Lecture 1 - Basics

Question 1

What is a parameter?

Answer 1

an attribute of a population, or relationship between populations or variables

Question 2

What is a population?

Answer 2

Complete set of items that you want to draw inferences

Question 3

What is a sample?

Answer 3

a random subset of population

Question 4

exploratory vs confirmatory

Answer 4

Exploratory is generating hypotheses, confirmatory is testing hypotheses

Question 5

how to calc SE

Answer 5

SD divided by the square root of sample number

Question 6

type 1 error

Answer 6

false rejection of H0

Question 7

type 2 error

Answer 7

false acceptance of H0

Question 8

internal validity

Answer 8

extent to which you believe results of the study

Question 9

external validity

Answer 9

extent to which results apply to real word

Question 10

observational vs experimental

Answer 10

in an experiment, only one factor varies between conditions, so if theres a diff you can be certain it is casual

Question 11

what is the mean? for norm dist

Answer 11

value that minimises the sum of SQUARED deviations of data values from it
The average (i.e. sum(x)/N)
The central value
The most likely value to get if you were to sample from the population
Centre of ‘mass’

Question 12

what is the median?

Answer 12

value that minimums the sum of abosulte UNSQUARED deviations of data values from it

Question 13

which test if data is categorical?

Answer 13

chi squared

Question 14

which test if data is ranked or ordinal?

Answer 14

non - parametric,
• Mann-Whitney U (or Wilcoxin Mann-Whitney) – t-test to compare medians of 2 independent groups (groups must be completely independent of each other)
• Wilcoxin One sample
• Wilcoxon signed-rank test – same as paired t-test, it compares two related samples, matched samples, or repeated measurements on a single sample
• Kruskal-Wallis (One-way ANOVA with independent measures) – extends Mann-Whitney U when there are >2 samples. It compares two or more independent samples of equal or different sample sizes
• Friedman test (one-way ANOVA with repeated measures)
• Spearman correlation (non-para version of Pearson correlation)

Question 15

what test to use for interval or ratio data?

Answer 15

parametic, t-test, anova, reg etc

Question 16

what is an outlier? and who made this definition

Answer 16

an observation which deviates so much from the other observations as to arouse suspicions that it was generated by a different mechanism - Hawkins

Question 17

real life examples of when we look for outliers

Answer 17

Fraud detection & credit card theft- Unusual spending patterns
Medical diagnosis - Problems suggested by test results that don’t fit normal pattern for age/sex/history
Detecting drug cheats in sport - Abnormally high/low blood steroids, etc.
Detecting measurement errors or unusual events

Question 18

3 ways to detect outliers

graphs used to detect them

boxplot- what do they need to be?

Answer 18

Analyse sample - data points that are ‘far from’ the rest are outliers
Fit model to data – outliers are points that don’t fit that model
Either approach can be statistical or purely graphical (‘by eye’)

Start with graphical methods

can use hist, scatterplot, normal probability plot (or QQ Plot), boxplot = Points higher than one-and-a-half inter-quartile ranges from the upper quartile, or lower than than one-and-a-half inter-quartile ranges from the lowerquartile, are plotted as circles and so identified as possible outliers.

Question 19

what is the R package for outliers? and what could be a drawback?

Answer 19

Dixon test (only works with small sample sizes (<30) only

Question 20

which two tests are robust to even quite large violations of normality and homogeneity of variance and when do they become less so?

Answer 20

ANOVA and t-test - One-way ANOVA only starts to give odd results if largest variance is >9x smallest

Question 21

what is homogeneity of variance? what test is it used in and when can this not be violated?

Answer 21

The assumption of homogeneity of variance is that the variance within each of the populations is equal. This is an assumption of analysis of variance (ANOVA). ANOVA works well even when this assumption is violated except in the case where there are unequal numbers of subjects in the various groups.

Question 22

what are Robust’ statistical methods? (there are 4 answers)

Answer 22

Non-parametric tests
Simple, accepted, but range of tests limited
Parametric tests on ranked data
Permutation tests
Flexible, but require decent sample size per group (see lecture on Monte Carlo methods)
Parametric methods that work on the ‘middle’ of the data

Question 23

non parametric of the following:
one sample t test
two sample t test
paired t test
one way anova 
one way repeated anova
corrrelation

Answer 23

one sample t test = Wilcoxin
two sample t test = Mann Whitney U
paired t test = Wilcoxin matched pairs signed rank
one way anova = Kruskal wallis
one wau repeated anova = friedman test 
corrrelation = spearman

Question 24

when residuals are normally distributed (and so parametrics are OK) the non-parametric equivalents are … less powerful.

Answer 24

5%

Question 25

When residuals are non-normal, what has more power? non para or para?

Answer 25

non parametric

Question 26

what are false positives?

Answer 26

type 1 error

Question 27

pros and cons of ranked parametric

Answer 27

Doing parametric stats on rank-transformed data seems to give you the same Type I error rate and power as the custom non-parametric test … and has the bonus of more possible tests being available (i.e. any parametric test) But, you can’t interpret the exact form of a relationship sensibly, so beware

Question 28

limitation of reg on ranked data

Answer 28

Regression of rank(Y) on rank(X) tells you they are related, but not the shape of curve robust regression ignores outliers

Question 29

why are missing values bad?

Answer 29

Lead to unbalanced design and so… | Loss of power (a shame but not tragic)

Question 30

types of missing values

Answer 30

Missing Completely At Random - good Missing At Random = Unobserved data are not random but follow the same pattern as the observed values Not Missing At Random = Unobserved values are different from the observed ones – a bigger problem.

Question 31

when are missing values okay?

Answer 31

when they are missing completely at random, or they are not random but follow the same pattern as the observed values.

Question 32

when are missing values bad?

Answer 32

if not missing at random and if the unobserved values are different from the observed ones

Question 33

what to do if missing at random?

Answer 33

ignore NA's, unless repeated measures.. Step 1 : investigate missing values, where are they Find whether the ‘NA’s are randomly distributed with respect to the predictors and responses can do Loglinear model on missing/non-missing to see if they are missing at random! or can Replace with values that don’t bias subsequent analyses - such as most common value for that variable if there is normal distribution BUT if data skewed use median!! Or using other variables that are correlated OR using 10 nearest neighbours

Question 34

what does DMwR package use when fitting most central value?

Answer 34

median for numeric variables | the mode for categorical variables

Question 35

survival analysis examples

Answer 35

-Parametric Specify distribution, e.g. exponential, Weibull -Cox regression ‘semi-parametric’ – assumes survival curves have same shape, but different rates -Non-parametric Can only test one factor

Question 36

what to do with outliers?

Answer 36

delete if known cause. Use robust statistics to reduce their influence Or replace with ‘non-influential’ values

Question 37

what is censoring?

Answer 37

Data points where the actual value isn’t known but you can set boundaries on what it must have been Censoring is a special case of ‘partial information’ (not missing) that can be dealt with by survival analysis

Question 38

what is the basis to a statistical model?

Answer 38

Pattern observed = signal + noise the mean is a fixed signal, as is a slope, as is the difference between two means Random normal variation – the ‘noise’

Question 39

what are modeling?

Answer 39

not the data, but the population from which our sample came from

Question 40

overfitting.. how can it come about

Answer 40

more parameters can mean better fit, but risk of overfiting and can just end up redescribing the data

Question 41

Can all population parameters be estimated accurately with a large sample size?

Answer 41

no, better to start with the mean - can estimate the population mean from your sample mean and the likely range of values around this from your sample standard deviation

Question 42

why is SD biased?

Answer 42

Because the values in a sample are more likely to come from near the mean So the sample is unlikely to have as many extreme values as the parent population So the variance (and stdev) of the sample are lower than that of the population

Question 43

how does a t test calculate its value?

Answer 43

sample mean measured in “standard errors” by dividing your sample mean by the standard error

Question 44

what is power? what do you need to know to calc it?

Answer 44

probablity of rejecting the null hyp if the null hyp is false i.e. correct rejection of H0 probability of a type II error need effect size and expected SD

Question 45

internal validity

Answer 45

Internal validity is the extent to which you believe the results of the study ``` Factors that increase internal validity: Homogeneous sample (e.g. single strain, single sex, single genotype) Homogeneous conditions (constant temperature, humidity, lighting regime, diet) Single experimenter administering treatments ```

Question 46

Is it ever justified to raise the threshold p-value?

Answer 46

yes if type 2 error is far worse than a Type I error

Question 47

problems of mulitple testing

Answer 47

the chance of at least one test being ‘significant’ (p<0.05) is around 40% EVEN WHEN THE NULL HYPOTHESIS IS TRUE!

Question 48

solutions to avoid multiple testing

Answer 48

Fix primary and secondary dependent variables a priori Control experiment-wise (family-wise) alpha and adjust test-specific alpha accordingly Use multivariate methods Data reduction

Question 49

pseduoreplication?

Answer 49

Improper inflation of sample size due to non-independence of data

Question 50

objects in R include..

Answer 50

Single variables Arrays and matrices Structures (containing, e.g., different types of variables: text or numeric

Question 51

sep "" sep '\t' sep '\n'

Answer 51

sep "" = space delimited data sep '\t' = tab-delimited data sep '\n' = new line delimited data

Question 52

correlation vs regression?

Answer 52

correlation requires norm dist, regression - Residuals around the line relating y to x must be normally distributed, x need not be normal (nor even y)

Question 53

Ordinary Least Squares

Answer 53

we minimise the squares of the residuals, (+ve/−ve diffs have same effect)

Question 54

MA vs RMA (diffs in variance)

Answer 54

``` Major Axis (MA) Regression if variances similar ``` Reduced Major Axis (RMA) Regression if variances unequal