Ch. 7 Statistics

s hat squared

SS/N-1, an unbiased estimator of sigma (population standard deviation)

sampling distribution

a probability distribution of a statistic when gathered over every possible sample of a given size is called a sampling distribution for that statistic

remember

a sample has a standard deviation but a sampling distribution has a standard error

probability distribution

a sampling distribution of a statistic is a probability distribution of that statistic when gathered from every possible sample of a given size

unbiased

a statistic whose value when averaged over all possible samples of a given size is equal to the population parameter

sampling distribution of the mean

a theoretical distribution consisting of the mean score of all possible samples of a given size

the sample mean

an unbiased estimator of the population mean

unbiased estimator

expected value is equal to its corresponding population parameter

variance of a sample

is a biased estimator of the variance of the population

smaller sample size from the same population

is broader and less closely approximates the normal distribution

larger sample size from the same population

means a smaller standard error of sampling distribution (and vice versa - small sample size = bigger standard error of sampling distribution)

variance estimate

s hat squared

standerd deviation of the sampling distribution of the mean

sigma/ \/N

mean square

sum of squares of a data set divided by its degrees of freedom, SS/df,

sampling error

the fact that the sample statistic may not be equal to its corresponding population parameter is the result of this, standard deviation of a sampling distribution

CMT: population mean (raw scores)

the mean of a sampling distribution of the mean will always be equal to the population mean (of raw scores)

degrees of freedom

the number of independent estimates of variability in the data, cannot be deduced from one another

standard deviation estimate

the positive square-root of s hat squared

and this too

the sample mean is a more accurate estimator of the population mean when the standard error fo the mean is small than when the standard error of the mean is large

also remember

the sampling distribution of the mean approximates a normal distribution given a sufficiently large sample size, this true regardless of the shape of the underlying population

sample size increases

the sampling distribution of the sample mean approaches the normal distribution

and remember

the standard error of the mean gets smaller as the sample size increases and as the variability of scores in the population decreases

the mean of the sampling distribution of the mean

u

central limit theorem

what defines the shape and parameters of the sampling distribution of the sample mean (given a population of with a mean of u and a standard deviation of o, the sampling distribution of the mean has a mean of u and the standard deviation of o/ \/N and approaches a normal distribution as the sample size on which it is based, N, approaches infinity)