Analysis of Variance 1

Question 1

The outcome of a chi-squared test is ____

Answer 1

nominal

e.g. frequency tables

Question 2

Chi-square goodness of fit test compares categorical data to a ________

Answer 2

theoretical standard

is it the same?

Question 3

Chi-squared test of association compares categorical data (e.g. frequency table) to _______

Answer 3

another frequency table

are they the same?

Question 4

In a t-test the outcome is _____

Answer 4

numeric

Question 5

T-tests compare ______

Answer 5

means

Question 6

One-sample t-tests compare a single mean to a ______

Answer 6

theoretical standard

Question 7

Independent samples t-tests compare _________

Answer 7

two means to each other

Question 8

Paired-samples t-tests compare

Answer 8

two means representing two time points to each other

Question 9

What sort of test should you use if you have more than 2 means (variables)?

Answer 9

ANOVA

Question 10

What does ANOVA stand for?

Answer 10

Analysis of Variance

Question 11

What is a one-way ANOVA?

Answer 11

Groups are defined by a single variable

E.g. ‘treatment’ could be ‘placebo, ‘drug 1’ or ‘drug 2’

Question 12

What is the test statistic for ANOVA?

Answer 12

F

Question 13

What might H0 and H1 look like for an ANOVA?

Answer 13

H0 = all x are equally effective at y

H1 = Some x are more effective at y

Question 14

What are the two types of variability, both captured with the sum of squares (SS)?

Answer 14

Between groups (SSb): how different are the group of means from one another

Within groups (SSw): how much do individuals within a group differ from the mean of that group

Question 15

What is the ‘sum of squares’?

Answer 15

The sum, over all observations, of the squared differences of each observation from the overall mean.

Question 16

Between groups variability (SSb) is low if…

Answer 16

SSb is low if the difference between group means and the global mean is low

Question 17

Between groups variability (SSb) is high if…

Answer 17

SSb is high if the difference between group means and the global mean is high

Question 18

What is within groups variability (SSw)?

Answer 18

How much individuals within a group differ from the group mean

Question 19

If you add SSb + SSw together to look for total variability, is this the test statistic (F)?

Answer 19

No, you need to correct for DOF

Question 20

What number should the F test statistic be if the means are different?

Answer 20

F is greater than 1

Question 21

If the null hypothesis is true, the sampling distribution of the F statistic is what?

Answer 21

An F-distribution

With N (sample size) and G (groups) as the association degrees of freedom

Question 22

If the null is true, the F statistic is typically?

Answer 22

Small

Question 23

R command for ANOVA?

Answer 23

ANOVA is performed in stages

aov() calculates the SS values etc

Creates an ‘aov’ object (variable) which contains lots of quantities of interest relating to ANOVA

summary() runs the hypothesis tests

other functions to pull out other things of interest

e.g. model1 <- aov( formula = speed ~ species, data = undead)

summary(model1)

Question 24

Explain the important outputs of an ANOVA table.

Answer 24

Question 25

How do you write up the results of an ANOVA table?

What are the important values to include in the stat block?

Answer 25

Stat block:

sampling distribution = F

G-1 degrees of freedom for SSb

N-g degrees of freedom for SSw

The value of the F statistic

the p-value

Question 26

In an ANOVA the test statistic reflects the total ______ of SStot

What is the formula for SStot?

Answer 26

variability

SStot = SSb + SSw

Question 27

The F-statistic is the ratio of these: ____/____

Answer 27

F = MSb/MSw

MSb = between groups variability corrected for DOF (SSb/(g - 1))

(g = seperate group means)

MSw = within groups variability corrected for DOF (SSw/(N-G))

N = total observations

G = group means from which they deviate