Lecture 5 - Statistical Power

Question 1

What are three examples of post-hoc tests?

Answer 1

Tukey hsd
T test
Scheffé

Question 2

What does hsd stand for? As in tukey hsd test

Answer 2

Honestly significant difference

Question 3

What does the tukey hsd test do

Answer 3

It establishes the smallest possible difference between two means

It uses a critical difference value. This comes from a fancy equation.

Any mean difference greater than the critical difference is significant.

Question 4

How can a t test be used as a post hoc test?

Answer 4

It is modified - t is given by 0.05/c where c is the number of comparisons being made.

This is called a bonferroni correction

Question 5

What do post hoc tests mean for error rates?

Answer 5

They’re conservative, which means they reduce the chance of type one errors but greatly increase the chance of a type two error

This means we can be very confident when we do find an effect

But it does mean null results are hard to interpret. There may still be an effect but we just can’t find it. (Low power??)

Question 6

What are the four assumptions of the f ratio

Answer 6

Independence of numerator and denominator

Random sampling

Homogeneity of variance

Normality (normally distributed populations)

Question 7

How can we test the assumptions of an ANOVA?

Answer 7

Independence and random sampling are down to the experimenter so we assume they’ve been met

But we can test homogeneity of variance and normality

Question 8

How can we test for homogeneity of variance?

Answer 8

In a between groups design:
Hartley’s F-Max
Bartlett
Cochran’s C

Within or mixed designs:
Box’s M

Question 9

How would you do Box’s M by hand?

Answer 9

You’d do (largest variance/smaller variance)

Question 10

What are the three most common tests of normality and how do they work?

Answer 10

Skew
Lilliefors
Shapiro-Wilks
(The bottom two are very hard to do by hand but SPSS has them)

They compare the actual distribution of data to a model of normal distribution

They are all pretty sensitive, and more so with large samples

Question 11

How do we test skew?

Answer 11

We can test if the skew is significantly different from 0. If everything was perfectly normally distributed skew would be 0.

We use a z-score distribution to do this

If the z score is greater than + or - 1.96 then the sample is significantly different than a normal distribution

Question 12

What is a transformation and why would we use one?

Answer 12

Mathematical operations that we can apply to the data before we conduct an ANOVA

we use them if we don’t meet the assumptions of an ANOVA but we really want to perform one

Question 13

What are the three circumstances where no transformations will make the data fit the ANOVA assumptions

Answer 13

Heterogenous (different) variances
Heterogenous distributions
Both of the above

Question 14

What is defined as moderate, substantial and severe skew?

Answer 14

Moderate - 1.96-2.33
Substantial - 2.34-2.56
Severe - 2.56 and above

Question 15

What transformation would you use for moderate positive skew

Answer 15

Square root

Question 16

What transformation would you use for moderate negative skew

Answer 16

Square root (K-X)

Question 17

In a transformation what is K?

Answer 17

The largest number in the data plus one

Question 18

What transformation would you use for substantial positive skew

Answer 18

Logarithm

Question 19

What transformation would you use for substantial negative skew

Answer 19

Logarithm (K-X)

Question 20

What transformation would you use for severe positive skew

Answer 20

Reciprocal

Question 21

What transformation would you use for severe negative skew?

Answer 21

Reciprocal (K-X)

Question 22

How does transforming the data affect error chances?

Answer 22

Increases type one error rate but decreases type two error rate

Question 23

What do we do if we can’t transform the data? (Eg those three situations)

Answer 23

We proceed with analysis but we take care to caution the reader when we are interpreting the results.

Question 24

What should you say instead of saying you can accept H0?

Answer 24

You must say you ‘fail to reject the null hypothesis’ it sounds much better and is more accurate!

Question 25

What is statistical power?

Answer 25

The probability of detecting an effect when one is present (so basically the probability of NOT making a type two error)

It’s given by 1-ß. Where ß is the probability of making a type two error

Question 26

What are the three things that power depends upon?

Answer 26

Alpha level
Sample size
Effect size

Question 27

What happens to power if we make alpha less strict? Such as 0.1 instead of 0.05

Answer 27

Power is increased as we are less likely to miss an effect if there is one

But of course type one error chance is increases as a result

Question 28

How does sample size affect power?

Answer 28

Small samples have less power than large ones

It does plateau out at a point though

Question 29

What can we do with power to help us plan out study

Answer 29

We can actually use power to calculate the ideal sample size for a piece of research

There are many different formula for this depending on experimental design

Question 30

How does variability affect power

Answer 30

Power decreases as variability around the mean decreases - you get more power THR further apart two means are (naturally)

Question 31

What are the measures of effect size for an ANOVA?

Answer 31

Measures of association:
Eta-squared : funny n symbol)
R-squared
Omega squared (boob shape symbol)

Measures of difference:
D
F

Question 32

What is eta squared?

Answer 32

a measure of effect size for anova

a measure of association

it is the proportion of total variance that can be attributed to an effect

Question 33

what is partial eta squared?

Answer 33

the proportion of the effect + error variance that is attributable to an effect

it is a measure of association and a measure of effect size for anova

Question 34

what is r squared

Answer 34

a measure of association used to measure ANOVA effect size

it thinks of ANOVA as a regression like model and it is the proportion of variance that this model is able to explain

Question 35

What is omega squared

Answer 35

a measure of association used to measure ANOVA effect size

it is an estimate of the dependent variable population variability accounted for by the independent variable

Question 36

What is d?

Answer 36

a measure of difference used to measure ANOVA effect size

it is used when there are only two groups and it is the standardised difference between these two groups

Question 37

what is f/cohens f?

Answer 37

a measure of difference used to measure ANOVA effect size

an average, standardised difference between the 3 or more levels of the IV

small effect f=0.1
medium effect f=0.25
large effect f=0.4

Question 38

What are the two strategies we may use to estimate effect size?

Answer 38

1 - deciding what effect size we want based on previous research in this area (best option)

2 - based on theoretical importance - do we want a small, medium or large effect size theoretically? (not as good)

Sometimes there is no previous research so we cant do 1, we must do 2

Question 39

what size effect size do we report?

Answer 39

ANY! especially when the result is non significant

Question 40

define retrospective justification

Answer 40

saying that there is a non significant result because power was low or that there cant be an effect as power is high so we would have found one if there was one

Question 41

When do I use tukey and when do I use Scheffé

Answer 41

Tukey can only be used when sample sizes are equal between groups

Scheffé can be used either way but normally is used for unequal samples