1.1 - Topic 1 Statistical Sampling Flashcards
Population:
all the individuals/objects you are interested in for a particular investigation
Census:
measures or observes every member of a population
Sample:
- a selection of observations taken from a subset of the population which is used to find out information about the population as a whole
- then assume the results for this sample are representative of the whole population
Advantages of census:
results should be completely accurate
Disadvantages of census:
- time consuming and expensive
- cannot be used when testing as process destroys the item
- hard to process large quantity of data
Advantages of a sample:
- less time-consuming and expensive than a census
- fewer people have to respond
- less data to process than in a census
Disadvantages of a sample:
- data may not be as accurate
- sample may not be large enough to give information about small sub-groups of the population
How does sample size affect the validity of conclusions drawn?
- size of the sample depends on the required accuracy and available resources
- the larger the sample, the more accurate it is -> but will need greater resources
- if population is varied, you would need larger sample than the population were uniform
- different samples can lead to different conclusions due to natural variation within a population
Sampling units:
individual units of a population
Sampling frame:
often sampling units of a population are individually named or numbered to form a list = sampling frame
Sampling fraction:
the proportion of the available items that are actually samples is called the sampling fraction
What is a 100% sample called?
a census
Sampling error:
- an estimate of the parameter (e.g. mean) derived from a sample usually differs from its true value
- the difference is called the sampling error
How would you reduce the sampling error?
would want sample to be as representative of the parent population as possible
When is a sample a representative sample?
- sample is a representative sample if it is typical of the whole population
- this means that dif. types of people should be represented in the sample that is chosen
- if sample includes certain group of people within population then sample = biased
Types of sampling:
Random sampling:
- simple random sampling
- systematic sampling
- stratified sampling
Non-random sampling:
- opportunity sampling
- quota sampling
Random sampling:
- every member of population has equal chance of being selected
- sample should therefore be representative of the population
- helps to remove bias from sample
Simple random sampling:
- a simple random sample of size n is one where every possible sample of size n has equal chance of being selected
- this can be achieved by ensuring very member of a finite population has equal chance of being selected as long as sampling is without replacement and selections are independent of each other
What do you need to carry out simple random sampling?
- need sampling frame - list of people/things
- each item is allocated a unique number and selection of these numbers is chosen at random
Methods of choosing numbers from sample frame in simple random sampling:
- random number generator - using calculator, computer or random number table
- lottery sampling - e.g. writing members of the sampling frame on tickets and drawing them out of a bag
Advantages of simple random sampling:
- free of bias
- quick, easy and cheap to implement for small populations and small samples
- each sampling unit has a known and equal chance of selection
Disadvantages of simple random sampling:
- not suitable when the population size/sample size is large
- sampling frame is needed
Stratified sampling:
- population is divided into mutually exclusive strata - e.g. divide pop into sub-groups like low income, middle income, high income
- sub-groups not expected to be representative of whole population
- random sample is taken from each
- proportion of each strata samples should be the same
number sampled in a stratum = (number in stratum)/(number in population) x overall sample size
Proportional stratified sampling:
if we randomly sample from each group in proportion to the size of the group then it is called proportional stratified sampling
What does stratified sampling ensure?
ensures that all strata are sampled with some kind of weighting used
Advantages of stratified sampling:
- sample accurately reflects the population structure
- guarantees proportional representation of groups within a population
Disadvantages of stratified sampling:
- population must be clearly classified into distinct strata
- selection for sample within each stratum suffers same disadvantages as simple random sampling
- need to know the structure of the population before you can take a stratified sample
- classification into mutually exclusive strata may be difficult to implement
Systematic sampling:
the required elements are chosen at regular intervals from an ordered lists
How do you carry out systematic sampling?
- From a list, choose a random starting item (can use random number generator or lottery sampling)
- Determine the interval by dividing population by the required sample e.g. every 5th item
Advantages of systematic sampling:
- simple and quick to use
- suitable for large samples and large populations
Disadvantages of systematic sampling:
- sampling frame is needed
- can introduce bias if sampling frame is not random
Quota sampling:
an interviewer or researcher selects a sample that reflects the characteristics of the whole population
How do you carry out quota sampling?
- population is divided into groups according to a given characteristic
- size of each group determines the proportion of the population that should have that characteristic
- similar to stratified sampling but specific number of people from each particular strata is sampled
- method often used for market research and used by interviewers
- as interviewer, you would meet people, assess their group and then, after interview, allocate them into the appropriate quota
- continues until all quotas have been filled -> if person refuses to be interviewed or quota into which this fit is full then simple ignore and move onto the n
ext person - actual selection of sample members is up to interviewer, whereas stratified samples are done at random
Advantages of quota sampling:
- allows small samples to still be representative of the population
- no sampling frame required
- quick, easy and inexpensive
- allows for each comparison between different groups within a population
Disadvantages of quota sampling:
- non-random sampling can introduce bias
- population must be divided into groups which can be costly or inaccurate
- increasing scope of study increases number of groups, which adds times and expense
- non-responses are not recorded as such
Opportunity sampling:
- one of ways of carrying out quota sampling
- consists of taking the sample from people who are available at the time the study is carried out and who fit the criteria you are looking
- aka convenience sampling
- e.g. could be first 20 people you meet outside of supermarket on Monday morning carrying shopping bags
Advantages of opportunity sampling:
- easy to carry out
- inexpensive
Disadvantages of opportunity sampling:
- unlikely to provide representative sample
- highly dependent on the individual researcher - may introduce bias
