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statistics > U1 - sampling methods > Flashcards

U1 - sampling methods Flashcards

1
Q

simple random sampling definition

A

where every person or item in the population has an equal chance of being in the sample, and each selection is independent of the others

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2
Q

how to choose a simple random sample

A
  • give a number to each population member, from a full list of the population
  • generate a list of random numbers and match them to the numbered members to select your sample
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3
Q

advantage of simple random sampling (1)

A
  • every member of the population has an equal chance of being selected, so it’s completely unbiased
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4
Q

disadvantage of simple random sampling (1)

A
  • it may be inconvenient if the population is spread over a large area (might be difficult to track down selected members) e.g. in a nationwide sample
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5
Q

simple random sampling practice question:

A zoo has 80 cotton-top tamarins. Describe how the random-number table given could be used to select a sample of five of them, for a study on tail lengths.
8330, 3992, 1840, 0330, 1290, 3237, 9165, 4815, 0766

A

1) draw up a list of the 80 cotton-top tamarins, and give each tamarin a unique 2-digit number between 01 and 80
2) use the random-number table to choose five numbers. five random numbers can be chosen by reading off every two digits that give a number between 01 and 80.
e.g. the first five numbers are:
83 (cant use, its too big), 30, 39, 92 (cant use, its too big), 18, 40, 03
3) select the cotton-top numbers with the numbers 30, 39, 18, 40, and 03

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6
Q

systematic sampling definition

A

a type of probability sampling which selects every nth member from the population you’re investigating

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7
Q

how to choose a systematic sample

A
  • number each member of the population from a full list
  • calculate a regular interval to use by dividing the population size by the sample size
  • generate a random starting point to choose the first member of your sample
  • keep adding the interval to the starting point to select your sample
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8
Q

advantages of systematic sampling (2)

A
  • it can be used for quality control on a production line - a machine can be set up to sample every nth item
  • it should give an unbiased sample
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9
Q

disadvantage of systematic sampling (1)

A
  • if the interval coincides with a pattern in the population, the sample could be biased
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10
Q

systematic sampling practice question:

50,000 fans attended a football match. Describe how systematic sampling could be used to select a sample of 100 people.

A

1) give each fan a 5-digit number between 00001 and 50000
2) 50,000 / 100 = 500, so select every 500th fan
3) use a calculator to randomly generate a starting point between 1 and 500
- – RanInt#(1,500)
4) keep adding 500 to the starting point to find the rest of the sample
- – e.g. if 239 is randomly generated, select the fans numbered: 00239, 00739, 01239, etc

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11
Q

stratified sampling definition

A

a type of probability sampling which involves dividing the entire population into homogeneous (similar) groups called strata. random samples are then selected from each stratum, in a number proportional to the population size

simpler explanation:: this uses the same proportion of each category in the sample as there is in the population

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12
Q

how to choose a stratified sample

A
  • divide the population into categories
  • calculate the number needed for each category in the sample using the formula:
    (size of category in population / total size of population) x total sample size
  • randomly select the sample for each category
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13
Q

advantages of stratified sampling (3)

A
  • if the categories are disjoint (i.e. there is no overlap), this should give a representative sample
  • its useful when results may vary depending on categories
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14
Q

disadvantage of stratified sampling (1)

A
  • the extra detail needed can make it expensive
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15
Q

stratified sampling practice question:

A teacher takes a sample of 20 pupils from her school, stratified by year group. The table below shows the number of pupils in each year group. Calculate how many pupils from each your group should be in her sample.
Year 7 : 120
Year 8 : 80
Year 9 : 95
Year 10 : 63
Year 11 : 42
A

1) find the number needed for each category, rounding to the nearest whole number
2) calculate the total population
— 120 + 80 + 95 + 63 + 42 = 400
3) calculate the number needed for each category by using the formula
— divide the size of the category in the population (i.e. the number of pupils in the year group) by the total size of the population (400) and then multiply by the total sample size (20)
4) year 7 : 120/400 x 20 = 6
year 8 : 80/400 x 20 = 4
year 9 : 95/400 x 20 = 4.75 (round to 5)
year 10 : 63/400 x 20 = 3.15 (round to 3)
year 11 : 42/400 x 20 = 2.1 (round to 2)
5) check that 6+4+5+3+2 = 20

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16
Q

quota sampling definition

A

a type of non-probability sampling (where elements from the population are chosen on a non-random basis) and all members of the population do not have an equal chance of being selected to be a part of the sample group.

extra info:: often used in market research. the interviewer will be given a quota of people in each category to interview (e.g. 20 women and 20 women). they then choose people to interview until the quotas are fulfilled

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17
Q

how to choose a quota sample

A
  • divide the population into categories
  • give each category a quote (number of members to sample)
  • collect data until the quotas are met in all categories (without using random sampling)
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18
Q

advantages of quota sampling (2)

A
  • it is easy for the interviewer as they don’t need access to the whole population (or a list of every member)
  • the interviewer continues to sample until all the quotas are met, so non-response is less of a problem
19
Q

disadvantage of quota sampling (1)

A
  • it can be biased by the interviewer - selection isn’t random, so they might exclude some of the population intentionally
20
Q

quota sampling practice question:

A video-game company wants to gather opinions on a new game. The interviewer is asked to interview 75 people aged under 30, and 25 people aged 30+. Give one advantage and one disadvantage of this quota sample.

A

advantage - the company doesn’t have a full list of everyone who has played the game, so random sampling isn’t possible
disadvantage - people with strong views on the game are more likely to respond to the interviewer, which may cause sampling bias

21
Q

opportunity sampling definition

A

opportunity sampling (aka. convenience sampling) is a type of non-probability sampling where the sample is chosen from a section of the population that is most convenient for the sampler

22
Q

how to choose an opportunity sample

A
  • choose members of the population that are the easiest to sample, e.g. ask the first people you walk past, or sample whatever products you can find
23
Q

advantage of opportunity sampling (1)

A
  • data can be gathered very quickly and easily
24
Q

disadvantages of opportunity sampling (2)

A
  • it isn’t random and can be very biased

- there’s no attempt to make the sample representative

25
Q

opportunity sampling practice question:

Mel thinks that most people watch her favourite television programme. She asks 20 friends whether they watch the television programme.

a) Name the sampling method Mel used.
b) Give two reasons why Mel’s sample may biased.

A

a) mel asked her friends because they’re easily available to sample, so she used opportunity (or convenience) sampling

b)
- mel’s friends could be of similar age / the same gender, which is not representative of the whole population
- because this is mel’s favourite tv programme, she might have encouraged her friends to watch it too

26
Q

cluster sampling definition

A

cluster sampling is a type of probability sampling where researches divide the the population into multiple groups (clusters) for research

extra info:: useful when the population can be divided into distinct groups. the clusters should be groups that you expect to give similar results to eachother

27
Q

how to choose a cluster sample

A
  • divide the population into clusters covering the whole population, where no member of the population belongs to multiple clusters
  • randomly select clusters to use in the sample, based on the required sample size
  • either use all the members of the selected clusters (a one-stage cluster sample), or randomly sample within each cluster to form the sample (a two-stage cluster sample)
28
Q

advantages of cluster sampling (2)

A
  • it can be cheaper in certain situations
  • it can be quicker in certain situations
  • you can incorporate other sampling methods, making it quite adaptable
29
Q

disadvantages of cluster sampling (2)

A
  • because you can only sample certain clusters, the results could be less representative
  • its not always possible to separate a population into clusters in a natural way
30
Q

cluster sampling practice question::

A researcher wants to conduct a taste test of a new energy drink of university students in the UK. (All uni students are included, and you can assume that no student belongs to multiple universities. You would also expect different universities to give similar results).

a) Explain why a cluster sample might be suitable in this situation.
b) Explain whether a one-stage or a two-stage cluster sample would be more appropriate.

A

a) Universities in the UK form clusters that are disjoint and cover the whole population, and that would be expected to give similar results to eachother. Using a cluster sample would also be convenient in this situation, as the researcher would only need to visit a few universities, rather than every one.
b) Conducting a taste test on every student at a university would be expensive and difficult to organise. It would be better to take a sample of the students and conduct the test on them, so a two-stage cluster sample would be more appropriate.

31
Q

self-selection sampling definition

A

a type of non-probability sampling in which people choose to be part of the sample - e.g. they choose to complete a questionnaire or volunteer to take part in a study

32
Q

how to create a self-selection sample

A
  • advertise or appeal to the whole population for participation in the sample (possibly offering payment)
  • either use everyone who responds as the sample, or take a sample of them to best represent the population
33
Q

advantages of self-selection sampling (3)

A
  • requires little time or effort in finding sample members (because they contact you)
  • people who have volunteered are less likely not to respond
  • it could be the only way to get people to take part in a study, or to find members of a population
34
Q

disadvantage of self-selection sampling (1)

A
  • there can easily be trends within the respondents, such as people having strong opinions, which would lead to bias
35
Q

self-selection sampling practice question:

A website puts an advert on their home page, asking visitors to complete a short survey about the site for a payment of £20. Give three ways that this sampling method could cause bias in their results.

A

1) people who are willing to complete the survey might have stronger opinions than other visitors, which would introduce bias into the results
2) certain people might not see the advert if the website does not display properly for them, or if they block adverts through their browser, which would exclude parts of the population from the sample, making it less representative
3) since the website is offering money for responses, people might be more likely to try to fill out the survey multiple times or not take the questions seriously, which would make the responses less representative of the views of all of their visitors

36
Q

probability sampling technique definition

A

probability sampling refers to the selection of a sample from a population where this selection is based on randomisation (random selection or chance)

37
Q

advantages of the probability sampling technique (6)

A
  • not exposed to systematic error and sampling bias (theres an equal chance for each member of the population to get selected)
  • cost-effective
  • simple and straightforward to do
  • useful in obtaining an accurate representation of the population
  • higher reliability of results
  • effective in collecting data from diverse populations
38
Q

disadvantages of the probability sampling technique (4)

A
  • finding the correct audience is difficult
  • more time-consuming
  • usually more costly than non-probability sampling
  • more complex than non-probability sampling
39
Q

non-probability sampling technique definition

A

non-probability sampling refers to the selection of a sample from a population using a subjective (non-random) method,

40
Q

advantages of the non-probability sampling technique (3)

A
  • quick
  • easy (finding correct audience is simple)
  • inexpensive way of collecting data
41
Q

disadvantages of the non-probability sampling technique

A
  • no way to estimate the probability of any one element being included in the sample
  • extremely biased (not everyone has an equal chance of getting selected)
  • ## is not representative of the population
42
Q

examples of which sampling techniques are probability

A
  • simple random, stratified, systematic, cluster
43
Q

examples of which sampling techniques are non-probability

A
  • quota, opportunity (convenience), judgement (purposive)

statistics (13 decks)

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