Biostats Chapter 4 and 5

Correlation coefficient r

measures strength and direction of linear relationship between two continuous variables, from –1 to +1.

when to use Pearson versus Spearman correlation

pearson for interval/ratio

spearman for ordinal data

both for linear correlations

coefficient of determination r2

the proportion of the variance in one variable that is accounted for, or “explained,” by the variance in the other variable

if Pearson r= .5 means .5 correlation between test scores and class attendance, then r squared = .25 or 25% of the variance in test scores can be predicted by class attendance

Regression

If two variables are highly correlated, it is possible to predict the value of one of them (the dependent variable) from the value of the other (the independent variable)

linear regression

Y= a + bx + e

x= age

a= the y intercept

b= slope

e= error

line of best fit to scattergrams

multiple regression

Y = a + B1X1 + B2X….

interval or ratio data

multiple independent variables

when predicting the value of a variable

logistic regression

transform the linear regression data so that the values of Y are limited to the range of 0 to 1, giving us the probability of the outcome Y occurring (like any probability, it can range only from 0 to 1) for given values of X

nominal data when predicting the value of a variable

outcome variable is dichotomous nominal variable

Survival analysis (aka Cox proportional Hazards analysis)

“time to event” data

interval or ratio data

Kaplan- Meier Analysis (cox regression)

type of survival curve

This plot shows the proportion of people surviving for any given length of time.

hazard ratios

used in survival analysis

quantifies the relative likelihood of an event occurring in one group compared to another at any given point in the study

hazard score less than 1, 1 and greater than 1

less than one indicates a protective effect

1= no effect

greater than 1 = a risk factor