# Lecture 5 - Statistical Power Flashcards

1
Q

What are three examples of post-hoc tests?

A

Tukey hsd
T test
Scheffé

2
Q

What does hsd stand for? As in tukey hsd test

A

Honestly significant difference

3
Q

What does the tukey hsd test do

A

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.

4
Q

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

A

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

5
Q

What do post hoc tests mean for error rates?

A

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??)

6
Q

What are the four assumptions of the f ratio

A

Independence of numerator and denominator

Random sampling

Homogeneity of variance

Normality (normally distributed populations)

7
Q

How can we test the assumptions of an ANOVA?

A

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

8
Q

How can we test for homogeneity of variance?

A

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

Within or mixed designs:
Box’s M

9
Q

How would you do Box’s M by hand?

A

You’d do (largest variance/smaller variance)

10
Q

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

A

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

11
Q

How do we test skew?

A

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

12
Q

What is a transformation and why would we use one?

A

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

13
Q

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

A

Heterogenous (different) variances
Heterogenous distributions
Both of the above

14
Q

What is defined as moderate, substantial and severe skew?

A

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

15
Q

What transformation would you use for moderate positive skew

A

Square root

16
Q

What transformation would you use for moderate negative skew

A

Square root (K-X)

17
Q

In a transformation what is K?

A

The largest number in the data plus one

18
Q

What transformation would you use for substantial positive skew

A

Logarithm

19
Q

What transformation would you use for substantial negative skew

A

Logarithm (K-X)

20
Q

What transformation would you use for severe positive skew

A

Reciprocal

21
Q

What transformation would you use for severe negative skew?

A

Reciprocal (K-X)

22
Q

How does transforming the data affect error chances?

A

Increases type one error rate but decreases type two error rate

23
Q

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

A

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

24
Q

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

A

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

25
Q

What is statistical power?

A

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

26
Q

What are the three things that power depends upon?

A

Alpha level
Sample size
Effect size

27
Q

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

A

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

28
Q

How does sample size affect power?

A

Small samples have less power than large ones

It does plateau out at a point though

29
Q

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

A

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

30
Q

How does variability affect power

A

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

31
Q

What are the measures of effect size for an ANOVA?

A

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

Measures of difference:
D
F

32
Q

What is eta squared?

A

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

33
Q

what is partial eta squared?

A

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

34
Q

what is r squared

A

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

35
Q

What is omega squared

A

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

36
Q

What is d?

A

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

37
Q

what is f/cohens f?

A

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

38
Q

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

A

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

39
Q

what size effect size do we report?

A

ANY! especially when the result is non significant

40
Q

define retrospective justification

A

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

41
Q

When do I use tukey and when do I use Scheffé

A

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