One-way ANOVA

Question 1

Why do you use ANOVA rather than doing lots of t-tests?

Answer 1

ANOVA reduces the amount of type 1 error

Question 2

What is a type 1 error?

Answer 2

A type 1 error is when you reject a true null hypothesis.

Question 3

What is alpha?

Answer 3

Alpha is the probability of a type one error

Question 4

What is a type 2 error?

Answer 4

Accepting a false null hypothesis

Question 5

What is MS error?

Answer 5

MS error is an estimate of the population variance

Question 6

How do you calculate MS error?

Answer 6

We calculate MS error by pooling (averaging) the variance in each of te groups

Question 7

What is MS treatment?

Answer 7

An estimate of the population variance (different from MS error)

Question 8

What is the central limit theorem?

Answer 8

The central limit theorem states that the variance of means drawn from the same population equals the variance of the population divided by the sample size.

Question 9

When do you use a One-way ANOVA?

Answer 9

You use a one-way ANOVA when you have 1 independent variable with more than 2 levels

Question 10

How many degrees of freedom are there in a one way ANOVA?

Answer 10

2

Question 11

What is the formula for an ANOVA? What do the symbols mean?

Answer 11

Xij = μ + τj + eij

X = the persons score
μ = the overall mean
τ = the effect of which group they're in (the treatment)
e = the difference between that persons score and the mean of that group (also called the error)

Question 12

What is another way of writing τ?

Answer 12

μj - μ

Question 13

What is another way if writing eij?

Answer 13

Xij - μj

Question 14

Put into the formula:

Average weight is 65kgs
Average weight for women is 60kgs
Your weight is 80kgs

Answer 14

You = average + effect for women + special to you
80 = 65 - 5 + 20

Question 15

What is the effect of treatment?

Answer 15

The difference between the groups

Question 16

What is an assumption of MS treatment?

Answer 16

That the null hypothesis is true

Question 17

If the null hypothesis is true what does f equal?

Answer 17

F = 1

Question 18

If the null hypothesis is false what should f equal?

Answer 18

F > 1

F should be more than 1

Question 19

What are the 3 types of df?

Answer 19

df total
df treatment
df error

Question 20

How do you calculate df treatment?

Answer 20

Number of people in the treatment - 1

Question 21

How do you calculate df error?

Answer 21

df total - df treatment

Question 22

What does MS mean?

Answer 22

Mean squares

Question 23

What does SS mean?

Answer 23

Sum of squares

Question 24

What is the sum of squares?

Answer 24

Sum of squares represents deviation from the mean.

Question 25

What is eta-squared η2?

Answer 25

Eta-squares is the measure for effect size for a one-way ANOVA.

Question 26

How do you calculate effect size?

Answer 26

SS treatment / SS total
Or
Cohens f

F= the square root of η2 / 1-η2

Question 27

What do you need to calculate power?

Answer 27

Effect size
Sample size
Alpha (α)
State whether or not the analysis is priori or post hoc

Question 28

What do you need to calculate an effective sample size?

Answer 28

Effect size
Power
Alpha (α)
Priori or post hoc

Question 29

What do you do when you find that p is significant after running an ANOVA?

Answer 29

Do follow up tests. Find where the significant difference is

Question 30

What is family wise error rate?

Answer 30

The probability that a family of comparisons (multiple comparisons) will contain at least one type 1 error

Question 31

How do you calculate family wise error rate?

Answer 31

α x number of comparisons

Question 32

What are the 2 post hoc tests we were taught and when do you use each?

Answer 32

SNK (Newman keuls test)
Or when there are differences in group sizes us the
Scheffe test