Teaching block 3 - Statistics - (weeks 7,8&9)

Question 1

what are the 2 largest categories for data

Answer 1

categorical and quantative

Question 2

what are the 3 types of categorical data

Answer 2

binomial - presence / absence
nominal - non ordered groups (yellow)
ordinal - ordered groups eg low med and high

Question 3

what are the 2 types of quantitative data

Answer 3

continuous and descrete
continuous data can also be interval or ratio data.

Question 4

what are the 3 main data types in EEA

Answer 4

continuous, descrete and nominal

Question 5

what practices should be avoided when carrying out statistical tests

Answer 5

cherry picking (selecting best data)
p-hacking (continuous analysis)
harking (hypothesising after result)
fishing experiments (testing between random variables to find an effect)

Question 6

what are good statistical practices

Answer 6

consider analysis and stats test before data collection
make sure data is quality as well as quantity
document all data prep ands analysis
make sure data meets assumptions of the stats test

Question 7

what is hypothesis testing

Answer 7

it tells us how different is different enough when looking at two supposedly differing groups.
it gives a chance to reject the null hypothesis

Question 8

probability distribution facts

Answer 8

area under curve = 1
they describe the probability of obtaining a certain value with in a range

Question 9

what is a p value

Answer 9

probability of either outcomes assuming the null
choose a significance level (0.05). this is the probability of a false positive (type I error)

Question 10

when should a chai squared test be used X^2

Answer 10

when both the explanatory and response variables are categorical

Question 11

give an example of when a X^” test should be used

Answer 11

do humming birds have a preference for flower color.
when setting this experiment up make sure the number of red and yellow flowers is in a ration 1:1

Question 12

how should a X^” test be carried out

Answer 12

1. calculate the expected frequencies under null hypothesis
2. quantify difference between expected and observed frequency’s using the X^” equation.
3. calculate degreed of freedom
4. find p-value with degrees of freedom
5. check to see if X^2 value is past the critical value on the probability distribution

Question 13

what is the chai squared equation

Answer 13

sum of - (observed - expected)^2/expected

Question 14

what is a degree of freedom?

Answer 14

the number of data points that are free to change independently without changing the statistical parameters of the sample

Question 15

why are degrees of freedom important

Answer 15

the probability distribution for the p value changes significantly depending on the degrees of freedom in the experiment

Question 16

what are the limitations of the chai squared test

Answer 16

• there must be more than 5 numbers in each class, if not they should be combined

Question 17

chai squared checklist

Answer 17

• always calculate observed and expected VALUES not proportions
• make sure null is biologically sound
• use null as basis to calculate the expected values
• always quote degrees of freedom

Question 18

when should a linear model be used

Answer 18

when the response variable is continuous

Question 19

when should an ANOVA model be used

Answer 19

continuous response variable and categorical explanatory variables

Question 20

what does an ANOVA model analyse

Answer 20

analyses the difference (ratio) between among group variation and with in group variation.

Question 21

what would a significant result look like from an ANOVA test

Answer 21

if the among group variability is greater than the within group variability. this means there is significant differences between groups but not a lot of variation with in the groups.

Question 22

what is mew

Answer 22

the global mean (across all groups)

Question 23

what does it mean if each group is very close to mew

Answer 23

there is no relationship between the groups

Question 24

what is a residual regarding ANOVA

Answer 24

the difference of each data point from the with in group mean

Question 25

what are the key assumptions of ANOVA

Answer 25

all observations are independent residuals are normally distributed variance of residuals between groups is equal

Question 26

what is heteroscedasticity

Answer 26

unequal variance occurs when residuals are unequally distributed

Question 27

what can be done of the data does not meet these assumptions

Answer 27

- transform the data do a non-parametric test

Question 28

what is a non-parametric test and which one should be used for ANOVA

Answer 28

non-parametric tests havemore relaxed assumptions and can be used when data and residuals do not meet requirements of ANOVA. the Kriskal-Wallice test should be used here. it ranks all data values and tests weather they fit into groups

Question 29

if an anova test is used what test can be used to see where the variation lies in the data

Answer 29

tukeys test it is a sequence of t-tests, the p-value is adjusted to account for multiple compatrisons

Question 30

what is a disadvantage of using a nonparametric test like the Kriskal-wallice test instead of ANOVA

Answer 30

increased risk of false negative results.

Question 31

how does anova classify variation

Answer 31

by classifying the data into discrete categories and tests weather differences between individuals falling into categories is significant

Question 32

how are the degrees of freedom calculated with anova

Answer 32

1. among group degrees of freedom - (number of categories -1) 2. with in group degrees of freedom (number of indipendant data points - number of categories)

Question 33

when should a linear regression be used

Answer 33

when the explanatory and response variables are both continuous

Question 34

what does a linear regression do

Answer 34

- does explanatory variable have a significant effect on the response variable - quantify relationship between explanatory and response variable - extrapolation of values

Question 35

what do residuals show in a linear regression

Answer 35

the line doesn't perfectly match up with the data points. The residuals are the difference between the regression line and the raw data - residuals are calculated in y direction only

Question 36

what is the equation of a linear regression line

Answer 36

y = bx + bo + E

Question 37

how can significance be calculated when using a linear regression

Answer 37

the slope of the line (B1) has a related p-value

Question 38

which non-parametric equation should be used if the data does not meet the assumptions of a linear regression

Answer 38

Spearman correlation - describes nonmonotonic relationships

Question 39

what is a nonmonotonic relationship

Answer 39

when ever X increases Y increases too

Question 40

what are the assumptions of a linear nmodel

Answer 40

- residuals are normally distributed - each data point is independent - results are linear - no error in response variable measurement - error in response variable does not depend on independent variable

Question 41

what did Anscombe stress the importance of

Answer 41

plotting raw data

Question 42

why is plotting raw data so important

Answer 42

1, make sure data follows linear model (normal distribution/nonmonotonic) 2, look for data poets with high leverage 3, helps you understand the nature of the data 4,looks foe heteroscedacitiy - variance of error is not constant

Question 43

what are the limitations of ANOVA and linear regression

Answer 43

- can only have one explanatory variable - strict assumptions to follow - response variable must be continuous

Question 44

how can an outlier have the highest leverage

Answer 44

if it is at a 90* angle to the other data points

Question 45

how can a diagnostic plot be coded on R

Answer 45

plot(tree_model)

Question 46

what are diagnostic plots

Answer 46

they make a series of plots showing the residuals. they can be used to determine weather the data fits linear regression assumptions

Question 47

what do diagnostic plots check for

Answer 47

Are residuals normally distributed? do residuals have equal variance? are there any outliers with vary high leverage?

Question 48

what does the R^2 value show

Answer 48

the proportion of variance explained by the model - high r^2 = model explains most of the variance

Question 49

when should a multiple regression model be used

Answer 49

when the 2 explanatory variables are continuous and the response variable is also continuous

Question 50

what should be checked for using a correlation matrix when choosing multicollinearity models

Answer 50

multicollinearity - This is when there is a near linear relationship between the explanatory variable

Question 51

what issues does multicollinearity cause

Answer 51

- inflates standard errors of coefficients - false p-values - poor predictive accuracy of model makes the estimates very imprecise (unbiased)

Question 52

When should an ANCOVA model be used and what does it analyse

Answer 52

models with multiple categorical explanatory variables it analyses covariance

Question 53

give an example of when ANCOVA should be used

Answer 53

relationship between humidity and flower length for 2 colors. ancova should be used here because there is something with in the response variable that is driving variance