3003PSY Final (mods 4-9)

multiple regression

multiple regression

predicts the association between one or more predictor variable and a criterion

bivariate regression

a type of multiple regression with only one predictor variable

equation for the multiple regression

Y = b0 + b1X1 + b2X2 + … + bkXk + e

b0

the intercept; what y equals when all predictors are equal to 0

b1

the slope; the change in y for every one-unit increase in predictor 1

e

the residual/ random error

b-weight/ unstandardised coefficient

the rate of change based on the unique metric of the predictor

beta-weight/ standardised coefficient

the rate of change based on a standardised metric so that all predictors can be compared in their relative strength

R²

the total variance in the criterion explained by the model

calculation of R²

ssregression / sstotal

sum of (Y’-Ymean)²/ sum of (Y-Ymean)²

SSregression

sum of (Y’ - Ymean)²

SStotal

sum of (Y-Ymean)²

SSresidual

sum of (Y-Y’)²

zero-order correlation

the pearsons correlation coefficient between each predictor and the criterion

partial correlation

the correlation between the given predictor and criterion but with the effects of all other predictors partialled out, including any shared variance

semi-partial correlation

the correlation between the given predictor and the criterion when the effect of all other predictors are partialled out only from the respective predictor

sr²

the unique effect of a given predictor, calculated by squaring the semi partial correlations

equation for shared variance

R² - sum of (sr²)

normality

are residuals normal and do they centre around 0

homoscedasticity

is there a constant variance of residual scores across predicted scores

independence of errors

residuals are uncorrelated with Y

linearity

the relationship between the predictors and the criterions falls along a straight line

steps for checking assumptions and diagnosing data

check data entry errors, scatterplots for relationships and linearity, check assumptions, check univariate outliers, check multivariate outliers, check skewness and kurtosis

univariate outliers

outliers with an extreme/unusual score on at least one variable; checked using boxplots

multivariate outliers

outliers with an extremely unusual combination of scores on at least two variables; checked using mahalanobis distance

parametric approaches

makes assumptions about the population that a sample comes from, eg normally distributed.

nonparametric approaches/ distribution-free tests

does not make assumptions about the population that data has come from

ranking

the ordering of a set of data from smallest to largest

spearmans rho (rs)

a non-parametric approach that uses ranked data

point-biserial correlation (pbs)

a non-parametric approach with one dichotomous and one continuous predictor, computes a pearsons r correlation

chi square analyses

a nonparametric approach that uses categorical data

one-way chi square/ goodness of fit test

analyses the difference between observed and expected frequencies across a single categorical variable with multiple levels

two-way chi square/ test of independence

analyses the independency of two categorical variables

frequency(expected) for a two-way chi square

f(expected cell) = (column total*row total)/grand total

chi²

sum of ((fobtained-fexpected)²/fexpected)

df total for parametric tests

total number of participants - 1

df total for chi square analyses

total number of groups - 1

phi

the effect size of a 2×2 chi square; interpreted the same as pearsons r

.1 = weak

.3 = moderate

.5 = strong

assumptions of chi square

cell frequencies equal at least 5, have all participants included, independence of observations

cramers phi

the same as regular phi but used for a larger than 2×2 chi square

longitudinal designs

designs based on the notion of causality

determinants of causality

covariance, temporal precendence, no confounding factors

covariance

where two variables are related in some way

temporal precendence

the assumption that one variable precedes, or causes, the other

panel designs

the gold standard for longitudinal designs; data is collected from the same participants in the same way over multiple time points

stability

the degree of consistency of scores from one time point to another

change

the degree of fluctuation of scores from one time point to another

unidirectional relationship

a clear one-way direction of relationship between the predictor and criterion

bidirectional relationship

the pedictor variable causes the crierion and vice versa

assumptions of longitudinal research

inter-individual stability, consistent measurement, synchronicity, timeframe, other variables (third variable effect)

inter-individual stability

there are no systematic differences in stability or change between participants

consistent measurement

measurement is the same when using repeated measures, including its interpretation by participants

synchronicity

measurement administration occurs with the same interval between timepoints

timeframe

the length of time between measurements is appropriate

other variables/ third variabe effect

no other important variables are omitted

replication crisis

in 2010 researchers were unable to replicate the finings of key psychology studies

reproducibility

reproducing the results of a publication using its original data

replication

reproducing results of a publication using your own data but coming from the same population

questionable research practices/ p-hacking

deliberately manipulating data to obtain significant results

HARKING

hypothesising after results are known

publication bias

the finding that journals are more likely to publish studies with significant findings

open science

the philosophy of making science transparent

unreviewed preregistration

preregistration where the researcher uploads their research design to a time-stamped, unedited archive

registered report

similar to unreviewed preregistration that is submitted to a journal rather than a website

registered replication reports

similar to registered reports but for replication studies where various researchers from different labs each replicate the same study and publish their findings together

open science badges

oped data badge, open materials badge, preregistration badge

nominal data

includes categorical data

ordinal data

includes ranked data

scale data

includes interval, ratio, and continuous data

the most common null hypothesis for one-way chi sqaures

the equiprobable distribution

rho

correlation for the population

r

correlation for the sample

percent of successful replications in the reproducibility project

36%

successful replications in social psychology

25%

successful replications in cognitive psychology

50%

effect size for the reproducibility project

effect size was half