Statistics/Research Design

1- way ANOVA

1 categorical IV (≥2 levels), 1 continuous DV

Does the mean of the DV differ across groups of the IV?

1-way ANOVA

Factorial ANOVA

≥2 categorical IVs, 1 continuous DV

Examines main effects of each IV and their interaction effect on the DV.

Factorial Anova

Main effect

when 1 IV independently influences DV, ignoring other IV

Interaction effect

when the effect of 1 IV depends on level of the other IV

Simple effect

examines effect of 1 IV within a specific level of another IV

Simple Regression

1 continuous IV, 1 continuous DV

Can we predict the DV from the IV?

Simple Regression

Multiple Regression

≥2 continuous IVs, 1 continuous DV

How well do multiple predictors explain variance in the DV?

Multiple regression

Logistic regression

≥1 continuous or categorical IVs, 1 categorical DV (binary or multinomial)

What is the probability of an outcome occurring based on predictor variables?

Logistic regression

MANOVA (multivariate ANOVA)

1+ categorical IVs, ≥2 continuous DVs

Does the IV(s) influence multiple DVs simultaneously?

MANOVA

Factor analysis

Multiple continuous variables - usually looking at some type of measure or instrument

Identifies factors that explain the correlations among items, simplifying the scale into meaningful components

Factor analysis

Exploratory FA

Discover underlying factor structure with no assumptions

Confirmatory FA

test predefined factor structure based on theory

Eigenvalues

Numerical values that indicate the amount of variance explained by each factor in a factor analysis, with values greater than 1 suggesting that the factor accounts for a significant amount of variance.

Descriptive discriminant analysis (DDA)

follow-up/post hoc to MANOVA, identifies which specific variables drive group differences

maximum likelihood estimation

a statistical method for estimating parameters of a statistical model that maximizes the likelihood function, providing estimates that are most likely to produce the observed data.

ordinary least squares regression

a method for estimating the relationships among variables by minimizing the sum of the squared differences between observed and predicted values.

Principle components ana

Multiple continuous variables

Data reduction—creates principal components that explain variance in data. Use for easier analysis

PCA

Structural equation modeling (SEM)

Multiple IVs, multiple DVs (can be categorical or continuous)

Tests complex theoretical models with latent variables.

Allows researchers to model both direct and indirect relationships bw variables, testing mediating and moderating effects

SEM

multilevel modeling/hierarchical linear modeling (MLM/HLM)

Nested data with IVs at multiple levels, DV can be continuous or categorical

Used to analyze data w hierarchical/nested structure

Can account for nested structure of nested data by examining both within-group and bw-group variance

HLM/MLM

Mediation

Continuous IV, Mediator, and DV

Does an IV affect a DV through another variable?

mediation

Moderation

Continuous or categorical IV, Moderator, and DV

Does the effect of an IV on a DV change depending on another variable?

moderation

Bootstrapping

Instead of relying on just one sample, you resample your data many times (with replacement) to create a distribution of estimates; Helps feel confident that findings are not a coincidence. Don’t want zero in the CI.

Canonical correlation

multiple continuous IVs and multiple continuous DVs

Examines relationships between 2 sets of variables

canonical correlation

Analyses that use MLE

logistic regression

SEM

MLM/HLM

Analyses that use OLS

simple regression

multiple regression

Variance

How spread out the data is; the average of squared differences from the mean.

r

Pearson correlation coefficient; measures the strength and direction of a relationship between two variables (-1 to 1)

Coefficient of determination (r²)

The proportion of variance in the dependent variable explained by the independent variable(s); shows how well the model fits the data

Residuals

The difference between actual values and predicted values in a regression model.

Blocking variable

A variable included to control for potential confounding effects and to detect possible interactions.

GLM

A framework that includes regression and ANOVA for modeling relationships between variables.

Planned contrasts

predefined comparisons before analyzing data

unplanned contrasts

comparisons chosen after looking at the data

orthogonal

comparisons that are independent of each other

non-orthogonal

comparisons that overlap or depend on each other

quasi experimental design

no random assignment, but has control and experimental groups

type 1 error

false positive

Internal validity

the degree of confidence that the observed effects are due to the manipulation and not other factors

External validity

the extent to which the results of a study can be generalized to other settings, people, and times

Comparing depression levels among individuals receiving CBT, ACT, or psychodynamic therapy

1-way ANOVA

Investigating whether therapy type and gender influences anxiety scores

Factorial ANOVA

Simple regression

Predicting self-esteem from social support levels

to what extent do self-efficacy and perceived stress predict levels of depression?

multiple regression

Predicting whether a client drops out of therapy (yes/no) based on symptom severity and motivation level

logistic regression

MANOVA

Does therapy type affect both anxiety and depression levels in client after treatment?

What are the underlying dimensions of a 15-item scale measuring anxiety?

EFA

Do the underlying dimensions of a 15-item scale measuring anxiety align with a specific theory?

CFA

Reducing a 30-item burnout questionnaire into key dimensions

PCA

Examining how childhood trauma impacts depression via self-esteem and coping skills (both directly and indirectly)

SEM

Investigating how therapy characteristics influence client therapy outcomes across different clinics`

MLM/HLM

Does social support have an effect on depression through self-efficacy?

Mediation

Does gender alter the relationship between trauma and PTSD symptoms?

Moderation

Investigating the relationships between personality traits (openness, conscientiousness, extraversion) and mental health outcomes (depression, anxiety)

canonical correlation