PSYC1040 Week 7

Question 1

Correlation (range and calculation)

Answer 1

• correlation is described with the correlation coefficient (R)
• r ranges from -1 to 1

Question 2

Factors affecting r (strength)

Answer 2

• outliers
• shape of the relationship (linear/non-straight, curved)
• restrictions of range of either variable
• the observable strength of our association is limited by the reliability of the variables.
• low reliability means lower observable strength
• therefore, the strength of an association between constructs may be under-estimated if one or both constructs are measured unreliably

Question 3

coefficient of determination

Answer 3

• when two variables are associated, they are said to ‘share variance’
• or, variance in one is said to explain or account for variance in the other
• the proportion of variance shared is given by r2, so to account for all criterion variance we would need four predictors, each correlated with the criterion at r

Question 4

Population

Answer 4

• studies investigate a narrow situation to inform generalisations about a population (broader range of situations)
• generalisations from a sample to a population are justifiable when the sample is representative
  Representativeness depends on:
• an unbiased sampling method - random sampling
• a large sample size

Question 5

Sampling error and variability

Answer 5

• in a large random sample, the distribution of a variable should, reassemble the population distribution
• a small sample’s distribution might be quite different from the population distribution
• given the population variability and sample size, we can:
  ~ estimate the population mean from a sample mean
  ~ estimate how often two random sample means would differ by a certain amount
• SAMPLING ERROR - statistics of a given sample will likely differ from the population parameters
• SAMPLING VARIABILITY - statistics of any two samples will likely differ from one another

Question 6

Sampling distribution of the mean

Answer 6

• Likelihood of different results (e.g mean)
• we can characterise the affects of sampling error and variability by imagining a distribution of sample means
• a (usually imaginative) distribution that we could get in we took an infinite member of samples and plotted their means in a histogram
• in a given sampling distribution, all the samples have the same size

Question 7

the qualities of a sampling distribution will depend on

Answer 7

• the populations mean and SD
• n.o of samples taken
• sample size

Question 8

the sampling distribution of the mean (SE): the standard error will depend on two things ~

Answer 8

• the population SD
• the sample size

Question 9

Finding the SD of the sampling distribution

Answer 9

• it has a positive linear relationship with population SD
• e.g halving the population SD halves the SE
• it has a negative, non-linear relationship with sample size
• increasing sample size decreases SE
• e.g to halve the SE, you have to quadruple sample size

Question 10

Sampling distribution

Answer 10

• tells us how often we should expect to get means of a given value
• will usually be normal if the sample size is reasonably large
• has the same mean as the population
• has a SE that depends on the population SD and the sample size
  Therefore, based on SD and SS, we can create a sampling distribution and from the sampling distribution, we can estimate the probability of sampling means
• in future, we can extend this logic to assess the reliability of any study results