1.1 - Topic 1 Statistical Sampling

Question 1

Population:

Answer 1

all the individuals/objects you are interested in for a particular investigation

Question 2

Census:

Answer 2

measures or observes every member of a population

Question 3

Sample:

Answer 3

• 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

Question 4

Advantages of census:

Answer 4

results should be completely accurate

Question 5

Disadvantages of census:

Answer 5

• time consuming and expensive
• cannot be used when testing as process destroys the item
• hard to process large quantity of data

Question 6

Advantages of a sample:

Answer 6

• less time-consuming and expensive than a census
• fewer people have to respond
• less data to process than in a census

Question 7

Disadvantages of a sample:

Answer 7

• data may not be as accurate
• sample may not be large enough to give information about small sub-groups of the population

Question 8

How does sample size affect the validity of conclusions drawn?

Answer 8

• 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

Question 9

Sampling units:

Answer 9

individual units of a population

Question 10

Sampling frame:

Answer 10

often sampling units of a population are individually named or numbered to form a list = sampling frame

Question 11

Sampling fraction:

Answer 11

the proportion of the available items that are actually samples is called the sampling fraction

Question 12

What is a 100% sample called?

Answer 12

a census

Question 13

Sampling error:

Answer 13

• 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

Question 14

How would you reduce the sampling error?

Answer 14

would want sample to be as representative of the parent population as possible

Question 15

When is a sample a representative sample?

Answer 15

• 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

Question 16

Types of sampling:

Answer 16

Random sampling:
- simple random sampling
- systematic sampling
- stratified sampling

Non-random sampling:
- opportunity sampling
- quota sampling

Question 17

Random sampling:

Answer 17

• every member of population has equal chance of being selected
• sample should therefore be representative of the population
• helps to remove bias from sample

Question 18

Simple random sampling:

Answer 18

• 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

Question 19

What do you need to carry out simple random sampling?

Answer 19

• need sampling frame - list of people/things
• each item is allocated a unique number and selection of these numbers is chosen at random

Question 20

Methods of choosing numbers from sample frame in simple random sampling:

Answer 20

• 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

Question 21

Advantages of simple random sampling:

Answer 21

• 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

Question 22

Disadvantages of simple random sampling:

Answer 22

• not suitable when the population size/sample size is large
• sampling frame is needed

Question 23

Stratified sampling:

Answer 23

• 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

Question 24

Proportional stratified sampling:

Answer 24

if we randomly sample from each group in proportion to the size of the group then it is called proportional stratified sampling

Question 25

What does stratified sampling ensure?

Answer 25

ensures that all strata are sampled with some kind of weighting used

Question 26

Advantages of stratified sampling:

Answer 26

- sample accurately reflects the population structure - guarantees proportional representation of groups within a population

Question 27

Disadvantages of stratified sampling:

Answer 27

- 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

Question 28

Systematic sampling:

Answer 28

the required elements are chosen at regular intervals from an ordered lists

Question 29

How do you carry out systematic sampling?

Answer 29

1. From a list, choose a random starting item (can use random number generator or lottery sampling) 2. Determine the interval by dividing population by the required sample e.g. every 5th item

Question 30

Advantages of systematic sampling:

Answer 30

- simple and quick to use - suitable for large samples and large populations

Question 31

Disadvantages of systematic sampling:

Answer 31

- sampling frame is needed - can introduce bias if sampling frame is not random

Question 32

Quota sampling:

Answer 32

an interviewer or researcher selects a sample that reflects the characteristics of the whole population

Question 33

How do you carry out quota sampling?

Answer 33

- 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

Question 34

Advantages of quota sampling:

Answer 34

- 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

Question 35

Disadvantages of quota sampling:

Answer 35

- 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

Question 36

Opportunity sampling:

Answer 36

- 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

Question 37

Advantages of opportunity sampling:

Answer 37

- easy to carry out - inexpensive

Question 38

Disadvantages of opportunity sampling:

Answer 38

- unlikely to provide representative sample - highly dependent on the individual researcher - may introduce bias