Biostats chapter three
Terms
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- false positive
- test incorrectly indicates the presence of a condition when the subject does not actually have that condition
- false negative
- test incorrectly indicates that the subject does not have a condition when the subject actually does have that condition
- true positive
- test correctly indicates that a condition is present when it really is present
- true negative
- test correctly indicates that a condition is not present when it really is not present
- test sensitivity
- the probability of a true positive
- test specificity
- the probability of true negative
- positive predictive value
- probability that the subject is a true positive given that the test yields a positive result
- negative predictive value
- probability that the subject is a true negative given the test yields a negative result
- 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
- for a procedure consists of all possible simple events, all outcomes that cannot be broken down any further
- rule one: relative frequency approximation of probability
- p(A)=number of times A occurred/number of times trial was repeated
- rule two: classical approach to probability
-
-requires equally likely outcomes
P(A)=number of ways A can occur/number of different simple events=s/n - rule three:subjective probabilities
- P(A) is estimated by using knowledge of the relevant circumstances
- law of large numbers
- as a procedure is repeated again and again, the relative frequency probability of an event tends to approach the actual probability
- simulation
- process that behaves inthe same ways as the procedure itself, so that similar results are produced
- complement
- of event A, denoted by A bar, consists ofa ll outcomes in which event A does not occur
- rounding off probabilities
- when expressing the value of a probability, either give the exact fraction or decimal or round off the final decimal results to three significant digits
- compound event
- any event combining two or more simple events
- formal addition rule
- P(A or B)=P(A)+P(B)-P(A and B)
- intuitive addition rule
- to find P(A or B), find the sum of the number of ways event A can occur and the number of ways that 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
- disjoint
-
-mutually exclusive
-events A and B cannot occur at the same time - rule of complementary events
-
P(A)+P(Abar)=1
P(Abar)=1-P(A)
P(A)=1-P(Abar) - tree digram
- picture of the possible outcomes of a procedure, shown as line segments emanating from one starting point
- independent
- two events a and b are independent if the occurence of one does nto affect the probability of the occurence of the other
- dependent
- if a and b are not independent they are said to be dependent
- formal multiplication rule
- P(A and B)=P(A)*P(B/A)
- intuitive multiplication rule
- when finding the probability that event A occurs in one trial and event B occurs in the next trial, multiply the probability of event A by the probability of event B, but be sure that the probability of event B takes into account that previous occurence of event A