PSYC2009 Study Guide - Quiz Guide: Coin Flipping, Bias Of An Estimator, Statistic
Distributions
Probability distributions
• Provides the categories (or scores) of a variable along with the probability that each occurs
• Often shown as a graph (or table)
• Cumulative probability: score is the probability of values at or below that score
• Theoretical distributions: based on a priori probabilities.
• Observed distributions: based on a sample of data (empirical results)
Discrete distribution
• Probability distributions for discrete variables
o Occurs when we conduct N independent trial, when each trials has two possible
outcomes
o Outcomes must be mutually exclusive
o Choose one outcome and count the number of times it occurs (and divide by total)
o Coin tossing
Continuous distributions
• Probability distributions for continuous variables
• Actually the area under the curve that tells us the probability of the values in a chosen interval
• Normal distribution is an example of a continuous distribution
o Theoretical distribution that approximates many naturally occurring observed
distributions
o Common examples are measures of height or weight in a large population
o Symmetrical bell-shaped curve that is described by stating its mean, represented by
and standarddeviation, as represented by ,
o Standard normal distribution is a normal distribution with mean , and a
sattandard deviation
o Standard score (z-score): probability of getting values above or below a given raw mark
(X), must change raw mark into z-score
•
• Can use a table of z-statistics (found in textbook) to find the "area below z" and
"area beyond z"
Sampling distributions
• Population statistic (or parameter): based on entire population
• Sample statistic (or estimate): based on a sample taken from the population
• Can estimate a population statistic from a sample statistic, need a statistical model to work
out how the sample statistic is expected to behave
o This works out the sampling distribution of the sample statistic
o How likely it is to get each possible value for the sample statistic, when we pick samples
from a population
• Expected value: the theoretical average of the sampling statistic under repeated sampling.
o If expected value = population statistic, then sample statistic is an unbiased estimator
• Sampling error: how much sampling statistic will vary around the value of the population
statistic
o Low sampling error: most of the samples will give a sampling statistic close to the
population statistic
• Standard error: standard deviation of sample statistic. Simple way to measure sampling error
find more resources at oneclass.com
find more resources at oneclass.com
