Lecture 8 - Statistical Tests IV: ANOVA, Kruskal-Wallis, ANCOVA

Question 1

the three statistical tests used for comparing two groups against a continuous variable:

Answer 1

students t-test: both groups are parametric with equal variances

welch’s t-test: both groups parametric but with unequal variance

Mann-Whitney U Test / Wilcoxon Test: non-parametric data (no assumptions

Question 2

what does ANOVA stand for?

Answer 2

ANOVA means “analysis of variance”

Question 3

what sort of variables are present in ANOVA testing?

Answer 3

response variables are continuous and explanatory variables are categorical

Question 4

ANOVA and linear regression are identical except for:

Answer 4

the type of explanatory variable

Question 5

what does ANOVA actually do?

Answer 5

ANOVA compares means of factor levels (treatment levels), by analysing variances associated with them

Question 6

ANOVA procedure:

Answer 6

(1) choose a model

(2) estimate the parameters of the model

(3) model fit: how well does the model describe out data?

Question 7

command for creating an ANOVA model in R:

Answer 7

> m1<-aov(y.v~x.v)

m1 = model name (can be anything)

> summary.aov(m1)
summary.lm(m1)
tapply(y.v, x.v, mean)

Question 8

ANOVA assumptions:

Answer 8

• residuals are normally distributed
• variance is associated with the distribution of the residuals is constant (i.e. variation in Y does not differ among the factor levels)
• individual measurements are independent
• data comes from a random sample

Question 9

diagnostic ANOVA plot in R:

Answer 9

> plot(m1)

• we want “sky at night” and a normal-q-q line with data stuck to the line

Question 10

after completing your ANOVA diagnostic plots [plot(m1)] you have results that show non-parametric data, what do you do?

Answer 10

if you dont recieve “sky at night” or residuals following the line tightly you must use the non-parametric equivalent of the ANOVA test - the Kruskal-Wallis test

Question 11

kruskal-wallis test command:

Answer 11

kruskal.test(y-variable ~ x-variable)

Question 12

what is the difference between the ANOVA and Kruskal-Wallis Test?

Answer 12

the difference is that ANOVA testing has assumptions but Kruskal-Wallis has no assumptions

Question 13

similarities in ANOVA and linear regression testing:

Answer 13

• both are parametric tests
• response variable continuous and explanatory variable categorical
• compares means of factor levels (treatment levels) by analysing variances associated with them
• assumptions: residuals are parametric, variance homogeneity; individual measurements are independent; data from random sample

Question 14

what is ANCOVA?

Answer 14

ancova is a analysis of co-variance

Question 15

what does ANCOVA combine?

Answer 15

ANCOVA combines elements of linear regression and ANOVA

Question 16

in ANCOVA, what are the response and explanatory variables:

Answer 16

response variable: continuous
explanatory varibale(S): categorical and continuous

Question 17

what is the ANCOVA process?

Answer 17

• number of factor levels (or categories) = number of linear regressions
• estimation of the slope and intercept for each factor level (category)
• model simplification (principle of parsimony)

Question 18

models should be simplified until:

Answer 18

they are minimal adequate

“model should be as simple as possible, but no simpler”

Question 19

what is the only difference between ANOVA and linear regression?

Answer 19

linear regression is the relationship between two continuous variables whilst ANOVA is a test for the relationship between a continuous response variable and an explanatory categorical value