Final Flashcards
The probability of either event A OR event B occuring if they are not mutually exclusive
Pr(A or B) = Pr(A) + Pr(B) - Pr(A and B)
Bayes theorem
Pr(A I B) = Pr(B I A) Pr(A) / Pr(B)
Steps of hypothesis testing
1) state hypothesis
2) compute test statistic
3) determine p-value
4) draw appropriate conclusions
significance level
- greek letter alpha
- commonly 0.05 in biology
- probability used as a critereon for rejecting the null hypothesis
- p-value less than or equal to alpha, reject null hypothesis
type I error
- rejecting a true null hypothesis
- determined by significance level
type II error
- failing to reject a false null hypothesis
- low type II error = high power
power
probability that a random sample will lead to rejection of a false null hypothesis
non-significant result
failing to reject the null hypothesis
assumptions of chi squared test
- none of the categories have an expected frequency of less than 1
- No more than 20% of categories have an expected frequency of less than 5
- random sample
poisson distribution
describes the number of successes in blocks of time or space, when successes happen independently of each other and with equal probability at every instant in time or point in space
- random (meets criteria for distribution)
- clumped or dispersed (do not meet critereon for distribution)
the odds ratio
- measures the magnitude of association between two categorical variables when each has only two categories
- one variable is response, other is explanatory (whose odds of success is being compared)
- odds(o) = probability of success / probability of failure
- odds ratio (o1/o2) = odds of success in one group divided by odds of success in a second group
relative risk
- another commonly used measure of the association between two categorical variables when both have just two categories
- RR = probability of undesired outcome in treatment group / probability of undesired outcome in control group
- will be relatively similar to the odds ratio when focal outcome is rare
positives vs. negatives for correlation coefficient
- sum will be positive if: most of the observations are in the lower left or upper right
- sum will be negative if: most observations lie in the upper left and lower right corners
- sum will be close to zero: if the scatter of observations fill all corners of the plane
assumptions of the correlation coefficient
- data has bivariate normal distribution
- relationship between x and y is linear
- frequency of distributions of x and y separately are normal
departures from bivariate normality
- funnel
- outlier
- non-linear
measurement error
the difference between the true value of a variable for an individual and its measured value
- error in either x or y tends to weaken correlation between variables
- same thing happens with uncorrelated error in both x and y
- w/ measurement error, r will tend to underestimate p (closer to zero than true correlation, a bias called attenuation)
regression
predicts the value of one numerical variable from values of another numerical variable
-fits a line through data to figure out how steeply one variable changes with another
least-squares regression line
the line for which the sum of all squared deviations in Y is the smallest
residuals
measure the scatter of points above and below the least-squares regression line
-crucial for evaluating the fit of the line to the data
deterministic vs. stochastic models
- deterministic: no randomness is involved –> will always produce the same output given the initial state
- stochastic models: non-deterministic –> subsequent states of the system determined probabistically
markov property
memorylessness
types of markov chains
- absorbing –> has at least one absorbing state and from every state it is possible to reach the absorbing state (does not have to be in 1 step)
- transient
ergodic (irreducible markov chains)
-it is possible to go from every state to every other state (not necessarily in one move)
regular markov chains
if some power of the transition matrix has only positive elements (they converge)
p-value
probability of getting the data, or something as or more unusual, if the null hypothesis were true
larger samples give more information because…
- more power
- tend to estimate parameter with smaller confidence interval
transformations
Y = aX^b –> ln(Y) = ln(a) + bln(X) –> power function
Y = ab^X –> ln(Y) = ln(a) + Xln(b) –> exponential function
-transformed data has a better residual plot
-try transformations to see if it brings the outlier closer to the rest of the distribution
________ are a subset of __________
-ergodic and regular markov chains
ergodic markov chains are a subset of regular markov chains
regression
- predicts x from y
- provides the rate of change
- assumes relationship between x and y can be described by a line
correlation vs. regression
- correlation measures the strength of the association
- regression measures the rate of change
residual plots assumptions
- a roughly symmetric cloud of points above and below the line y = 0
- little noticeable curvature as we move along x-axis
- approximately equal variance of points above and below the line at all values of x
