Week 5 Lecture - Relationship Statistics

Covariate

An extraneous or confounding variable that can affect the outcome variable.

ANCOVA

Analysis of covariance; an ANOVA that controls for covariates using adjusted means.

MANOVA

Tests for differences between groups when there are multiple dependent variables.

MANOVA Advantages

Controls familywise error rate and accounts for relationships among dependent variables.

Discriminant function analysis

used to determine which of the DV's are best at discriminating (which is the best at separating DV's into groups)

What is the relationship between raters' scores

inter-rater reliability

What is the relationship between the two sets of scores from the same rater

intra-rater reliability

What is the relationship between gait speeds captured by the Vicon in patients following a stroke at time 1 and again at time 2....can each of the patients walk at about the same speed

test-retest reliability

Are the items in a test or survey consistent with each other

internal consistency

Can a score on one outcome measure predict another outcome measure

predictive validity

Can two different outcome measures get similar results at the same time

concurrent validity

Can two different outcome measures (one is a gold standard) get similar results

criterion validity

Can sub-groups of items in an outcome measure explain factors of the same complex construct....such as satisfaction, coordination, etc.

construct validity

Pearson Correlation (r)

Measures strength and direction of a linear relationship between two interval/ratio variables.

Pearson Correlation must have

quantitative data

Pearson r Range

Ranges from -1.00 (perfect negative) to +1.00 (perfect positive).

Pearson r Effect Sizes

Small is ±0.1, medium is ±0.3, and large is ±0.5.

Coefficient of Determination (r²)

The proportion of variability in one variable predicted by the other variable.

r=0 therefore r²=

0 (two circles don't touch)

r=.8 therefore r²=

.64 (two circles overlap 64%)

r=1.0 therefore r²=

1.00 (two circles overlap 100%)

Correlation vs. Agreement

Correlation measures association, not how closely the actual values agree.

Point-Biserial Correlation (rpb)

Measures relationship between two levels of a categorical variable and an interval/ratio variable.

Spearman Rank Correlation (rs)

Non-parametric equivalent to Pearson's correlation, used with ordinal or ranked data.

Intraclass Correlation Coefficient (ICC)

Reliability coefficient for multiple raters; measures agreement or association.

Agreement vs Consistency

Agreement - use fewer options to rate (scale of 1-3: "no, maybe, yes")

Consistency - use more options to rate, looking for similar rating (exact gait speed)

Standard Error of the Mean (SEM)

Measures how accurately a sample mean represents the population mean.

Standard Error of Measurement (SEmeasurement or SEm)

Estimates expected measurement error around a patient's true score.

Regression

A statistical technique used to predict an outcome variable from predictors.

Linear regression

one predictor, one I/R outcome

Multiple linear regression

multiple predictor, one I/R outcome

Logistic regression

1+ predictors, one categorical outcome, two levels only

Multinomial logistic regression

1+ predictors, one categorical outcome, multiple levels

Ordinal logistic regression

1+ predictors, one ordinal outcome, multiple levels

Homoscedasticity

The assumption that outcome variance is equal across all predictor levels. Creates a residual, the residual score is the distance from the score (Y) and the line (Y') that the data points create.

Homoscedasticity values

Similar to a z score...

+1 represents one standard deviation above the model line.

-1 represents one standard deviation below the model line.

0 represents a score on the model line.

Linearity

The data points are arranged in a somewhat linear pattern.

Curvilinear

The data points are arranged in a somewhat curved pattern (lots of errors)

Skewness/kurtosis values

>+2 or

Standardized Residual

A residual score converted to standard deviations to identify outliers.

Cook's Distance

A statistical test evaluating an outlier's influence on a regression model. Scores of >+1 are a problem

Shapiro-Wilk

Measures normality. Values less than alpha indicate there is statistical evidence that your data is not normally distributed. p < alpha = bad/non-normal

Levene's Test

Measures HOV. Values less than alpha indicate that your group variances are significantly different from one another. p < alpha = bad/significant difference

Multicollinearity

High correlations (r > 0.9) among multiple predictors in a model.

Variance inflation factor (VIF) and Tolerance

Multicollinearity diagnostics; VIF should be < 10, Tolerance > 0.1.

Durbin-Watson Test

Checks the assumption of independence of observations in regression. Values range from 0-4 and 2 is perfect

Cronbach's Alpha

Measures internal consistency of a scale; 0.7 is acceptable, 0.8 is good.

Kappa (K)

Measures inter-rater agreement for nominal data, accounting for chance.

Chi-Square Test for Independence

Tests whether two nominal variables are independent of one another.

Exploratory Factor Analysis (EFA)

Identifies underlying constructs or factors by analyzing correlations among items.

Minimal Detectable Change (MDC)

Minimal change falling outside measurement error; considered real but not necessarily meaningful.

Minimally Clinically Important Difference (MCID)

The smallest change in a score that is meaningful to the patient.