Lecture 8 - ANOVA

Question 1

What is does ANOVA test?

Answer 1

The difference between two or more population means

Question 2

What kind of test is the ANOVA? parametric or non-parametric

Answer 2

Parametric test

Question 3

What are the 4 assumptions of an ANOVA?

Answer 3

1) Random sampling
2) Homoscedasticity (=equal variances)
3) Independent measurements or observations
4) Normal distribution

Question 4

What is a variable?

Answer 4

a variable is what is measured by experimentalist = response or dependent variable

Question 5

What is a Factor?

Answer 5

The effect under investigation = independent variable

ie. salinity, temperature, etc.

Question 6

What are Factor Levels?

Answer 6

different treatment levels in an experiment it is something that the experimenter varies
ie. PCB or temp at various levels

Question 7

What are the 2 types (and sub-types) of ANOVA’s?

Answer 7

1) Univariate - one variable (response) measured
sub-types: one way (one factor) or multi-way (two or three factors)
2) Multivariate - more than one variable measured

Question 8

What are two main sources of variation?

Answer 8

1) between sample or population means = factor

2) Within samples or populations = error

Question 9

What is the variance in ANOVA?

Answer 9

is the difference between the population means high or low

Question 10

What kind of output do we want with sources of variation in regards to ANOVA?

Answer 10

We want to see a high factor variance between factors and a low error within the samples or populations

Question 11

When are samples unlikely to come from the same population?

Answer 11

If the variation between the sample means is large relative to the variation within the samples

Question 12

What does accuracy mean?

Answer 12

Accuracy means we know the true value. However this is not often the case

Question 13

If the means are almost the same, what happens to the residuals?

Answer 13

The residual becomes zero

Question 14

What is the ability to detect change in the response?

Answer 14

sensitivity and is related to the number of levels

high sensitivity is detecting change

Question 15

What happens when sample (level) means are close together?

Answer 15

high internal variability

Question 16

What is precision related to?

Answer 16

related to the error, and repeatability of the experiment.

Question 17

What happens when precision is close?

Answer 17

high repeatability

Question 18

What happens when precision is far?

Answer 18

low repeatability

Question 19

What happens with the null hypothesis when there is high within variance and low between?

Answer 19

Get closer to accepting the null that the populations come from the same population (there is no real difference between the populations

Question 20

What happens to the null hypothesis when there is high within variance and higher between variance?

Answer 20

End up mid-way between accepting and rejecting (not significantly accepting or rejecting)

Question 21

What happens to the null hypothesis when there is low within variance but higher between variance?

Answer 21

Reject the null and the two means/populations are in fact different from each other. No overlap with the between variance means significantly different

Question 22

Why was the Crakenback river Univariate ANOVA criticized?

Answer 22

The sites are not independent of each other because they flow into each other and the same statistics that were designed for manipulation were used for a monitoring study

Question 23

What was the result of the Crackenback river sites (factors) not being independent?

Answer 23

Huge bias and pseudoreplication

Question 24

What is pseudoreplication?

Answer 24

Treating data that is dependent as independent

Question 25

What should we do with faulty ANOVA stats (improper study such as dependent variables)?

Answer 25

Use descriptive non-parametric statistics

Question 26

What is a Type I error? How does alpha/critical value relate to this?

Answer 26

Type I error is the possibility of rejecting the true null hypothesis.
Critical value relates to this by the fact that you could be rejecting the null the same percent of the time as the critical value stands for
ie if alpha =0.05 then 5% of the time you could be rejecting the true null

Question 27

When do you reject the null hypothesis?

Answer 27

When the calculated p-value is less than the critical
or
when the calculated f-value is greater than the critical f (from a table)

Question 28

When do you significantly reject the null hypothesis?

Answer 28

When the p-value is very close to zero or the f-calc is far greater than the critical

Question 29

What are the 3 test assumptions for ANOVA regarding a residual diagnostics plot?

Answer 29

1) homogeneity of variance (constant variability: Scale location plot and levenes test
2) Independence: Residual vs.Fitted plot and Durbin-Watson test
3) Normality: Normal Q-Q plot and Shapiro-wilk normality test

Question 30

When do we see compliance with homogeneity?

Answer 30

When the residuals appear to fluctuate uniformly about zero
ie. uniform dispersion of square root residuals vs. fit
No detectable pattern

Question 31

When do we not see compliance with homogeneity?

Answer 31

When there is heterogeneity indicated by a tendency for the residuals to fan or funnel
Fan can face either direction

Question 32

Where is the value of the calculated f when it is greater than the critical f?

Answer 32

It is in the rejection region under the area of the curve (calculus)
this means different populations

Question 33

In an ANOVA table what are the residuals?

Answer 33

The replicates subtracted by 2?

n # of replicates-2 is the degrees of freedom of the residuals

Question 34

If the data doesn’t pass the parametric assumption tests, what can we do to continue with testing?

Answer 34

Log transform the data and test again. If the log data passes, you can continue with parametric statistics

Question 35

What is the TukeyHSD?

Answer 35

Honestly Significant Difference and is a pairwise comparison of all possible combinations of factors to determine which factors (ex. Sites) are no different or are different from each other

Question 36

What is the equation for determining how many comparisons are made in a pairwise comparison?

Answer 36

k x (k-1)/ 2

Question 37

How do you interpret a TukeyHSD plot?

Answer 37

If there is 0 difference between the means of the pairs then the confidence interval will encapsulate 0 and they are similar or the same
If the confidence interval does not touch 0 then the means are different. The further from 0 it lies means the closer the p-value is to 0 and rejecting the null and are significantly different.

Question 38

How do you interpret a TukeyHSD with respect to which sides an interval falls upon?

Answer 38

If the interval falls to the left then there is a positive difference
If it falls to the left then there is a negative difference