Part 3 Flashcards
inferential statistics
making inferences from distributions
the normal distribution
describes a common probability distribution of values of a continuous variable around the mean
vertical axis=
frequency of values
horizontal axis=
continuous values (scores total)
properties of the normal distribution:
symmetric, unimodal, mean mode and median are the same value and are equal to the centre of distribution
the specific shape of the curve depends on :
mean (location of peak on x-axis), standard deviation (how spread out the curve is)
standardization of normal distribution
allows comparison of relative standing for different scales, standardize by converting raw score deviations into standard deviation units (z-scores)
properties of standard normal distribution
- the cumulative area (read left to right) is close to zero for z-scores close to -3.49
- the cumulative area increases as the z-scores increases
- the cumulative area for z=0 is 0.50
- the cumulative area is close to 1 for close to z=3.49
z-score correlates directly to:
standard of deviation from the mean
properties of probability with continuous variables:
limitless number of possible values for this variable, probability of event falling in an interval, described as the area under the curve for a specified interval
properties of probability with discrete variables:
can take on limited number of possible values, probability of specific outcomes
importance of probability in everyday life:
- probability judgments
- knowledge of probability helps us understand human limitations
- consumer judgment
what are the types of probabilities?
subjective probability, analytic or theoretical probability, expected relative frequency (empirical) probability
probability experiment
an action, or trial, through which specific results are obtained
outcome
the result of a single trial in a probability experiment
sample space
the set of all possible outcomes of a probability
event
consists of one or more outcomes and is a subset of the sample space
range of probabilities rule
the probability of an event E is between 0 and 1
subject probability
personal judgment of event likelihood
analytic or theoretical probability
determines probability of specific outcomes by looking at all possible outcomes (P(E)=number of outcomes in event E/number of outcomes in sample space)
expected relative frequency (empirical) probability
probability in the long run or on average (apply law of large numbers)
law of large numbers
as an experiment is repeated over and over, the empirical probability of an event approaches the theoretical (actual) probability of the event
sample with replacement
sampling in which the item drawn on trial is replaced before drawing trial N+1
sample without replacement
sampling in which the item drawn on trial is not replaced before drawing trial N+1
what are the types of events
independent events, (dependent events), mutually exclusive events
independent events
occurrence of one event has no effect on the occurrence of another
opposite of independent events are:
dependent events (occurence of one event has an effect on the occurrence of another)
mutually exclusive events
when the occurrence of one event precludes the occurrence of another, i.e., two events cannot occur at the same time
if two events can occur at the same time, then the event is:
not mutually exclusive
given a set of mutually exclusive events…
the probability of the occurrence of one event or another is equal to the sum of their separate probabilities (ADDITION RULE)
to find the probability of the co-occurrence of two or more independent events:
calculate JOINT PROBABILITIES
probability of the joint occurrence of two INDEPENDENT events is….
the product of their probabilities (MULTIPLICATION RULE)
conditional probability
the probability of an event occurring, given that some other event has already occurred
denotation of conditional probability
P(B | A) = probability of B, given A
