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Module 6 - Correlation & Regression
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45 Terms
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Correlation
relationship between two continuous variables, measure degree data points cluster around regression line
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Line of Best Fit
show general pattern of relationship between dependent & independent variable
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Correlation Coefficients
measure direction & magnitude of relationship between independent & dependent variable
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Magnitude of Association
Numerical value of correlation coefficient, show strength of association, 0 = no linear association, -/+ 1 = perfect linear association
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Direction of Association
If correlation coefficient positive or negative, show directionality of relationship (pos or neg correlation)
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Pearson Correlation
measure degree of relationship between linear related variables
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Assumptions of Pearson Correlation
scale measurements, normal distribution, 2 variables = paired, no outliers, linearity, homoscedasticity
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Linearity
straight line relationship between 2 variables, as x increase -> y increase/decrease, check with scatter plot visualization
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Homoscedasticity
equal spread of data around line of best fit, data = homoscedastic or heteroscedastic, check with scatter plot
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r
correlation coefficient
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Spearman's Rank Order Correlation
Non-parametric Pearson's correlation, ranks data to explore relationship between 2 variables
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Assumptions of Spearman's Rank Order Correlation
scale/ordinal data, any distribution, linear relationship between variables
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Intraclass Correlation Coefficient (ICC)
used to evaluate inter-rate reliability, test-retest reliability & intra-rater reliability; for data structured as groups (not pairs)
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Inter-Rater Reliability
variation between >=2 raters, measuring same event
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Test-Retest Reliability
variation in 2 measurements under same conditions
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Intra-Rater Reliability
variation within 1 rater across >= 2 trails
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Factors Impacting Correlations
Restricting Data Range (can sometimes be good), Heterogenous Samples, Outliers (alter correlation)
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Clinical use of correlation
reliability to clinical assessments tools, impact medical decision making
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Regression
also explore relationship between variables, how explanatory variable impact response variable
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Response variable
variable you are predicting, outcome/dependent/y variable
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explanatory variable
variable you use to predict, x/independent variable
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residuals
distance observed y lies from regression line
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epsilon
error term, represent residual
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beta 0
y-intercept
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beta 1
slope of regression line
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Least Squares Method
regression - chooses values of y-intercept & slope that minimize sum of squared residuals
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what does a lower squares value mean?
smaller difference between data points & line of best fit
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Regression Assumptions
scale data, residuals of regression line are normally distributed, no outliers, linear relationship between 2 variables, data = homoscedastic
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Least Squares Regression Model
Sum of residuals = 0, line of best fit passes through mean of x & mean of y
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R square
coefficient of determination, amount of variation in y explained by x
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interpret image coefficients
y-intercept = -77.283, slope = 3.33
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Interpret model summary
R = simple correlation between variables, 57% of variation of y is explained by X
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Interpret ANOVA results
model significantly predicts y
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r squared characteristics
always positive, as approached 0 = low variation in Y determined by x, max = 1 (all variability in y is determined by x
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Linear Regression
1 explanatory & 1 response variable, scale measurements
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Multiple Linear Regressions
1 response variable, >1 explanatory variable, scale measurements
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Logistic Regression
1 explanatory variable, 1 response variable (dichotomous)
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statistical significance
probability of event occurring due to random chance
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clinical significance
event/difference is meaningful for a clinical reason
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biological significance
whether finding has biological relevance
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Data reproducibility
ability to reproduce/replicate findings
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Replication crisis
our current inability to reproduce scientific results
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causes for replication crisis
publication bias, bad study design & power, questionable research practices
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Questionable Research Practices
p-hacking, selective reporting, sampling bias, HARKing ( Hypothesis After Result is Known)
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Solutions to replicability crisis
preregistration of studies, replication studies, open science, alternative statistical approaches, education
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