Final

Question 1

The probability of either event A OR event B occuring if they are not mutually exclusive

Answer 1

Pr(A or B) = Pr(A) + Pr(B) - Pr(A and B)

Question 2

Bayes theorem

Answer 2

Pr(A I B) = Pr(B I A) Pr(A) / Pr(B)

Question 3

Steps of hypothesis testing

Answer 3

1) state hypothesis
2) compute test statistic
3) determine p-value
4) draw appropriate conclusions

Question 4

significance level

Answer 4

• 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

Question 5

type I error

Answer 5

• rejecting a true null hypothesis

- determined by significance level

Question 6

type II error

Answer 6

• failing to reject a false null hypothesis

- low type II error = high power

Question 7

power

Answer 7

probability that a random sample will lead to rejection of a false null hypothesis

Question 8

non-significant result

Answer 8

failing to reject the null hypothesis

Question 9

assumptions of chi squared test

Answer 9

• 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

Question 10

poisson distribution

Answer 10

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)

Question 11

the odds ratio

Answer 11

• 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

Question 12

relative risk

Answer 12

• 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

Question 13

positives vs. negatives for correlation coefficient

Answer 13

• 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

Question 14

assumptions of the correlation coefficient

Answer 14

• data has bivariate normal distribution
• relationship between x and y is linear
• frequency of distributions of x and y separately are normal

Question 15

departures from bivariate normality

Answer 15

• funnel
• outlier
• non-linear

Question 16

measurement error

Answer 16

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)

Question 17

regression

Answer 17

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

Question 18

least-squares regression line

Answer 18

the line for which the sum of all squared deviations in Y is the smallest

Question 19

residuals

Answer 19

measure the scatter of points above and below the least-squares regression line
-crucial for evaluating the fit of the line to the data

Question 20

deterministic vs. stochastic models

Answer 20

• 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

Question 21

markov property

Answer 21

memorylessness

Question 22

types of markov chains

Answer 22

• 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

Question 23

ergodic (irreducible markov chains)

Answer 23

-it is possible to go from every state to every other state (not necessarily in one move)

Question 24

regular markov chains

Answer 24

if some power of the transition matrix has only positive elements (they converge)

Question 25

p-value

Answer 25

probability of getting the data, or something as or more unusual, if the null hypothesis were true

Question 26

larger samples give more information because…

Answer 26

• more power

- tend to estimate parameter with smaller confidence interval

Question 27

transformations

Answer 27

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

Question 28

________ are a subset of __________

-ergodic and regular markov chains

Answer 28

ergodic markov chains are a subset of regular markov chains

Question 29

regression

Answer 29

• predicts x from y
• provides the rate of change
• assumes relationship between x and y can be described by a line

Question 30

correlation vs. regression

Answer 30

• correlation measures the strength of the association

- regression measures the rate of change

Question 31

residual plots assumptions

Answer 31

• 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