Stats Review

total variance

R²

unique variance

the square (²) of each outcome of predictors in the “part” column

shared variance

R² minus the sum of all the unique variances

Statistical significance (p-value)

p < .05 = significant

standardised coefficients

Beta weights, based on standard deviation units, allows for comparison between strength of predictors

unstandardised coefficients

b weights, how much the outcome changes based on a 1 unit increase in that predictor

explain direction of unique relationships

Positive or negative b weights indicated the direction of the relationship that the predictor has on the outcome

degrees of freedom

total number of participants = degrees of freedom + 1

when is multiple regression the appropriate analysis to conduct?

when there is one continuous dependent variable and multiple predictor variables

regression equation

Y = b0 + b1x1 + b2x2 …

what does each part of the regression equation mean?

b0 = constant, b1 = slope (b weights), x1 = score

univariate outliers

extreme of unusual data points, significantly outside of the range of values

multivariate outliers

unusual combination across multiple variables

removal of outliers

use SYSMIS to recode the variable

limitations of removing outliers

reduces sample size, can bias results, may remove real variability

when should variables be transformed?

if there is severe skew (log) or moderate skew (square root)

when is reflecting of variables needed?

when data is negatively skewed, it converts a negative into a positive

why and when would we retain a transformed variable?

if the results remain the same regardless of if it is transformed or not

when are non-parametric approaches useful?

when there is extreme skew or outliers, ranked data, or a small sample

what do parametric tests do?

make assumptions about the population

examples of parametric tests

ANOVA, Pearson correlation, multiple regression

what do non-parametric tests do?

makes fewer assumptions, utilized when assumptions are violated

example of non-parametric test

Spearman’s Rho - use of ranked data

point biserial correlation

extremely similar to t-test, used when one variable is dichotomous and one is continuous

interpretation of t-test

mean differences between groups

interpretation of point biserial correlation

how strongly two variables are correlated

assumptions for parametric tests

normal distribution, interval/ratio data, linearity, independence of observations

one-way chi square

does one categorical variable differ from expected frequencies (observed vs expected frequencies)

two-way chi square

are two categorical variables associated with each other (test of independence)

what is Phi?

the effect size - strength of relationship between two categorical variables (.10 = small, .50 = large)

crosstabulation table

provides observed and expected frequencies

effect of large sample size in chi-square test

small differences may be flagged as statistically significant

effect of small sample size on chi-square test

they lack statistical power, may fail to reach significance

what is the logic of the calculation of chi square?

it measures the gap between what you observe and what you expect to see

explain the selection and calculation of expected frequencies

it is the frequency we would expect if no relationship existed. for example, a sample of 100 people and if they like dogs or cats, it would likely be 50/50

three conditions when testing for causality using survey data

temporal precedence, covariation, elimination of alternative explainations

what is covariation?

variables must be related

what is elimination of alternative explanations?

the need to rule out third variables, we are looking to see if one variable influences another. for example, sleep problems cause stress and depression, stress may not truly cause depression

what is temporal precedence?

cause must occur before effect, for example stress must be measured before depression increases to determine if there is a relationship over time

explain stability and change

longitudinal studies separate stable traits from developmental change over time

panel design

same participants measured repeatedly over time, examines individual change (ex. 200 students measured yearly)

trend design

different samples from the same population measured over time, cannot track individual change (ex. students from a university are surveyed each year)

cohort design

follows a specific subgroup over time, examines generational/developmental patterns

simplex model

estimates change over time (does anxiety at time 1 predict anxiety at time 2, and does that predict anxiety at time 3?)

residualised longitudinal regression

does X predict change in Y over time (does stress at time 1 predict increases in depression at time 2?)

cross-lagged model

tests for bidirectional relationships - does X predict change in Y and does Y predict change in X?

assumptions in longitudinal research

normality, independence of observations, linearity, homoscedasticity