Studied by 235 peopleprobability
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
Note
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