1 introduction to multivariate methods and statistics

Question 1

What are continuous, discrete and categorical variables?

Answer 1

Continuous = can take any value within a given range

Discrete = Can take certain values within a given range

Categorical = Can only be a relatively small number of categories

Question 2

What are nominal, ordinal, interval, and ratio scales?

Answer 2

Nominal = unordered categories
gender

Ordinal = can be ordered
likert scale

Interval = ordered, and equal intervals
temperature (celsius, Fahrenheit)
calendar years
IQ
longitude, latitude

Ratio = ordered, equal, absolute zero
height, weight

Question 3

What research designs exist?

Answer 3

experimental
quasi-experimental
correlational

between participants
within participants

Question 4

What is the normal distribution?

Answer 4

• bell shape
• symmetrical around the mean
• mean, mode, median are same if perfect
• distribution of many natural phenomena follow it

Question 5

what are the most important categories in a dataset?

Answer 5

central tendency (where are most scores?)
variability (spread)

skew - measure of asymmetry
It indicates whether the data points are skewed to the left (negative skew) or to the right (positive skew) relative to the mean.

kurtosis - measure of tailedness (to what degree do u have extreme values)

Question 6

What are multivariate methods and statistics?

Answer 6

more than one variable

more than one dependent variable
e.g. investigating the type of effect that listening to music has on participants verbal creativity and non-verbal creativity
determine specificity vs generality of effects
common variance

more than one independent variable
e.g. investigating the impact of treatment type, clinical population, and timepoint on either a single or multpile outcome measure
understand mediation, moderation, and confounding

moderation, mediation, confounds

Question 7

What could a possible research design be with multivariate measures?

Answer 7

clinical:
psychopathology and intervention/prevention research

multiple dependent variables
→ is there common variance?
higher reliability, predict longitudinal course

multiple independent variables
one grouping variable
or multiple (sick vs healthy AND old vs young)
combined effect of two or more covariates?
moderation?
inclusion of confounds

Question 8

How can multivariate methods be applied to intervention and prevention research?

Answer 8

intervention - random assignment to treatment group

people cannot be randomly assigned to have psychopathology

multiple dependent variables
standard practice
specificity of treatment effect
assessment from multiple informants → efficacy
mediation of intervention/prevention
correlate of outcome (Kraemer et al., 2001)

multiple independent variables
Paul (1967) - what treatment, by whom, is most effective for this individual with that specific problem, and under what set of circumstances? (p.111)

Question 9

What specific research question could be answered with a MVA?

Answer 9

• examining associations between two continuous variables
• examining differences between groups on a continuous dependent variable
• multiple independent variables with one dependent variable

Question 10

How can you find out how many independent (predictor) variables a study entails?

Answer 10

look at the differing variables

if one has multiple conditions
-> these are manipulated levels of the same variable

need to be distinct constructs!

Question 11

What is a poisson distribution?

Answer 11

It deals with discrete events: That means it’s used for scenarios where you’re counting the number of times something happens, like seeing squirrels, getting emails, or buses arriving at a bus stop.

Events occur independently: The chance of seeing a squirrel now doesn’t change whether or not you just saw one a moment ago.

Steady average rate: There’s a known average rate of occurrence, like an average of 3 squirrels seen per hour. This rate is constant over time.

Random occurrence: Even with a steady average rate, you can’t predict exactly when the next squirrel will show up, but you can estimate the probability of seeing a certain number of squirrels in a fixed time.

Question 12

How can ANCOVA be briefly described?

Answer 12

compare the means of more than two groups to see if at least one is significantly different from the others

dependent variable should be continuous (interval or ratio scale), and the independent variables (or factors) are categorical.

multiple linear regression
only continuous predictor variables

multiple dependent variables and multiple levels in within-subjects variables
in longitudinal design or effects of experimental design → ANOVA

Question 13

What is MANOVA?

Answer 13

multiple measures of the same construct at the same point in time

allowing for the simultaneous analysis of two or more dependent variables. It determines whether the mean differences among groups on a combination of dependent variables are likely to have occurred by chance

dependent variables should correlate to some extend

Question 14

What are the key differences between ANOVA and MANOVA?

Answer 14

the key difference lies in the number of dependent variables: ANOVA is used for one, while MANOVA is used for two or more

Question 15

What is structural equation modelling SEM?

Answer 15

SEM models include direct relationships from one latent variable to another latent variable
longitudinal stability and changes
do constructs demonstrate the same measurement properties across development and samples
→ measurement invariance

adjust for SE → multilevel modeling, random coefficient modeling, random regression, linear mixed modeling, …

Question 16

What is the difference between correlation and regression analyses?

Answer 16

Purpose: Correlation assesses the strength and direction of a relationship. Regression explains the nature of the relationship and predicts outcomes.

Output: Correlation provides a single coefficient indicating the strength and direction of a linear relationship. Regression provides an equation that models the relationship.

Causality: Neither correlation nor simple regression confirms causation, but regression is more commonly used for causal inference in conjunction with other evidence.

Symmetry vs. Directionality: Correlation is symmetric and does not imply direction, while regression is directional and differentiates between dependent and independent variables.

Question 17

What are limits of multivariate methods?

Answer 17

• missing data
  more modern techniques allow for incomplete data inclusion
• use of ANCOVA
  assumed to estimate group differences
  cannot actually correct for this design limitation
• critical that all predictor variables have a meaningful zero
• designs relying on case versus control designs
  random assignment not possible with psychopathology
• tests of moderation
  typically ANOVA and regression

assumptions:
homoskedasticity = residual error for the dependent variable is constant across the full range of the predictor otherwise false suggestion of interaction

Question 18

What are the differences between univariate, bivariate and multivariate methods?

Answer 18

Univariate Studies: These involve only one variable. The analysis focuses on understanding the distribution, central tendency, and variability of this single variable.

Bivariate Studies: These examine the relationship between two variables. Common bivariate analyses include correlation and simple linear regression, where the focus is on how one variable affects or is associated with another.

Multivariate Studies: Multivariate analysis involves three or more variables simultaneously. These studies can examine complex interactions and relationships among multiple variables, providing a more comprehensive view of the data.

Question 19

What is validity?

Answer 19

does the process measure what it actually want to measure

-> accurate prediction
-> measure behaves as the construct itself

Question 20

What is face validity?

Answer 20

measurement superficially appears to measure what it claims to measure

Question 21

What is concurrent validity?

Answer 21

measurement is directly related to another established measure of the same construct

scores on a newly developed measure follow a very similar pattern to scores obtained from a measure that have been previously found to measure the same variable of interest.

Question 22

What is predictive validity?

Answer 22

measurement accurately predicts behaviour according to a theory

Question 23

What is construct validity?

Answer 23

measurement behaves as the construct itself

Question 24

What is convergent validity?

Answer 24

strong relationship between multiple measurements of the same construct

Question 25

What is divergent validity?

Answer 25

weak relationship between multiple measurement of different constructs

Question 26

What is reliability?

Answer 26

does the process measure the thing well, across studies

Question 27

How do validity and reliability go together?

Answer 27

you cannot be valid if you are unreliable

but you can be reliable and not valid

Question 28

What is a theory?

Answer 28

set of statements about the mechanisms underlying a particular behaviour

help organise and unify different observations of behaviour and relationships

Question 29

What is an operational definition?

Answer 29

procedure for indirectly measuring and defining a variable that cannot be observed or measured directly