Biostats Exam 3

Correlation

a relationship between two variables

Positive relationships

an increase in one variable predicts an increase in the other

Negative relationships

an increase in one variable predicts a decrease in the other

A correlation alone cannot be used to make a definitive statement about

causation

Sign in a correction

Direction

Number in a correction

Strength

Which graph is the most effective way of presenting relationship data

Scatterplots

Negative relationship scatterplot

slanting downward

Positive relationship scatterplot

Slanting upward

Curvilinear relationships scatterplot

Curve in the graph

Assumptions of the Pearson Correlation

- Uses two variables

- Both quantitative*

- Linear relationship

- Minimal skew/no large outliers

- Must observe the whole range for each variable

Pearson r correlation coefficient

a way of numerically expressing correlation

Pearson r range

-1 to +1

(Nonparametric Analysis) Spearman's Rank data

for ordinal and skewed data

Kendall's tau-b

for ordinal and skewed data, less affected by error

ETA

a special coefficient used for curvilinear relationships

Interpreting Correlation Values calculation

r^2 * 100

r^2 * 100 meaning

% change in variable accounted by another variable

Regression

Predict an output

How does Regression differ from Correlation? (correlation)

quantifies the strength of the linear relationship

How does Regression differ from Correlation? (regression)

Expresses the relationship in the form of an equation.

Finding a linear regression line equation

y = mx + b

What is a requirement regarding the number of variables in linear regression?

Requires 2 or more scalar variables

What types of variables are involved in linear regression?

Dependent variable and one or more Independent variables

What type of relationship does linear regression assume between variables?

Linear relationship

What is the homoscedasticity assumption in linear regression?

The data must be homoscedastic

Homoskedasticity

the property of a dataset having variability that is similar across it's whole range

heteroskedastic

Graph gets wider the more time goes on

Linear Regression Output (R)

correlation of model output

R^2

coefficient of determination

Adjusted R2

independent variables and the sample size

Std. Err. of the Estimate

A measure of how accurately the model predicts the dependent variable

ANOVA tells us

the independent variables overall predict the dependent

Unstandard B

the unit change in the dependent per unit change in the independent

Beta

tells you how strongly this variable predicts the dependent

t & sig

if the variable was a significant predictor of the dependent

t-test

evaluate the size and significance of the difference between two means

One-sample t-Test

When you want to compare a sample mean to some known or hypothesized value

Independent samples t-Test

compare two groups to one another

Repeated Measures t-Test

How a group changes over time

One sample t-test data

interval or ratio data

What is unknown in a One sample t-test

The true standard error of the mean

Degrees of freedom in a one-sample t-test.

n -1

one-sample t-test statistics (t)

test statistic

one-sample t-test statistics (df)

degrees of freedom

one-sample t-test statistics (sig)

p value for the test statistic

Independent Samples t-test data

interval or ratio data

What makes a Independent Samples t-test different from one another

The samples are independent from one another

Independent Samples t-test Degrees of freedom

n-2

Test Variables

the variables you want to investigate

Grouping Variable

the variable that will split your data into two groups

Paired Samples t-Test data

interval or ratio data

Paired Samples t-Test measures

two variables with values paired by subject

Paired Samples t-Test Degrees of freedom

(n / 2) -1

Reporting Pearson correlation

r(N) = .sig, p =

Nonparametric tests

No need for normality

Nonparametric tests data

ranked/ordinal data

The 1-Sample Kolmogorov

Smirnov is used to test normality of data

Independent Samples will produce

Mann-Whitney U

Related Samples will let you calculate

Wilcoxon Rank-Sum

Exact significance

the exact significance is calculated from all potential distributions

Asymptotic significance

calculated using an estimated curve

Monte-Carlo significance

uses a random process to estimate the significance using areas under the curve

One Sample T

comparing a sample to a hypothesized mean

Independent Samples T

comparing two groups on some value

Repeated Measures T

comparing two variables within a set of subjects

Parametric or Nonparametric?

Parametric because they are more statistically powerful

ANOVA stand for

ANalysis Of VAriance

ANOVA concerns

sources of variance in a dataset

One-Way ANOVA is more similar to

t-Tests than it is to the other ANOVA tests

F-ratio

The variability between groups divided by the variability within groups

What kind of test is ANOVA

Omnibus test

Omnibus test

an overall difference exists, without going into the specifics of any differences

One Factor ANOVA type of data

interval or ratio data

Samples in One Factor ANOVA

ndependent from one another

Degrees of freedom in One Factor ANOVA

(number of scores) - 1

Repeated Measures ANOVA subjects

independent from one another

Repeated Measures ANOVA data

Normal

sphericity for ANOVA

variance of each variable is equal

Multivariate Tests

How strongly the factor accounts for changes in the variables

Mauchly's Test

if the variances are equal

Greenhouse-Geisser Correction

Adjustment for violations of sphericity in ANOVA.

Multivariate tests

Allows for investigating the effect of multiple independent variables on one dependent variable

Main Effect

This is the effect of a single factor on the dependent variable

Interaction

Interactions ask if the main effects of two different factors affect one another

Post-Hoc analyses

statistical analyses that the researcher did not plan for before data collection or analyses began.

when will a Post-Hoc analyses get run

Getting a significant result on the initial test

Fisher's LSD (Least Significant Differences)

Only used after a significant F test, but tends to raise alpha

Bonferroni Correction

Tests each comparison at α / n

Tukey's HSD

Alternative to the LSD, called "Tukey" in SPSS

Dunnett

Used to compare many groups to a single control