Lecture 3

Question 1

statistical inference:

what represents type A error?

what represents type B error?

Answer 1

type A/type 1 error: false positive

> reject h0 while its true

type B/type 2 error: false negative

> retain h0 while its wrong

Question 2

type A related to?

type B related to?

Answer 2

type A: related to h0 being true

type B: related to h1 being true

Question 3

how to describe the power of a test?

Answer 3

power: the probability of rejecting h0 when its not true

> probability of discovering a true effect

Question 4

what are 7 factors that influence power?

Answer 4

power depends on:

1. size of the effect

> bigger effect, more power

2. variation in population

> less variation, more power

3. sample size

> bigger sample size, more power

4. design type

> within subjects more power than between

5. significance level

> greater alpha, more power (not recommended)

6. one vs two sided testing

> one sided more power

7. type of test: parametric vs nonparametric

Question 5

what factors contribute to effect size?

what factors do not?

Answer 5

effect size: the intrinsic size of an effect depends on

1. the measured effect (m1-m2)
2. the standard deviation

it does not depend on sample size!

N never contributes to measures of effect size

Question 6

cohen’s d: what is small/medium/large effect?

Answer 6

cohen’s d

small: 0.2
medium: 0.5
large: 0.8

Question 7

why would you use non parametric tests

Answer 7

parametric tests make assumptions

> observations interval/ratio level

> normally distributed populations

> equal population variance for different groups

>>> if those are violated, use non parametric tests

Question 8

what are 2 general ideas of non parametric testing?

Answer 8

non parametric testing

1. use of ordinal/nominal scales of measurement
2. no assumptions over underlying distributions

Question 9

how to apply non parametric test to interval/ratio level data?

Answer 9

transform data to ordinal scale by rank ordening

Question 10

how to calculate mann-whitney U

Answer 10

mann-whitney u

1. rank order scores of both groups in one dimension
2. count for each observation how many higher observations there are in the other group

> sum A / sum B

3. check whether n1 x n2 = A + B
4. U = smallest of A / B
5. smaller u, more evidence for difference

Question 11

how to calculate a wilcoxon matched pairs signed rank test

Answer 11

wilcoxon matched pairs signed rank

1. rank order differences, ignoring sign
2. W is the sum of the rank corresponding to the least occurig sign in the difference column
3. smaller w > greater evidence for difference

Question 12

chi-squared test: what general procedure?

Answer 12

chi square:

> nominal data: frequencies

> transform percentages to “raw frequencies” (numbers)

> compare observed frequencies to expected frequencies

Question 13

chi square:

how to interpret chi X²

how to determine degrees of freedom

Answer 13

X²

> if 0, then there is no difference between observed and expected >>> H0 true

> greater X², greater evidence for H1

degrees of freedom:

> df = (An-1)(Bn-1)

> An and Bn are the number of categories for A and B

Question 14

3 advantages of distribution free tests

Answer 14

distribution free tests

1. are simple
2. do not assume normality / equal variances
3. can be applied regardless of the scale of measurement

Question 15

3 disadvantages of non parametric tests

Answer 15

distribution free tests

1. involve loss of information due to transformation to ordinal scale
2. have less power than corresponding parametric test.
3. advanced statistical procedures require parametricitiy