Chapter 4: Probability Flashcards
test sensitivity
The probability of a true positive, given that the subject actually has the condition being tested.
test specificity
The probability of a true negative, given that the subject does not have the condition being tested.
positive predictive value
Probability that a subject is a true positive, given that the test yields a positive result (indicating that the condition is present).
negative predictive value
Probability that the subject is a true negative, given that the test yields a negative result (indicating that the condition is not present).
prevalence
Proportion of subjects having some condition.
rare event rule for inferential statistics
If, under a given assumption, the probability of a particular observed event is extremely small, we conclude that the assumption is probably not correct.
event
Any collection of results or outcomes of a procedure.
simple event
An outcome or an event that cannot be further broken down into simpler components.
sample space
All possible simple events in a procedure; all outcomes that cannot be broken down any further.
What does the notation “P” denote?
probability
What do the notions “A,B, and C” denote?
specific events
What does the notation “P(A)” denote?
the probability of event A occurring
When using the classical approach to find the probability of an event, it is important to verify that the each simple event in the procedure are what?
equally likely to occur
law of large numbers
As a procedure is repeated again and again, the relative frequency probability of an event tends to approach actual probability.
How is relative frequency probability calculated?
number of times “A” occurred divided by the number of times the procedure was repeated
Are the results of a relative frequency probability calculation exact values or approximations?
Approximations. A probability estimate based on only a few trials can be off by a substantial amount, but with a very large number of trials, the estimates tend to be more accurate.
How is probability calculated using the classical approach?
The number of ways “A” occurred is divided by the number of different simple events.
How are subjective probabilities determined?
The probability of event “A” is estimated by using knowledge of the relevant circumstances. In other words, you make an educated guess.
When the occurrence of an event is impossible, what is its probability?
0
When an event has a 50-50 chance of occurring, what is its probability?
0.5
When an event is certain to occur, what is its probability?
1
What is a complement of an event consist of?
All of the outcomes in which event “A” does NOT occur.
Which is more likely to occur, an event with 0.00001 probability or an event with 0.15 probability?
An event with 0.15 probability.
How often, on average, does an event with a probability of 0.001 occur?
Once in a thousand trials.
An event is unlikely to occur if its probability is at or below what number?
0.05
When does an event have an unusually low or unusually high number of outcomes?
When the number of outcomes is far from what is typically expected.
actual odds against
The actual odds against event “A” occurring are the ration P(A-)/P(A), usually expressed in the form of a:B (or “a to b”, where “a” and “b” are integers having no common factors.
actual odds in favor
The actual odds in favor of event “A” occurring are the ratio P(A)/P(A-), which is the reciprocal of the actual odds against that event. If the odds against “A” are a:b, then the odds in favor of “A” are b:a.
payoff odds
The payoff odds against event A occurring are the ratio of net profit (if you win) to the mount bet:
payoff odds against event A= (net profit):(amount bet)
false positive
WRONG result in which test incorrectly indicates the presence of a condition when the subject actually does not have that condition.
false negative
WRONG result in which the test incorrectly indicates that the subject does NOT have a condition when it really is present.
true positive
CORRECT result in which the test correctly indicates that a condition is present when it really is present.
true negative
CORRECT result in which the test correctly indicates that a condition is not present when it really is not present.
What is a simulation of a procedure?
A process that behaves in the same ways as the procedure itself so that similar results are produced.
What is a compound event?
Any event combining 2 or more simple events.
What is the intuitive addition rule for compound events?
To find P (A or B), find the sum of the number of ways event A can occur and the number of ways event B can occur, ADDING IN SUCH A WAY THAT EVERY OUTCOME IS COUNTED ONLY ONCE. P(A or B) is equal to that sum, divided by the total number of outcomes in the sample space.
When are events A and B be considered to be “disjoint” (or mutually exclusive)?
When they cannot occur at the same time. (That is, disjoint events do not overlap)
Whenever A and B are disjoint, what does P (A and B) become?
Zero.
What is the formal addition rule for compound events?
P(A or B)= P(A)+ P(B)- P(A and B)
