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)