Correlation

Curvilinear Relationships

A mathematical relationship with variables clearly related. Ex: How much caffeine consumption affects testing scores.

What is the range for results of correlation?

Above .05 = not real Below .05 = REAL

What type of relationships do Correlations have?

- Used to describe LINEAR relationships. -Can also describe non-linear monotonic relationships: never goes the opposite direction (does not turn or goes down).

Important notes about Correlation Coefficients (r):

- Make no distinction between variables -r has not units of measurement. It uses standardized score (or rank scores)>

Direction

- Negative or positive relationship? r(correlation coefficient)

How is a correlation low or high?

- The low correlation is less together while the high correlation is closer together on the line.

Example of Reporting Correlations if significance?

"Pearson correlation was used to assess the relationship between excersice (hours/weel) and resting heart rate (BPM). There was a significant negative correlation between amount og exercise and resting heart rate, r-.829

Example of reporting correlations if not significant?

"Pearson correlation was used to assess the relationship between medication time (weeks) and body weight (lbs). The correlation was not significant, p=.36.

P-Values

(Probability Value) Real Def: probability of getting the result you got if the null hypothesis was true. Functional Def: probability that the results favor a random pattern.

"Spearman's Rho" rank correlation coefficient

- Does not assume normal distributions of raw data. -Variables do not have to form linear relationships.

Correlation: Basic Premise

- If 2 variables are correlated, they are in some way: As values of one variable changes, the value of the other variable tends to change. (Linear Correlation)

"Pearson" correlation coefficient

-Assumes normal distribution of raw quantities (continuous data) -Assumes linear relationships between 2 quantitative variables -Interval or ration scales only.

Strength

-Does relationship appear to hold for most people?

What is the first step when working with correlation?

-Get a picture of your data because it the determines which statistic to use. --> SCATTERPLOT.

Form (Shape)

-Is pattern linear or at least monotonic? - Are there dramatic deviations or "outliers"

Statistical Significance

-Stats can interpret results only if it is significant. - Significant = low probability

Two important points of Correlation

1) Correlation describes a general tendency (does not occur for everyone, but does occur for most). 2) Correlation does not mean causation.

Using SPSS to graph a scatter plot?

1) Define Variables, enter data 2)Select "graphs" from top menu 3) Select "scatter/dot" 4) Select "simple scatter"

What do you see from a scatterplot?

Form(Shape),Direction, Strength

Interpreting Results of Correlations

Look at the one with 3 boxes; Tells us 1) Correlation Significance(2-tailed)-1 to 1 2)The direction 3) Strong N = number totalof people

Negative Correlation

Two variables changes in opposite ways: If one variable increases then other variable decreases.

Positive Correlation

Two variables changes in the same way: If one variable increases then other variable increases.

P- Value is low good?

Yes, because the chance that is real is high. -The lower the p-value, the lower the chance your finding is just some random pattern.This means the higher the change your finding is a real systematic pattern.

Correlation (r):

r = # between -1 and 1 -1 correlation: perfect negative 1 correlation: perfect positive 0 correlation: no relationship