population.

Question 3

What is haphazard sampling?

Answer 3

This is the same as convenience sampling. A field interviewer collects data from anyone willing to give it.

Question 4

What is equal allocation?

Answer 4

This is when you divide the population into different strata then select the same number of units from each strata to make up your sample.

Divide the desired sample size by the number of strata to work out number to be sampled in each strata.

Question 5

How do you calculate equal allocation?

Answer 5

Number in the sample divided by the number of strata.

Question 6

What is multi-stage sampling?

Answer 6

A more complex cluster sampling method. It involves selecting a sample from within each chosen cluster, rather than including the whole of the selected cluster in the sample.

Question 7

What is multi-stage stratified sampling?

Answer 7

This involves adding strata at one of the stages of a multi-stage. This is common in social surveys looking to benefit from low costs of a multi-stage design and improved estimates from stratified sampling methods.

Question 8

What is optimal (Neyman) allocation under stratified sampling?

Answer 8

This involves selecting a relatively large sample from strata that have high variability and smaller samples from strata that have less variability. This should improve the precision of survey estimates and minimise the sampling error of the survey estimates as the sample should closely resemble the population.

Question 9

What is optimal allocation with costs?

Answer 9

Using survey costs with optimal allocation gives optimum precision of a particular estimate if the sampling fractions in the different strata are made proportional to the ratio of the standard deviation of responses in the stratum and the square root of the cost per unit sampled in the stratum.

This can be used when you know the cost per unit to sample from each strata, the standard deviation and stratum population size. If you have a set budget you can then work out how many units you can afford to sample from each strata.

Question 10

What is multi-stage cluster sampling?

Answer 10

You assign the population into geographic clusters, such as counties. These are known as Primary Sampling Units. Then randomly select a sample of those clusters, then from those chosen clusters, randomly select smaller clusters, such as villages from the counties and so on. You could go all the way down to households then individuals.

Only units from the selected clusters are studied. (This is different to stratified sampling when units from each strata are studied.)

Question 11

In stratified sampling, what is proportional allocation?

Answer 11

The number of units selected for the sample from each stratum is proportional to the size of the stratum.

Question 12

What does it mean if you allocate the sample using a uniform sampling fraction?

Answer 12

This is another term for proportional allocation in stratified random sampling.

Question 13

What are primary sampling units?

Answer 13

This is the name for non-overlapping groups that the population is first divided into when using multi-stage cluster sampling.

Question 14

What is quota sampling?

Answer 14

This is a type of non-probability or non-random sampling where an interviewer collects data from a pre-specified quota of respondents. For example, they may need to speak to 25 men and 25 women.

Question 15

Random number tables?

Answer 15

Lists of digits 0-9 in random order, arranged in rows and columns.

Random numbers can be generated using Excel or a calculator.

Question 16

What is a sample?

Answer 16

This is a subset of the population of interest. The hope is that the characteristics of the sample are present in the same degree and are distributed in the same way as the population.

Question 17

What is a sampling fraction?

Answer 17

This is the proportion of the total population that is included in the sample.

n/N

The sampling fraction can be calculated for each sample selected under probability sampling.

Every unit has this chance of being selected.

Question 18

What are common problems with sampling frames?

Answer 18

• They are out of date
• It doesn’t include the whole target population
• There is over coverage
• There is under coverage
• There is duplication
• The contact details are incomplete

Question 19

What is the sampling interval?

Answer 19

The interval used in systematic sampling. This is when you choose the random start point and survey every xth item.

Question 20

What is simple random sampling?

Answer 20

This is a type of probability or random sampling when all units in the population are assigned a unique number, the number of units required for the sample are then selected at random.

Question 21

What are stratum?

Answer 21

Stratum are groups of units in the population and are designed using a characteristic that is related to the subject of the survey. For example, dividing the students of a university by the subject they study to find out about free time and contact hours.

Question 22

What is stratified random sampling?

Answer 22

This is a type of probability sampling that involves dividing the population into homogeneous groups and taking a random sample from each group. The samples are then collated to form the total sample of the population.

Question 23

What is systematic random sampling?

Answer 23

A type of probability sampling which involves creating a list of all units in the population of interest, then after the sampling interval K is calculated and a random start point r is chosen, every kth unit in the population is selected to become part of the sample.

Question 24

What is the uniformed sampling fraction?

Answer 24

This is the sampling fraction used in proportional allocation?

Question 25

What is variable error?

Answer 25

This is a type of non-sampling error - these are errors where the responses are just as likely to be too small as they are to be too large. There should be as many variable errors in one direction as the other, hence the errors should balance out. As a result, survey estimates should not be shifted up or down and should be correct. For example, when some businesses round up profits and some round down so roughly evening out.

Question 26

What is the formula for working out proportional allocation under stratified sampling?

Answer 26

There are 2 approaches which get the same result.

Ni / N x n

or

n / N x ni

Where Ni is the number of units in the strata, N is total population size and n is total required sample size.

Question 27

What is a sampling fraction?

Answer 27

The proportion of the total population that is included in the sample. This is worked out as n/ N

It is also the probability that a particular unit is chosen from the population.

Question 28

How do you work out the sample size for each strata under optimal allocation?

Answer 28

• Ni x Si for each strata (number in strata by SD)
• Calculate sum of Ni x Si
• Ni x Si / sum of Ni x Si
• x this by total required sample size
• round to nearest whole number

Question 29

Why is optimal allocation in stratified sampling ‘optimal’?

Answer 29

This will help to reduce sampling error as your sample should accurately represent the total population, more so than in random sampling.

Question 30

What are the problems in non-probability sampling?

Answer 30

• People who volunteer or are the first you manage to get hold of may not represent the total population.
• Researchers might pick people for ease or to promote an agenda.
• There will be no statistical basis for evaluating how well the sample represents the population, you won’t be able to calculate confidence intervals.

Question 31

Is the sampling technique probability or non-probability sampling?

Aim: to find out if having a tablet improves student performance of English secondary school students.

Sampling technique: teacher chooses 4 schools they have access to then using simple random sampling to select 50 students from each school.

Answer 31

This is non-probability sampling.

Although there is random sampling from within the chosen schools, the initial method of the teacher choosing 4 schools for convenience means that not every member of the population had a chance of selection.

Question 32

Why is probability sampling so powerful?

Answer 32

The idea is that characteristics of a randomly selected sample would be similar distributed as in the total population. We can therefore use estimates from the probability sample to carry out statistical procedures such as hypothesis tests, confidence intervals etc. We can also calculate the standard error if we take a probability sample. This estimates the precision of the sample estimate.

Question 33

When might systematic sampling be inappropriate?

Answer 33

If there is some pattern to the sampling frame. For example, if you were sampling from a list of club members and they were listed by couple, if you were going to pick every other item, you might end up with all male and no females or vice-versa.

Question 34

What are national samples typically stratified by?

Answer 34

By region and by rural and urban.

Question 35

What is a benefit of cluster sampling?

Answer 35

You will not need a fully detailed sampling frame as you first randomly sample regions, then you would need to get more details of the units on those selected regions. (This can save money but is not as accurate as if the sample were drawn from across the whole population.)

Question 36

How important is sample size?

Answer 36

The size of the sample must be considered on a case by case basis, depending on the goals of each study. Most sample sizes do not focus on estimates for the total population but on the minimum sample sizes required so that the smallest sub-groups of interest are accounted for within the study. The reduction of non-sampling error, an effective sampling method and a representative sample of the distribution of characteristics is more important than sheer size.

Question 37

If a researcher uses non-probability sampling, what should they include when the publish their findings?

Answer 37

• How the sample was drawn
• Fact that it is likely to be bias in favour of those who were willing and available to respond
• Normal assumptions for calculating sampling error do not apply

Question 38

What is uniform sampling fraction?

Answer 38

The number of units selected from each stratum is proportional to the total number of units in that stratum - this is stratified proportional allocation sampling.

Question 39

What is the difference between stratified sampling and cluster sampling?

Answer 39

On the surface these seem similar as they are about assigning units to groups. However, in stratified sampling you sample units from every strata whereas in cluster sampling you randomly select clusters and sample those. The drawback is that those clusters may not be representative of the population.