Statistics

Question 1

P-value

Answer 1

probability of rejecting H0 with the value of the test statistic obtained from the data given H0 is true (small p value is preferred)
(if p value is small then it’s saying that the observation is unlikely to happen, so the data is statistically significant enough to reject the null hypothesis)

Question 2

Confidence interval

Answer 2

measures the degree of uncertainty or certainty in sampling method, and is the range of plausible values for an unknown parameter (finding test statistic)

Question 3

Odds ratio

Answer 3

describes the strength of the association between two events, ad/bc (the ratio of the odds of A in the presence of B and the ratio of the odds of A in the absence of B. p1/1-p1 / p2/1-p2)

Question 4

Z distribution

Answer 4

normal distribution when variance is known with a large sample size

Question 5

t distribution

Answer 5

normal distribution when variance is unknown with a small sample size

Question 6

power

Answer 6

probability of avoiding a type 2 error (when the type 2 error is to accept a false hypothesis), (1 - p(type 11 error)

Question 7

Type 1 error

Answer 7

h0 is rejected but h0 true

Question 8

Type 2 error

Answer 8

h0 is accepted but h0 false

Question 9

Unbiased

Answer 9

expected value of the estimator is the parameter (when the estimator is an estimate of the parameter)

Question 10

MSE

Answer 10

variance(T) + bias(T)^2

Question 11

consistent

Answer 11

statistic tends to the parameter as n increases

Question 12

Method of moments

Answer 12

equating E(t) = mu and solving in terms of parameter, can also do for variance if sample has multiple parameters

Question 13

MLE

Answer 13

method for choosing the ‘best’ parameter which maximises the probability that the parameter produces the sample

Question 14

Sufficient

Answer 14

statistic is sufficient if it contains all the information about the parameter in it

Question 15

Neyman-Fisher factorisation theorem

Answer 15

the likelihood can be factorised in terms of h(x) and g(t, theta) where t is a sufficient statistic

Question 16

Cram´er-Rao lower bound.

Answer 16

smallest the variance of any unbiased estimator can become is 1/I(θ)

Question 17

Invariance property

Answer 17

g is a 1-1 monotonic function and theta is an MLE then g(theta) is the MLE of g

Question 18

significance level/ size

Answer 18

p(type 1 error) = p(reject Ho| Ho true)

Question 19

Statistic to use when comparing two variances

Answer 19

F statistic (chi over chi)

Question 20

What to do if testing two means (non independent)

Answer 20

find difference between the two samples then use t test

Question 21

difference between classical and Bayesian

Answer 21

classical: theta would be an unknown fixed parameter and the likelihood is a function of the sample
Bayesian: assumes the parameter is a random variable which we assign prior beliefs onto

Question 22

model deviance

Answer 22

sum of the squared difference between true and estimate

Question 23

least squares

Answer 23

approximate a solution (parameters of the model) by minimising the squares of the residuals

Question 24

Gauss-Markov Theorem

Answer 24

m If βˆ is the least squares estimator of β, then aTβˆ

is the unique linear unbiased estimator of aTβ with minimum variance

Question 25

test for existence of regression

Answer 25

using F statistic (finding difference of model deviances etc)

Question 26

When to transform variables of a model

Answer 26

we need to transform the variables of a model (Y or X) if the residuals don’t look random

Question 27

total sum of squares

Answer 27

the total variability in y

Question 28

coefficient of determination (R^2)

Answer 28

proportion of variability explained by the regression (model)

Question 29

ANOVA

Answer 29

uses/ finds F to measure the existence of regression (where regression is strength of relationship)

Question 30

decision rule

Answer 30

formal rule which spells out the circumstances under which you would reject the null hypothesis

Question 31

Bernoulli distribution

Answer 31

two outcomes (success or failure), with probability p

Question 32

Binomial distribution

Answer 32

two outcomes (success or failure), repeated n times, probability p, x is number of successes

Question 33

Geometric distribution

Answer 33

two outcomes (success or failure), x is number of trials until a success occurs

Question 34

Poisson distribution

Answer 34

used to measure ‘frequency’ given a parameter (originally used to approximate the binomial distribution with large n and small p)

Question 35

chi distribution

Answer 35

normal distribution squared with 1 degree of freedom if not a sum, and n degrees of freedom is sum of n

Question 36

Central limit theorem

Answer 36

independent random variables are added, their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed

Question 37

Confounding variable

Answer 37

say we want to show the effects of X on Y then C is a confounder if it has an effect on X and Y. So confounding is when the true effect of X on Y is hidden by another variable.

Question 38

Interaction

Answer 38

an interaction is when the effect of one variable on the outcome depends on another variable.

Question 39

What information would you need from a clinician in order to perform a sample size calculation?

Answer 39

We need the power, type 1 error rate, type 11 error rate, the clinically relevant difference the known variance sigma, and for two sample we need the ratio in each treatment group. The we approximate n via the Z distribution (normal) and iteration to find n based on the t distribution.

Question 40

Standard error

Answer 40

a measure of the statistical accuracy of an estimate, equal to the standard deviation of the theoretical distribution of a large population of such estimates.

Question 41

Standard deviation

Answer 41

a quantity expressing by how much the members of a group differ from the mean value for the group