Sampling and Probability

Question 1

Name three common sampling techniques.

Answer 1

self-selection
quota sampling
random sampling

Question 2

Self-selection

Answer 2

participants sign up
- convenient
- might over-represent people with strong opinions etc.

Question 3

Quota sampling

Answer 3

determine what proportions of people to sample based on whether they fit some pre-set constraints or categories
- might miss some important categories
- might miss participants who don’t fit pre-set categories

Question 4

Random sample

Answer 4

selected from the population by a process that ensures each possible sample of a given size has an equal chance of being selected
- avoids sampling bias; should be representative
- sometimes impractical but best option

Question 5

Sampling with or without replacement

Answer 5

with: same individual can be chosen twice (name can go back in before next draw)

without: individual can only be chosen once

Question 6

Hypothesis testing

Answer 6

determine which process best accounts for the data
- systematic processes (rare)
- random processes (default assumption - simpler and more conservative)
- a combination

Question 7

Randomness

Answer 7

variability that cannot be accounted for (prediction error) –> with certainty
may be due to some systematic process that we don’t understand yet or haven’t measured

• can say something about the relative likelihood of different outcomes: probability

Question 8

Probability

Answer 8

p(A) = the probability of the occurrence of event A –> always falls between 0 and 1
if A is certain to occur, p(A) = 1
if A is certain not to occur, p(A) = 0

allows us to quantify uncertainty and use it to make predictions

a priori:
p(A) = # outcomes classifiable as event A [divided by] total # of possible outcomes

or a posteriori:
p(A) = # of times A occurred [divided by] total # of occurrences

Question 9

Chances

Answer 9

probabilities expressed as percentages

Question 10

Odds

Answer 10

probability that the event happens, compared to the probability that it doesn’t happen

Question 11

Sample space

Answer 11

contains all possible outcomes of a random process (exhaustive set of events)

coin toss: {heads, tails}
die roll: {1, 2, 3, 4, 5, 6}

p(sample space) = 1

Question 12

Event

Answer 12

possible outcome

Question 13

Mutually exclusive events

Answer 13

events that cannot occur together
ie, one event’s occurrence precludes the other event’s simultaneous occurrence

p(A and B) = 0

when there are only two mutually exclusive outcomes, they can be “P” and “Q”
P = 1 - Q

Question 14

A priori probability

Answer 14

before the fact (without experience)
theoretically derived
not based on collected data

p(A) = # outcomes classifiable as event A [divided by] total # of possible outcomes

Question 15

A posteriori probability

Answer 15

after the fact (with experience)
empirically derived
based on collected data

p(A) = # of times A occurred [divided by] total # of occurrences

Question 16

The addition rule

Answer 16

used to calculate the probability of any one of several events
p(A or B) = p(A) + p(B) - p(A and B)

p(A and B) = 0 when A and B are mutually exclusive

eg,
p(king or queen) = p(king) + p(queen)
= 4/52 + 4/52 (- 0) = 8/52 = .15

Question 17

The multiplication rule

Answer 17

used to calculate probability of joint or successive events (rolling two dice, flipping a coin twice)
p(A and B) = p(A) x p(B|A)

p(B|A) = probability of B given A

for two independent events:
p(A and B) = p(A) x p(B)

eg, a lady tasting tea (8 cups, choose the right 4)
four successive events, without replacement
4/8 x 3/7 x 2/6 x 1/5 = 1/70 = 0.014

Question 18

Conjunction fallacy

Answer 18

failure to recognize that the joint probability of A and B is always less than or equal to the probability of A

Question 19

Gambler’s fallacy

Answer 19

assumption that, if a certain outcome hasn’t happened for a while, it is “due”
failure to account for the fact that events are independent