Module 6 - Correlation & Regression

relationship between two continuous variables, measure degree data points cluster around regression line

show general pattern of relationship between dependent & independent variable

measure direction & magnitude of relationship between independent & dependent variable

Numerical value of correlation coefficient, show strength of association, 0 = no linear association, -/+ 1 = perfect linear association

If correlation coefficient positive or negative, show directionality of relationship (pos or neg correlation)

measure degree of relationship between linear related variables

scale measurements, normal distribution, 2 variables = paired, no outliers, linearity, homoscedasticity

straight line relationship between 2 variables, as x increase -> y increase/decrease, check with scatter plot visualization

equal spread of data around line of best fit, data = homoscedastic or heteroscedastic, check with scatter plot

correlation coefficient

Non-parametric Pearson's correlation, ranks data to explore relationship between 2 variables

scale/ordinal data, any distribution, linear relationship between variables

used to evaluate inter-rate reliability, test-retest reliability & intra-rater reliability; for data structured as groups (not pairs)

variation between >=2 raters, measuring same event

variation in 2 measurements under same conditions

variation within 1 rater across >= 2 trails

Restricting Data Range (can sometimes be good), Heterogenous Samples, Outliers (alter correlation)

reliability to clinical assessments tools, impact medical decision making

also explore relationship between variables, how explanatory variable impact response variable

variable you are predicting, outcome/dependent/y variable

variable you use to predict, x/independent variable

distance observed y lies from regression line

error term, represent residual

y-intercept

slope of regression line

regression - chooses values of y-intercept & slope that minimize sum of squared residuals

smaller difference between data points & line of best fit

scale data, residuals of regression line are normally distributed, no outliers, linear relationship between 2 variables, data = homoscedastic

Sum of residuals = 0, line of best fit passes through mean of x & mean of y

coefficient of determination, amount of variation in y explained by x

y-intercept = -77.283, slope = 3.33

R = simple correlation between variables, 57% of variation of y is explained by X

model significantly predicts y

always positive, as approached 0 = low variation in Y determined by x, max = 1 (all variability in y is determined by x

1 explanatory & 1 response variable, scale measurements

1 response variable, >1 explanatory variable, scale measurements

1 explanatory variable, 1 response variable (dichotomous)

probability of event occurring due to random chance

event/difference is meaningful for a clinical reason

whether finding has biological relevance

ability to reproduce/replicate findings

our current inability to reproduce scientific results

publication bias, bad study design & power, questionable research practices

p-hacking, selective reporting, sampling bias, HARKing ( Hypothesis After Result is Known)

preregistration of studies, replication studies, open science, alternative statistical approaches, education