Statistics Week 3

Statistics Week 3

1. Sampling error & distributions

   • Sampling error - error associated with examining a sample rather than a population - occurs because in our sample we do not have all members of pop.
   • Sampling distribution - repeatedly sample from a distribution and calculate a sample statistic (e.g mean/s.d), plot a histogram of the sample stat and we get a sampling distribution
   • Sampling distribution of the mean - particularly important - provided we know the parameters of pop. from which data were sampled, then we also know about the parameters of the sampling distribution of the mean
     • For a normal population, SDM has the same mean, but a different s.d. - sometimes called standard error of the mean or just standard error
       • Standard error is s.d of the pop. divided by the square root of the sample size (N) so where sample was 6, N = 6.
     • Note SDM is a distribution of sample means of scores, not scores themselves

2. Confidence intervals

   • Allow us to pin down the population parameter in question to a range of most likely values
     • We are interested in sample mean and its relation to the pop. mean
       • So we consider the SDM, which we know is normally distributed
   • For any normal distribution, 95% of scores are within 1.96 S.D of the mean
     • So we know that theres a 95% that a sample mean we have obtained is within 1.96 S.Ds of the SDM of the mean of the SDM
       • So we know that there's a 95% chance that a sample mean we have obtained is within 1.96 standard errors of the mean of the population
         • confidence interval = SAMPLE mean +- 1.96 x s.e of the POP./sqrt of sample size
           • Once we work this out we can estimate a 95% confidence interval for population mean as all the values between CI lower and CI higher