Populations and samples

Question 1

RECAP: What is the definition of standard deviation?

Answer 1

How dispersed scores are within a data set i.e. how well the mean represents the data

Question 2

What is the Standard Error?

Answer 2

How well the sample mean represents the true population mean

Question 3

What is the 95% Confidence Interval?

Answer 3

Range of scores constructed such that the true population mean will fall within this range in 95% of samples
OR
Range within which 95% of sample mean falls within 1.96 SEs of the population mean

Question 4

What are parameters?

Answer 4

Population features - collection of ALL data of interest

Question 5

What are Statistics?

Answer 5

Data from a subset of the population, and should be generalisable to the population when done properly
i.e. statistics ESTIMATE parameters, and we can use probability to work out likelihood that our inferences are true

Question 6

What are the features of a Normal Distribution

Answer 6

MEAN = 0
SD = 1
i.e. the distribution is symmetrical around 0

Question 7

Why are z-scores calculated?

Answer 7

Our data sets collected from our samples will never have a mean of 0 and SD of 1, so we calculate z-scores to standardise values and thus make them directly comparable to the general population

Question 8

How are z-scores calculated?

Answer 8

z = (value - sample mean)/SD of sample

Question 9

A student scores 55 in a verbal test, and 60 in numerical reasoning.
Class scores are normally distributed - verbal and numerical means are both 50, while SDs are 5 and 12 respectively.
We want to know how the student performed relative to everyone else. Calculate the z-scores to answer this question

Answer 9

Verbal z=1.00
Numerical z=0.83

So z is bigger in the verbal test i.e. would be further right on the standardised distribution so she did better on this test relative to everyone else, than on the numerical test (1SD above average compared to <1SD above average)

Question 10

How can we use z-scores?

Answer 10

We can look up values in tables which illustrate probability for values between 0-z and z-infinity, i.e. larger and smaller portions of area under curve

Question 11

What is meant by “Sampling Error”?

Answer 11

Deviation of selected sample from true population data - we can multiply up from samples to estimate parameters but we are still only getting an incomplete picture.
LAW OF LARGE NUMBERS - using larger samples gets sample mean closer to true population mean

Question 12

How do we calculate Standard Error of the mean?

Answer 12

SE is the SD of the sample mean i.e. how close it is to the true mean.
We calculate many sample means with new samples, and by the law of large numbers the mean of all of these means should be equal to the true population mean - sample mean in samples above 30 are considered to have a normal distribution

Calculation is sample SD/square root of N (value gets closer to 0 as N increases)

Question 13

What is the magnitude of the Standard Error determined by?

Answer 13

Sample size and SD of population from which sample selected

Question 14

Define sampling bias

Answer 14

The weighting of a sample with an over-representation of one particular category of people

Question 15

What are 3 ways in which we can control for participant variables when drawing samples?

Answer 15

1) Random allocation
2) Pre-testing (however may still miss some variables, and is also very time-consuming)
3) Representative allocation - make sure groups equally representative on several relevant variables, deciding which ones are going to be most important to balance for in the given circumstances of the research question and aims

Question 16

What is EPSEM?

Answer 16

Equal probability selection method
A procedure for producing a sample into which every case in a target population has an equal probability of being selected

Question 17

What is meant by a “simple random sample”?

Answer 17

Every case in the target population has equal chance of selection and so does every possible COMBINATION of cases

Question 18

What are three possible selection methods for simple random sampling?

Answer 18

1) Computer selection (random endless number strings)
2) Random number tables
3) Manual selection (think of how numbered balls are selected in Bingo - as long as they are shuffled well enough the selection will be random)

Question 19

What is done for a “systematic random sample”?

Answer 19

Select every nth case from the population where n is any given number
To satisfy the EPSEM definition, before starting selection, every case needs to have an equal chance of being in the sample so we select a starting point at random e.g. if nth is going to be 10th, choose starting point anywhere between 1-10

Question 20

Distinguish between random sampling and random allocation

Answer 20

Random sampling involves selecting cases entirely at random from a population of cases and it is very difficult to fully achieve (always some degree of bias)
Random allocation is when you already have your sample and choose which condition each participant is going into for the study - this is much easier, can simply toss a coin!

Question 21

What is meant by “Stratified sampling”?

Answer 21

Strata are subsections of a population
e.g. say you wanted a representative sample of university students, the strata here would be students from different disciplines e.g. business, arts etc.
Relevant strata will depend on the exact research question
STRATA MUST BE EXHAUSTIVE i.e. x+y+z=100%
Randomly sample from within each strata

Question 22

What is meant by “cluster sampling”?

Answer 22

A more convenient and economical alternative to stratified sampling
For example, instead of taking a geography class and sampling at random from within that stratum, just choose a random class - this is the cluster and as long as all classes are roughly equal in size this is still an epsem method

Question 23

What are 4 examples of non-probability-based (non-epsem) sampling methods?

Answer 23

1) Quota sampling
2) Self-selecting samples
3) Opportunity/convenience sampling
4) Purposive sampling

Question 24

What is Quota sampling?

Answer 24

As with stratified sampling, this method consists of obtaining people from categories in proportion to their occurrence in the general population
However, selection from each category is left entirely up to the interviewer who is unlikely to use pure random methods
e.g. once quota for 18-21 year old males reached, stop asking within this category
May not always identify an exhaustive list of categories and often consists purely of those individuals who are easiest to contact

Question 25

What is meant by a self-selecting sample?

Answer 25

e.g. volunteers for an experiment, or individuals in social psychology experiments who happen to become involved in observational methods

Question 26

What is meant by an opportunity sample?

Answer 26

e.g. commonly students are a good convenience sample, as are samples available in natural experiments

Question 27

What is a haphazard sample?

Answer 27

A special kind of opportunity sample - e.g. you go to the library and just pick from whoever is present

Question 28

How is purposive sampling conducted?

Answer 28

Selection choice made on the basis of those who are most representative for the issues involved in the research or those who are likely to have expertise in the relevant matter

Question 29

What are three examples of purposive sampling methods?

Answer 29

1) Snowball sampling - Select several key people for interview and these people can then lead to other people who may also have the relevant experience and can be contacted and so on
2) Critical cases
3) Focus groups and panels - Researchers may bring together a panel of experts, those with relevant interests, or in the case of focus groups simply a representative sample of general population