Chapter 6 Flashcards
Standardization
a way to convert individual scores from different normal distributions to a shared one with a known mean, standard deviation, and percentiles
z score
standardized version of a raw score which determine the number of standard deviations that particular score is from the mean; part of its own distribution (z distribution)
2 important features of the z-distribution
mean is 0 and standard deviation is 1
Z distribution
a normal distribution of standardized scores or a distribution of z scores
Standard normal distribution
a normal distribution of z scores
What does the z distribution allow us to do?
transform raw scores into standardized scores called z scores, transform z scores back to raw scores, compare z scores, and transform z scores into percentiles
What makes z scores useful?
gives us a sense of where a score falls relative to the mean of its population and allows us to compare scores from different distributions
Central limit theorem
a distribution of sample means is a more normal distribution than a distribution of scores even when the population distribution is not normal as long as the sample size is at least 30
2 important principles of the CLT
repeated sampling approximates a normal curve even when the original population is not normally distributed and a distribution of means is less variable than a distribution of scores
Distribution of means
composed of many means that are calculated from all possible samples of a given size, all taken from the same population
Standard error
standard deviation of a distribution of means, which is the typical amount that a sample mean varies from the population mean
Z statistic
tells us how many standard errors a sample mean is from the population mean
Formula for standard error
population standard deviation divided by square root of sample size
Formula for z score
(raw score minus population mean)/standard deviation
Formula for z statistic
(sample mean minus population mean)/standard error
