lec 4 /5 /6/7

Question 1

What are CI?

Answer 1

suggest that 95% of sample CI would be expected to include true population mean

Question 2

What do we use for computer based random sampling

Answer 2

monte carle methods

Question 3

sampling without replacement

Answer 3

permutation

Question 4

sampling with replacement and what is this?

Answer 4

Bootstrapping - values can be picked at random more than once

Question 5

what is a residual?

Answer 5

the diff between the observed value of the dv and the predicted value. Each data point has one residual, it is the error/unexplained variation

Question 6

what is the line of best fit/

Answer 6

finding a slope and intercept that minimise variation of data around the line (in other words minimise the residuals)

Question 7

how to calc total vairance

Answer 7

variation predicted by x + unexplained variation

Question 8

if x doesnt predict y, what is the total variance?

Answer 8

unexplained variation by x

Question 9

if x predicts y well, what is the total variance?

Answer 9

variation predicted by x

Question 10

When to use reduced major axis or major axis?

Answer 10

if both x and y have error and the ‘true’ relationship is of interest (they must be correlated)

MA if variances similar

Reduced Major Axis (RMA) Regression
if variances unequal

Question 11

what to use to predict y from x?

Answer 11

Ordinary Least Squares - this requires norm distribution of residuals not x

Question 12

what to do with non-linear relationship?

Answer 12

transform to data to linear
fit functions using maximum likelihood
or polynomial regression.

Question 13

which contrast does this desribe? ‘if squared, values will be independent’

Answer 13

polynomial

Question 14

why is a balanced design good?

Answer 14

it is orthogonal and so increases power

Question 15

assumption of mixed model is that

Answer 15

repeated measures must be uncorrelated

Question 16

Why might you chose to use monte Carle methods over non parametric ?

Answer 16

When data is skewed and the two have diff shapes, wilcoxin / Mann Whitney u assume they have the same shape

Question 17

Permutation test

Answer 17

Assumes that if groups aren’t different, then group membership should be arbitrary, therefore re labels groups lots and lots of times and this shouldn’t make a difference to group means or medians

Question 18

What is the p value in permutation test?

Answer 18

The probability of the observed mean if the null hypothesis is true

Question 19

Why would you use permutation over para or non para? What are the advantages?

Answer 19

Not limited to measures of location like mean and median, can use any measure to do calculations on probability from the sample

Question 20

Pros and cons of permutation test

Answer 20

Good - no distribution assumptions, can be customised for any problem, can see where p value comes from

Bad - unfamiliar to referees, sums can’t be readily checked, need to be customised

Question 21

How to do permutation on anova type (multi group differences)

Answer 21

Can use the average difference between group means/medians

Or can use F (total variance - within group variance / within group variance) - f usually requires norm dist but not in this case

Can also use order of means and then find the probability that this order occurs by chance

Question 22

Wilcoxin is distribution free but not ..

Answer 22

Assumption free

Question 23

If data can’t take values <0 what do we do? Eg number of frogs in a pond.. not sensible to transform

Answer 23

Estimate the mean and ci as this would be more useful to see where population will lie, can use maximum likelihood - pick known distribution that matches sample and estimate mean/median and ci
(The sample mean is a maximum likelihood estimate of population mean)
Can still do this if distribution is not normal! Stats package does for you

or if distribution isn’t like any off the shelf distribution use bootstrapping (but this does require large sample, not so good for hypothesis testing)

Question 24

What are CI?

Answer 24

95% of sample CI will include the true population mean

Question 25

Permutation vs bootstrapping

Answer 25

Permutation tests a shuffle of the sample,

Bootstrapping re-samples with replacement

Question 26

How large does sample need to be for bootstrapping?

Answer 26

> 50

Question 27

what is centering?

Answer 27

when there is multiple colinearity in polynomial regression so Use (x – mean(x))2 so there is no multiple colinearity

Question 28

why do reg and ANOVA get diff results when there is more than 2 groups?

Answer 28

If we have more than two groups, then the regression and the ANOVA will yield different results: regression will fit a straight line through all three groups (and thus not necessarily joining the means), whereas ANOVA fits separate means to each group.

ANOVA tests for significance of the two differences between the three means

Regression tests for significance of a single line fitted through all the data

Question 29

what is ordinary least squares?

Answer 29

is a method for estimating the unknown parameters with the goal of minimizing the sum of the squares of the differences between the observed responses and the predicted