Lecture 9: Statistical Tests V: ANCOVA, Complex Models & Simplification

Question 1

is anova parametric or nonparametric?

Answer 1

anova is a parametric statistical test

Question 2

what assumptions are identical to those of ANOVA?

Answer 2

the assumptions in ANOVA and linear regression are identical

Question 3

why not have many models with just one explanatory variable? (why ancova and just not many anova?)

Answer 3

(1) explanatory variables might influence each other

(2) multiple test on the same data sets should be avoided

Question 4

ancova meaning:

Answer 4

analysis of covariance

Question 5

what does ancova combine?

Answer 5

ancova combines elements of linear regression and anova

Question 6

type of response and explanatory variable in ancova:

Answer 6

response variable in ANCOVA testing is continuous

explanatory variableS are both categorical and continuous

Question 7

what is the ANCOVA process:

Answer 7

(1) number of factor levels (or categories) = number of linear regressions

(2) for each of those factor-levels (categories) we estimate the slope and intercept [similar to linear regression]

(3) model simplification (using the principle of parsimony - simpler is better)

Question 8

principle of parsimony in statistical terms:

Answer 8

• should be simplified until minimally adequate with as few parameters as possible

Question 9

first line for model simplification command in R when you have interactive affects between groups (2 slopes, 2 intercepts):

Answer 9

asterics between explanatory varibales shows there is an interaction between them also the individual effects of age and sex

(1) > m1<-aov(y-variable ~ explanatory-variable-1 * explanatory-varibale-2)

you could instead write the below line of code with (:) and (+) instead of an asterisks however for now the asterisks will cover it in less amount of code

Question 10

first line for model simplification command in R when you have additive affects between groups (1 slope [parallel], 2 intercepts):

Answer 10

m2<-aov(response-variable ~ explanatory-1 + explanatory-2)

Question 11

when we have 1 slope the slopes are the same, how can we tell this?

Answer 11

we can tell if only one slope is present if the two slopes are parallel to one another - [parallel - just one slope]

Question 12

what symbol do we use to connect interactive explanatory variables?

Answer 12

asterisks ( * )

e.g: explanatory-1 * explanatory-2

Question 13

what symbol do we use to connect additive explanatory variables?

Answer 13

plus (+)

e.g: explanatory-1 + explanatory-2

Question 14

how do we simplify our model if we have [1 slope, 1 intercept] or [2 intercepts, 0 slope]?

Answer 14

in this case you simply apply a normal ANOVA test as there is only one significant explanatory variable that has an effect

> m3 <- (response variable ~ explanatory variable)

Question 15

what do we do if we have a graph in which neither of our explanatory variables have an effect on our response variable?

Answer 15

we simple create a model where:

> m4 <- aov(weight ~ 1)

Question 16

because we want the “minimal adequate model” how can we test to see if we can simplify our model given we initially have the more complicated > m1<-aov(y~x*x) model?

Answer 16

you create two models - m1 & m2 where m1 is the complicated asterisks model and m2 is the less complicated plus model

you input both of these models and then you can put those aov models 1 & 2 into the following command

> anova(m1,m2)

if the p-value is bigger than 0.05 this means we CAN simplify to the plus model as the explanatory difference is not significantly less than the asterisks

if the p value is smaller than 0.05 we cannot simplify the asterisks model to the addition model as the explanatory power of the simpler model is significantly less

Question 17

SIMPLE model simplification procedure:

Answer 17

(1) fit the maximal model [through graphical slope & intercept interpretation]

(2) start model simplification

(3) stop model simplification when minimal adequate model is reached [do this via > anova(m1,m2) and looking for p > 0.05]

Question 18

anova and linear regression are identical except for (X) and the R-code is (Y)

Answer 18

(X) the type of explanatory variable

(Y) identical for both of these tests

Question 19

what statistical tests are all somewhat the same in their r-code?

Answer 19

one-way-anova, factorial anova, ancova & linear regression