Z scores, Zxbar, sampling distributions

z scores are reffered to

standard scores, because they use standard deviation

z formula

z= (x-u)/ Q (sigma)

what is the foundation for many inferential stats

the Z test

the numerator in a z test reflects?

how a score deviates from a population parameter u (pop mean)

the denominator in a Z test reflects

the variability of scores in a pop

the ratio between the numerator and denominator of the Z test represents?

a score (z) that can be compared to a theoretical distribution (the normal distribution)

• the assumption is the scores take the shape of a normal distribution

what is the problem with the z test

it only deals with individuals, we don’t care about a single person we care about samples so we can make inferences about the population

uxbar

same as u

σxbar

σ/sqrt(n)

-standard error of the mean

information

2nd pillar of statistical wisdom

Root N Rule --- If we gain information by collecting observations, how is the gain related to the number of observations? Not N but the square root of N

-ex: interested in how students like class, first student is all new info, 2nd student similar but some new info, if we gain info

central limit theorem (our friend who smokes and drinks) addresses

•The Zxbar test requires “leaps of faith” pertaining to mxbar and sxbar

•Many variables in the real-world are NOT distributed normally --- can the Zxbar test be employed in those circumstances?

sampling distribution

is a theoretical distribution of possible values of some sample statistic (e.g., the mean) that would occur if we were to draw ALL possible samples of a fixed size from a given population!

variability in a sampling distribution

is less as the n becomes greater

• the outliers have less affect when you have a greater amount

• ex: only 5 compared to 50