Week 2: One-way ANOVA, SS, Df, MSE, Fstat, Effect sizes

Question 1

what is the underlying ANOVA equation?

Answer 1

Score = Grand mean + treatment effect + residual error (measurement and individual differences)

Question 2

Essentially, how does ANOVA break down variance? and what does the comparison of this breakdown produce?

Answer 2

Into 2 parts

• Variance due to treatment
• Error variance

Comparison of these two variances produces the F STATISTIC

Question 3

What are the assumptions of a between ANOVA?

Answer 3

Homogeneity of variance: SD for all groups is about the same
Normality: error is normally distributed
Independence of observation: truly between design

Question 4

What are degrees of freedom?

Answer 4

They represent the number of independent pieces of data, or values that are free to vary after a mean has been estimated

Can have total, treatment and error df

Question 5

What is the calculation for total degrees of freedom?

Answer 5

Number of observation - 1

N-1

Question 6

What is the calculation for treatment degrees of freedom?

Answer 6

Number of groups - 1

k-1

Question 7

What is the calculation for error degrees of freedom?

Answer 7

df(total) X df(treat)

k(N-1)

Question 8

What is mean square?

Answer 8

Variance. Obtained by dividing the sum of squares for each effect by the corresponding degrees of freedom
So for total =SS(total)/Df(total)
Treatment = SS(treat)/Df(treat)
Error = MSE/df(error)

Question 9

F statistic calculation?

Answer 9

MS(treatment)/MS(error)

Question 10

What can the F statistic tell us about the null hypothesis?

Answer 10

Because of the way is is calculated, if the null is true these values should be similar and therefore F= close to 1

The further away from 1 F is, the less likely it is that the null is true

Question 11

How do you set up data in jamovi for a one-way ANOVA?

Answer 11

One column for each IV and the DV

One row for each participant

Question 12

How do you do a one-way ANOVA in Jamovi?

Answer 12

ANOVA -> ANOVA
Drag DV into the dependent variable box
IV into fixed factors
Descriptives (explore)

Question 13

What do we do then if the ANOVA output is significant (one-way)?

Answer 13

Click on the post hoc section under analysis
Put IV into the box on the right and click on post hoc desired - typically tukey

Can go into estimated marginal means - get a plot

Question 14

Reporting a one-way ANOVA?

Answer 14

Means, SD, sample sizes

F(dfb,dfw) = F, p = p

Significant:
Tukey post hoc tests at an alpha level of 0.05…

Question 15

What is the difference between statistical significance and psychological significance?

Answer 15

Statistical: tells us whether it would occur by chance or not - relates to alpha

Psychological: Asks whether a finding is meaningful - relates to effect size

Question 16

What are d family effect sizes and what do they do?

Answer 16

Cohens d, hedges g, cohens f

They quantify the size of the difference between means in terms of SD units

Question 17

What are R family effect sizes and what do they do?

Answer 17

Eta squared, omega squared, adjusted Rsquared

Look at how strongly associated the IV and DV are

Question 18

Explain cohens D

Answer 18

part of d family so looks at the difference in means in terms of their SD
The further away this is from 0, the larger the effect

Question 19

What is considered a small, moderate and large cohens d?

Answer 19

0. 2 small
1. 5 moderate
2. 8 large

Question 20

Is cohens d biased at all? how do you correct this?

Answer 20

It can be biased when you have a smaller sample size (overly generous for treatment effect)
- apply a correction factor. in this case you can use hedges g. It is equivalent to cohens d but accounts for small sample size bias

Question 21

What is cohens f?

Answer 21

Used when there are 3+ means

1/2 D so a small is 0.1, moderate 0.25, large 0.4

Question 22

What is eta squared and r squared?

Answer 22

They are squared correlations between the IV and DV

=SS(treatment)/SS(total)
Gives a score between 1 and 0
close to 1 as possible is best but not common in psychology

Question 23

What does it mean if we have a smaller eta squared?

Answer 23

There is more variation in DV measurement from other things, not IV

Question 24

How would we interpret, say an eta squared value of 0.477?

Answer 24

Means that 47.7% of the variance in the DV can be explained by the IV

Question 25

Eta squared and Rsquared can be biased… what can we use instead?

Effect stengths?

Answer 25

Omega squared and adjusted R squared
(eta squared can be biased because the means are sample means derived from a larger population)

Small effect - 0.02, medium - 0.15, large - 0.35

Question 26

What are confidence intervals?

Answer 26

Interval estimate that attempts to set limits which have a high level of encompassing the true population mean

Question 27

Explain a 95% confidence interval

Answer 27

If we repeated 100 times, 95% of these will include the true population mean

Question 28

In relation to confidence intervals, how do we know if the difference in means is statistically significant?

Answer 28

If 0 is outside range (doesn’t contain null hypothesis value)