Statistics

Question 1

Inferential statistics

Answer 1

Allows for generalisations to be made about a population from a sample representative

Question 2

What are common problems in biological data

Answer 2

• small sample size
• unequal sample size
• correlation within data (measurements from subject over time, or measurements from brain regions at the same time will always be correlated)
• unequal variance (heterogeneity)
• non-normal (skewed) distribution

Question 3

Discrete variables

Answer 3

variables who values are finite, or countably infinite values within a range
- eg: ‘pain relief’ vs ‘no pain relief’ or subjective rating scales

these numbers do not have the same academic integrity as continuous variables (thus means have ‘less’ meaning)

Question 4

continuous variables

Answer 4

variables whose values exist on an infinite continuum/are uncountable
- e.g. frequency, temperature, amplitude, enzyme concentration, receptor density

Question 5

Binary variables

Answer 5

Yes or No outcomes

Question 6

Nominal variables

Answer 6

Represents groups with no ‘rank’ or ‘order’ within them
- eg: species, colour, brands

Question 7

Ordinal variables

Answer 7

Groups that are ranked in a specific order
- eg: likert scales,

Question 8

Parametric statistics

Answer 8

that the data follows a normal distribution, and that there is equal variance within each group (homogeneity of variance)

Question 9

Nonparametric statistics

Answer 9

used when the data does not follow a normal/known distribution
- tend to be less statistically powerful

Question 10

Parametric test used for 2 unpaired groups

Answer 10

Unpaired t-test

Question 11

Non-parametric test used for 2 unpaired groups

Answer 11

Man-Whitney U test

Question 12

Parametric test used for 2 paired groups

Answer 12

Paired t-test

Question 13

Non-parametric test used for 2 paired groups

Answer 13

Wilcoxon test

Question 14

Parametric test used for ≥3 unmatched groups

Answer 14

1 way ANOVA

Question 15

Non-parametric test used for ≥3 unmatched groups

Answer 15

Kruskal-wallis test

Question 16

Parametric test used for ≥3 matched groups

Answer 16

Repeated measures ANOVA

Question 17

Non-parametric test used for ≥3 matched groups

Answer 17

Friedman test

Question 18

Parametric test used to determine association between two variables

Answer 18

Pearson correlation

Question 19

Non-parametric test used to determine association between two variables

Answer 19

Spearman correlation

Question 20

Parametric test used to predict a value for one variable from other(s)

Answer 20

Simple linear/non-linear regression
Multiple linear/non-linear regression

Question 21

Parametric test used to predict a value for one variable from other(s)

Answer 21

Non-parametric regression

Question 22

Central limit theorem

Answer 22

As the sample size increases, the probability that the data will be normally distributed increases

Question 23

The null hypothesis

Answer 23

Assumes that there is no difference between groups

Question 24

Power

Answer 24

(1-b)
the probability of rejecting the null hypothesis
- increasing sample size results in decreased variability, and thus greater power

Question 25

a

Answer 25

Type 1 error rate; rate of incorrect rejection of null hypothesis **this is equal to the significance level (which is typically 0.05, meaning 5% probability of falsely rejecting the null hypothesis)

Question 26

b

Answer 26

type II error rate; rate of incorrect acceptance of null hypothesis

Question 27

What metrics cannot be altered to increase power?

Answer 27

- variability, as it is fixed depending on type of data - type I error

Question 28

T-test

Answer 28

Ratio of the difference between two groups in relation to a measure of variability (standard error)

Question 29

Examples of the two types of t-test

Answer 29

- non-paired: comparing cannabis treatment to placebo treatment in different groups - paired: comparing cannabis treatment to saline treatment in the same group

Question 30

ANOVA

Answer 30

Analysis of variance Used to determine whether ≥3 means are significantly different Takes into account variance both between (treatment variance) and within (error variance) groups

Question 31

1 factor ANOVA

Answer 31

Used when examining different treatments on different groups

Question 32

Repeated measures ANOVA

Answer 32

Used when investigating different treatments on the same group

Question 33

Multilevel ANOVA

Answer 33

Used when investigating ≥2 independent variables and the interactions between then - provides a separate F value for each independent variable and interaction

Question 34

Multiple comparisons

Answer 34

Using multiple t-tests is advised against, as it increases the type I error - Bonferroni corrections counteracts this Hence why ANOVAs are preferred for ≥3 groups

Question 35

Post-hoc tests

Answer 35

aka multiple comparisons tests Used after completing an ANOVA to determine which groups are significantly different - Dunnett test - Tuker-kramer test

Question 36

Pseudo-replication

Answer 36

occurs when the number of measured values or data points exceeds the number of genuine replicates - eg: confusing # slices with # animals Leads to an inflation of sample size, thus artificial inflation of power

Question 37

Linear mixed model analysis (when used + assumptions)

Answer 37

A statistical method used when data is not independent, and errors are correlated Assumptions: - does not assume independence of data - does not assume balanced design - does not assume homogenous variance - assumes random sampling - covariance structure must be specified

Question 38

Covariance

Answer 38

Provides the relationship between two variables from slope gradients and sample size - relationship defined by slope valence - does not inform gradient or derivation

Question 39

Correlation (R)

Answer 39

Measures the degree of association between two variables - not sensitive to scale - quantifies strength of correlation Defined as a number, r where -1

Question 40

R^2

Answer 40

The coefficient of determination: - A metric of correlation that allows comparison of two correlations = variance around mean - variance around line / variance around mean = 1 - RSS/TSS R^2 should be ≥ 0.80 eg: R^2 = 0.80 = the relationship between two variables accounts for 80% of the variation

Question 41

Regression analyses

Answer 41

Statistical method that allows examination of the relationship between 2+ variables of interest through the generation of a line of best fit - linear or non-linear - t-tests/ANOVA can be used to determine significance of regression

Question 42

Sum of squares

Answer 42

Total sum of squares (TSS) = variation of data about the mean Residual sum of squares (RSS) = variation not explained by the regression line sum of squared regression (SSR) = variance explained by regression

Question 43

Simple regression

Answer 43

A statistical method that allows examination the relationship between two variables of interest - Calculate residual sum of squares - Smaller RSS indicates a better fit - used for all standard curves

Question 44

T-test for regression

Answer 44

The regression co-efficient (slope) / standard error of slope co-efficient = b/SE(b) - can also be expressed as a confidence interval = b ± taSE(b) - typically set at 95%, indicating that 95% of the data will fall between a set of values

Question 45

ANOVA for regression

Answer 45

Determines whether the amount of variation accounted for by the regression line (SSR/SSE) is greater than variation NOT explained (RSS) - signal > noise

Question 46

Assumptions for t-test/ANOVA for regression

Answer 46

- residuals are normally distributed - constant variance (SD) of residuals - independent samples If these are not fulfilled type I error increases

Question 47

Non-linear regression

Answer 47

A statistical test that used calculus and matrix algebra to determine the line of best fit for a non-linear relationship - requires initial estimated parameters (mean, SD) - can be used to interpolate values - useful for obtaining Bmax, Ka, EC50 etc...

Question 48

Linearising transform

Answer 48

Data can be transformed so that it fits the assumptions for linear regression eg: - scatchard plots for binding data - lineweaver-burke plots for enzyme kinetics - logarithmic plots for kinetic data TRANSFORM DISTORTS THE ERROR - violates assumptions of regression of normal distribution of error and ~equal SE for each x value

Question 49

Issues with Scatchard plots

Answer 49

X (bound drug) is often used to calculate Y (bound/free) i.e. the independent variable is part of the dependent) - results in inaccurate Y values - violates assumptions of linear regression (normal distribution and homoscedasticity; equal variance of errors)

Question 50

Multivariate statistics

Answer 50

Statistical analysis that are used when there are multiple dependent and/or independent variables - used commonly in clinical neuropharmacology - becoming more common in genomics and proteomics

Question 51

Multiple linear regression

Answer 51

An equation composed of multiple regression coefficients for different independent variables (x1,x2) but with a single dependent variable (y) y = b1x1 + b2x2 +... + c requires adjusted R^2 to take into account multiple variables as a function of sample size

Question 52

Multi-collinearity

Answer 52

Occurs when regression variables are highly correlated, resulting in an inflation estimate of variance through sum of squares - inaccurate coefficients - can lead to a significant F value but no significant differences between any specific groups The highly correlated variable should be removed as they are REDUNDANT

Question 53

Principal component analysis

Answer 53

- identifies the most important features (principal components) that contribute to variation - Plots these variables in order of importance according to 'eigenvalue' - the second PC is always perpendicular to the first

Question 54

Discriminant analysis

Answer 54

A statistical method that helps you to identify the most important variables that distinguish the different groups in data - Principal component analysis - Factor analysis

Question 55

Factor analysis

Answer 55

Used to simplify complex data by identifying common factors that explain the relationships between dependent variables

Question 56

Random forest classification

Answer 56

A machine learning method that utilises multiple 'decision trees' and finds the average to give a final result - can be used to determine how good an independent variable is at predicting dependent - error plateaus after ~100 trees

Question 57

Eigenvalues

Answer 57

‘components’ or ‘factors’ (mathematically known as ‘roots’) that explain most of the variation in the data - In an analogous way to ANOVA, these eigenvalues represent the major sources of variation in the covariance matrix

Question 58

Cluster analysis

Answer 58

An exploratory technique often used on very large data sets to show variables that typically vary together, i.e. have a relationship - Results often shown using a ‘dendrogram’ - often requires a 'z' transform - Different algorithms can be used to determine clusteres

Question 59

Canonical correlation analysis

Answer 59

used to identify and measure the associations among two sets of variables. Canonical correlation is appropriate in the same situations where multiple regression would be, but where are there are multiple intercorrelated outcome variables.

Question 60

Non-parametric multivariate analysis

Answer 60

- few assumptions about data eg: random forest classification/regression, PCA, and cluster analysis

Question 61

Scree plot

Answer 61

Way of interpreting data from PCA - plots each principal component in order based on amount of variation that it explains (eigenvalue)