PY 211 - Exam Two

properties of a normal distribution

Symmetric about the mean; Mode, median, and mean are at the same point; Area under the curve and to the right of the mean is equal to area to left of mean; Curve approaches but does not touch zero; Area under the curve is exactly 1

68-95-99.7 rule (empirical rule)

Within a normal distribution, 68% of scores will fall within +/- 1 standard deviation (SD) of the mean; 95% within 2 SDs of the mean; and 99.7% within 3 SDs of the mean.
(Almost all scores will fall between 3 SDs of the mean.)

z-score

a measure of how many standard deviations you are away from the norm (average or mean)

raw score

A test score that has not been transformed or converted in any way

positive z-scores

reflect deviations from above the mean; above average

negative z-scores

reflect deviations below the mean; below average

what are z-scores used for

to compare raw scores from two different distributions on the same playing field

z-score formula (finding z-score from a raw score)

(raw score-population mean)/population standard deviation

raw score formula (finding raw score from z-score)

standard deviation(z-score)+population mean=raw score

what does it mean when you have a larger standard deviation

the z-score is closer to 0

random process

a situation in which we know what outcomes could happen, not which particular outcome

probability

likelihood that a particular event will occur; cannot be less than zero or greater than one

probability formula

number of desired outcomes/number of possible outcomes

Law of Large Numbers

as a sample size grows, its mean gets closer to the average of the whole population

disjoint outcomes (mutually exclusive)

two outcomes that cannot happen at the same time (i.e., a coin cannot land on heads and tails at the same time)

non-disjoint outcomes

two outcomes that can happen at the same time (i.e., a student can get an A in stats and an A in Econ in the same semester)

random variable

a variable whose value is a numerical outcome of a random event

discrete random variable

variable that only takes integer values (i.e., number of credit hours)

continuous random variable

variable that takes a decimal value (i.e., the cost of books this semester)

sampling distribution of means

a probability distribution that represents a statistic (i.e., mean) for all possible sample sizes of a given size from a population (i.e., why is the true population mean of homeless people in Atlanta)

central limit theorem

as sample size (n) increases, the sampling distribution of means follows a normal distribution of means; the mean of the sampling distribution will be the population; the standard of distribution of means is the standard error of the mean

what is the standard error of mean

the standard deviation of the sampling distribution of the mean

formula for SEM

standard deviation/sqr(n)

what happens to error as the population mean changes

as population mean increases, error decreases

what makes a good hypothesis

if-then statement; testable

hypothesis test

a method to make informed decisions/ draw conclusions about a population based on a sample; helps determine if there is enough evidence to support and claim or hypothesis about a population

difference between a hypothesis v. hypothesis testing

hypothesis describes a population and hypothesis testing deals with a sample and then the results are generalized to the larger population

null hypothesis

a statement or idea that can falsified, or proved wrong

research hypothesis

a definite statement that a relationship exists between variables

directional research hypothesis

prediction of the specific outcome of an experiment

nondirectional research hypothesis

a specific prediction concerning the outcome of an experiment is not made

what do words like more, greater than, less, etc. indicate

direction (when direction is indicated only focus on that information)
=

example of a nondirectional research hypothesis

the average score of 9th graders is different from the average score of 12th graders on a memory test

Example of a null hypothesis

There is no difference in plant growth between nutrients present and no nutrients present groups

example of a directional research hypothesis

the average score of 12th graders is greater than the average score of 9th graders on a memory test

one-tailed test

a hypothesis test in which the research hypothesis is directional

two-tailed test

a hypothesis test in which the research hypothesis is non-directional

when do you use a one-tailed test

if you have a specific prediction about the direction of the difference

when do you use a two-tailed test

if you want to determine if there is any difference between the groups you are comparing; null hypothesis testing

steps of hypothesis testing

formulate a hypothesis, determine alpha levels and critical values, calculate the statistics (SEM and z-score), report

cutoff scores (critical values)

If reached or exceeded, the null hypothesis is rejected

What happens when the alpha value is adjusted

there is a larger range of p values for which we would reject the null hypothesis

what happens to alpha level during a two-tailed test

divided by two

structure of reporting the results of a hypothesis test

With a z-score obtained of __________ we __________ the null hypothesis and conclude that ___________, p</>0.05 (< is used when rejected, > is used when accepted)

type I error

Rejecting null hypothesis when it is true

Type II error

failing to reject a false null hypothesis

Effect Size (Cohen's d)

the magnitude or size of the experimental treatment

Power Estimation

Power is the ability of a statistical test to detect significant differences between subgroups of a population when differences really do exist; studies with more participants have more power.

small effect size

d=.20-.49

moderate effect size

d=0.5-0.79

large effect size

d=.8