psyc 60- steiner- quiz 2

probability

the chance or likelihood of some event occurring

event

the outcome of a trial

independent events

the occurrence of one has no effect on the probability of the occurrence of the other

example: how 2 people vote when they don't know each other

dependent events

the outcome of one event is related to the outcome of another event

example: how 2 family members vote are often dependent events

mutually exclusive

the occurrence of one precludes the occurrence of the other

example: tossing a coin will result in one of two events (heads or tails)

• if you get heads, you will not get tails on said toss

exhaustive

a set of events that represent all possible outcomes

example: heads, tails, and side in a coin toss

Additive Law of Probability

the rule giving the probability of the occurrence of 2 or more mutually exclusive events

Multiplicative Law of Probability

rule giving the probability of the joint occurrence of independent events

Joint Probability

the probability of the co-occurrence (at the same time) of two or more events

Conditional Probability

the probability of one event given the occurrence of some other event

Risk

the number of occurrences on one event divided by the total number of occurrences of events

risk ratio

the ratio of two risks

Odds

The frequency of occurrence of one event divided by the frequency of occurrence of another event

odds ratio

the ratio of two odds

sampling error

variability of a statistic from sample to sample due to chance

hypothesis testing

a process by which decisions are made concerning the value of parameters

sampling distribution

the distribution of a statistic over repeated sampling

• the statistic is usually the mean

sampling distribution of the mean

the distribution of sample means over repeated sampling from one population

standard error

the standard deviation of a sampling distribution

• each sample in a sampling distribution has a standard deviation, but the whole distribution also has a standard deviation

research hypothesis

the hypothesis that the experiment was designed to investigate

alternative hypothesis (H1)

the hypothesis that is adopted when H0 is rejected, usually the same as the research hypothesis

null hypothesis (H0)

the statistical hypothesis tested by the statistical procedure; usually a hypothesis of no difference or no relationship

test statistic

the results of a statistical test

significance level (rejection level)

the probability with which we are willing to reject H0 when it is in fact correct

rejection region

the set of outcomes of an experiment that will lead to rejection of H0

critical value

the value of a test statistic at or beyond which we will reject H0

one-tailed test (directional test)

a test that rejects extreme scores in one specified tail of the distribution

two-tailed test (non-directional)

a test that rejects extreme scores in either tail of the distribution

type 1 error

the error of rejecting H0 when it is true

-far more common

alpha (α)

the probability of a type 1 error

type 2 error

the error of not rejecting H0 when it is false

-false negative

beta (β)

the probability of a type 2 error

power

the probability of correctly rejecting a false H0

increasing the type 1 error rate

decreases the type 2 error rate

increasing the type 2 error rate

decreases the type 1 error rate

correlation

a measure of the relationship between variables

correlation coefficient

same as correlation

Pearson product-moment correlation coefficient (r)

most common kind of correlation coefficient

• it ranges from -1 to +1

scatterplot (scatter diagram/scattergram)

a figure in which the individual data points are plotted in two-dimensional space

predictor variable

the variable from which a prediction is made

• often the IV

criterion variable

the variable to be predicted

• often the DV

the predictor (IV) generally goes on which axis?

the x axis

the criterion (DV) goes on which axis?

the y axis

regression line

the line of best fit drawn through a scatterplot

• it is the line that minimizes the distance between all of the data points and itself

if the regression line goes up from left to right on the scatterplot, the correlation coefficient is

positive

if the regression line goes down from left to right on the scatterplot, the correlation coefficient is

negative

the closer the data points are to the regression line,

the stronger the correlation

the closer the correlation coefficient is to 0,

the weaker the correlation

linear relationship

a situation in which the best-fitting regression line is a straight line

curvilinear relationship

a situation that is best represented by something other than a straight line

population correlation coefficient rho (ρ)

the correlation coefficient for the population

degrees of freedom

the number of independent pieces of information remaining after estimating one or more parameters

Spearman's correlation coefficient for ranked data (rs)

a correlation coefficient on ranked data

range restrictions

refers to cases in which the range over which x or y values are artificially limited

heterogeneous subsamples

data in which the sample of observations could be subdivided into two distinct sets on the basis of some other variable

point-biserial correlation coefficient (r_pb)

the correlation coefficient when one of the variables is measured as a dichotomy

dichotomous variables

Variables that can take on only two different values

phi (Φ)

the correlation coefficient when both variables are measured as dichotomies

regression

the prediction of one variable from knowledge of one or more other variables

regression equation

the equation giving the regression line

ŷ=bx+a

ŷ

predicted value of y

b

the slope of the regression line

a

the y intercept

slope

amount of change in y for a one-unit change in x

intercept

the value of y when x is 0

regression coefficients

the general name given to the slope and the intercept (most often refers to slope)

errors of prediction (residual)

The differences between Y and Ŷ

least squares regression

regression of Y on the basis of X where we minimize the squared deviations of predicted scores from obtained scores

to calculate slope

b= r (sY/sX)

to calculate the intercept

a= ȳ- bx̄

standard error of estimate

the average of the squared deviations about the regression line

residual variance (error variance)

the square of the standard error of the estimate