Probabilities

Question 1

What values can probabilities take?

Answer 1

Between 0 and 1

• Pr = 0 is impossible, will never happen
• Pr = 1 will definitely happen

Question 2

What is the complement of an event F?

Answer 2

Pr(F bar) = 1 - F

Question 3

What is the intersection of F and G?

Answer 3

• probability F and G both occur

- Pr(F∩G)

Question 4

How is the intersection of F and G calculated when the two values are independant?

Answer 4

Pr(F∩G) = Pr(F) x Pr(G)

Question 5

What is the union of F and G?

Answer 5

• either F or G occurs

Pr(F∪G) = Pr(F) + Pr(G) - Pr(F∩G)

Question 6

What happens when F and G are mutually exclusive?

Answer 6

• F and G cannot occur together

- Pr(F∩G) = 0

Question 7

What is conditional probability?

Answer 7

• Pr of F occuring given G

Pr(F | G) = Pr(F∩G) /Pr(G)

Question 8

What is the equation for the Probability Mass Function?

Answer 8

Σ pr(x) = P(X=k) + P(X=k+1) + … + P(X=n) = 1

Question 9

What is the expected value of X and the variance (notation)?

Answer 9

E(X) = Σ x pr(x)
var(X) = E[x^2] - (E[x])^2

Question 10

In the binomial distribution, what does a low probability of success mean? What happens when its 0.5?

Answer 10

p is low: expect right skewed

p = 0.5: expect symmetry

Question 11

In the binomial distribution, what do p, x and n mean?

Answer 11

p - pr of success
x - x successes in a row
n - number of trials

Question 12

What are the conditions for the Binomial Distribution?

Answer 12

• two outcomes (eg yes/no)
• fixed number of trials
• independant observations
• constant pr of success

Question 13

How are the confidence intervals for a binomial distribution calculated?

Answer 13

“CI for a proportion” on formula list.

Question 14

What do we need to be able to assume that estimates for a proportion are normally distributed?

Answer 14

Require large samples.

Question 15

When can we not assume that proportions are normally distributed? What do we use to calculate confidence intervals in this case?

Answer 15

• when p is close to 0 or 1 (p < 0.05, p > 0.5)

- Wilson intervals are used instead

Question 16

How many cases are there for proportions (for calculating the standard error)?

Answer 16

3

• proportions from independant samples
• one sample of size n, several response categories
• one sample of size n, many yes/no items

Question 17

What is an odds ratio?

Answer 17

• used to quanitfy the extent of the association between two groups
• a relative measure of effect (eg. comparison of an intervention group of a study relative to a control/placebo group)

Question 18

How is an odds ratio calculated?

Answer 18

• numerator is the odds in group 1

- denominator is the odds in group 2 (/control)

Question 19

What does an odds ratio of 1 mean?

Answer 19

• outcome is the same in both groups

- no differece between the two groups in the study

Question 20

What does an odds ratio > 1 mean? What about OR < 1?

Answer 20

OR > 1: intervention is better than control
OR < 1: control is better than intervention
never negative

Question 21

What is an alternative way to calculate the odds of success (way not on formula list)?

Answer 21

p/(1 - p)

Question 22

What does an odds of success ratio of 4 mean?

Answer 22

Success is 4x more likely.

Question 23

How is a probability calculated from its odds?

Answer 23

p = odds/(odds + 1)

Question 24

How is the standard error for the odds ratio calculated?

Answer 24

se(OR) = sqrt((1/n11) + (1/n12) + (1/n21) + (1/n22))

where n11…n22 are based on the number of observations in each group/outcome category

Question 25

How is the confidence interval for the odds ratio calculated?

Answer 25

ln(θ) ± z x se(OR)