KRIGOLSON TEACHING
  • NEUROSCIENCE
    • NEUROSCIENCE 100 >
      • NEURO 100 INTRODUCTION
      • NEURO 101 ADVANCED
      • NEURO 102 AGING
      • NEURO 103 MEMORY
      • NEURO 104 DECISION MAKING
      • NEURO 105 LEARNING
      • Research Statistics
    • NRSC 500B / MEDS 470
  • Kinesiology
    • EPHE 245 >
      • LABORATORY
      • PRACTICUM
    • EPHE 357
  • STATISTICS
    • LECTURE >
      • INTRODUCTION TO R
      • DESCRIPTIVE STATISTICS
      • VISUALIZING DATA
      • Correlation and Regression
      • MULTIPLE REGRESSION
      • LOGIC OF NHST
      • T TESTS
      • ANOVA
      • POST HOC ANALYSIS
      • NON PARAMETRIC STATISTICS
      • FACTORIAL ANOVA
      • Repeated Measures ANOVA
      • Mixed ANOVA
      • MULTIVARIATE ANOVA
      • THE NEW STATISTICS
      • Bayesian Methods
    • ASSIGNMENTS >
      • Introduction to R >
        • INTRODUCTION TO R
        • LOADING DATA
        • DATA TABLES
      • Descriptive Statistics >
        • Mean, Median, and Mode
        • VARIANCE
        • CONFIDENCE INTERVALS
        • SHORTCUTS
      • Visualizing Data >
        • PLOTTING BASICS
        • BAR GRAPHS
        • BOXPLOTS
        • HISTOGRAMS
        • USING GGPLOT I
        • USING GGPLOT II
        • USING GGPLOT III
      • Correlation and Regression >
        • CORRELATION
        • REGRESSION
      • MULTIPLE REGRESSION >
        • MULTIPLE REGRESSION
      • Logic of NHST >
        • Sample Size and Variance
        • DISTRIBUTIONS
        • TESTING DISTRIBUTIONS
      • T-Tests >
        • Single Sample TTests
        • Paired Sample TTests
        • Independent Sample TTests
      • ANOVA >
        • ANOVA ASSUMPTIONS
        • ANOVA
      • POST HOC ANALYSIS >
        • POSTHOC ANALYSIS
      • NON PARAMETRIC STATISTICS >
        • WILCOXON TEST
        • WILCOXON SIGNED TEST
        • MULTIPLE GROUPS
      • FACTORIAL ANOVA
      • REPEATED MEASURES ANOVA >
        • RM ANOVA
        • TREND ANALYSIS
      • MIXED ANOVA
      • MULTIVARIATE ANOVA
      • THE NEW STATISTICS
      • BAYESIAN TTESTS
    • RESOURCES
    • R TIPS
  • Directed Studies
    • Advanced Topics in Motor Control A
    • Advanced Topics in Motor Control B
    • An Introduction to EEG
    • Advanced EEG and ERP Methods
    • Neural Correlates of Human Reward Processing
    • Independent Research Project
  • MATLAB
    • THE BASICS >
      • Hello World
      • BASIC MATHEMATICS
      • VARIABLES
      • Matrices
      • Writing Scripts
      • PATHS AND DIRECTORIES
      • USER INPUT
      • FOR LOOPS
      • WHILE LOOPS
      • IF STATEMENTS
      • RANDOM NUMBERS
    • STATISTICS >
      • LOADING DATA
      • DESCRIPTIVE STATISTICS
      • MAKING FUNCTIONS
      • BAR GRAPHS
      • LINE GRAPHS
      • TTESTS
    • EXPERIMENTS: THE BASICS >
      • DRAWING A CIRCLE
      • DRAWING MULTIPLE OBJECTS
      • DRAWING TEXT
      • DRAWING AN IMAGE
      • PLAYING A TONE
      • KEYBOARD INPUT
      • BUILDING A TRIAL
      • BUILDING TRIALS
      • NESTED LOOPS
      • RIGHT OR WRONG
      • SAVING DATA
    • EXPERIMENTS: ADVANCED >
      • STROOP
      • N BACK
      • Oddball
      • Animation
      • VIDEO
    • EEG and ERP Analysis >
      • ERP Analysis
  • RESOURCES
    • EXCEL
    • HOW TO READ A RESEARCH PAPER
    • HOW TO WRITE A RESEARCH PAPER
  • Workshops
    • Iowa State EEG Workshop 2018
  • Python
    • The Basics >
      • Setting Up Python
      • Hello, world!
      • Basic Math & Using Import
      • Variables
      • Matrices
      • Scripts
      • User Input
      • For Loops

CORRELATION

Picture
Load the data HERE into a table called data.

Let's plot the data using the following command: plot(data)

You should see something that looks like the plot to the right.

In statistics, sometimes we interested in the relationship between two variables. For example, is there a relationship between income and happiness? Is there a relationship between average hours of sleep per night and grade point average?

To test the extent of a relationship in statistics we use correlation. A Pearson correlation analysis return a number, "r", between -1 and 1 that represents the extent of a relationship. Positive numbers reflect a relationship wherein both the X and Y variables increase concomitantly. Negative numbers reflect a relationship wherein while one number variable increases the other decreases. A Pearson value of 0 suggests there is no relationship. However, the following relationship "strengths" are typically used: 

0.1 to 0.3 = Weak correlation
0.3 to 0.5 = Medium correlation
0.5 to 1.0 = Strong correlation
The same ranges are true for negative correlations.


Returning a correlation value in r is very easy. Try: cor(data$V1,data$V2)
You will see that there is a medium strength correlation of 0.3585659 between these two variables.

In addition to interpreting correlations using the above ranges you can also use a formal statistical test against the null hypothesis. You do this by typing: cor.test(data$V1,data$V2)

You should see that the p value in this case is less than 0.001 indicating that the correlation of the sample differs from zero.

Assignment
1. The data HERE contains 6 columns of numbers. Test the correlation between column 1 and the other 6 columns. Report both the relationships as defined above and also the p values for each correlation test.

  • NEUROSCIENCE
    • NEUROSCIENCE 100 >
      • NEURO 100 INTRODUCTION
      • NEURO 101 ADVANCED
      • NEURO 102 AGING
      • NEURO 103 MEMORY
      • NEURO 104 DECISION MAKING
      • NEURO 105 LEARNING
      • Research Statistics
    • NRSC 500B / MEDS 470
  • Kinesiology
    • EPHE 245 >
      • LABORATORY
      • PRACTICUM
    • EPHE 357
  • STATISTICS
    • LECTURE >
      • INTRODUCTION TO R
      • DESCRIPTIVE STATISTICS
      • VISUALIZING DATA
      • Correlation and Regression
      • MULTIPLE REGRESSION
      • LOGIC OF NHST
      • T TESTS
      • ANOVA
      • POST HOC ANALYSIS
      • NON PARAMETRIC STATISTICS
      • FACTORIAL ANOVA
      • Repeated Measures ANOVA
      • Mixed ANOVA
      • MULTIVARIATE ANOVA
      • THE NEW STATISTICS
      • Bayesian Methods
    • ASSIGNMENTS >
      • Introduction to R >
        • INTRODUCTION TO R
        • LOADING DATA
        • DATA TABLES
      • Descriptive Statistics >
        • Mean, Median, and Mode
        • VARIANCE
        • CONFIDENCE INTERVALS
        • SHORTCUTS
      • Visualizing Data >
        • PLOTTING BASICS
        • BAR GRAPHS
        • BOXPLOTS
        • HISTOGRAMS
        • USING GGPLOT I
        • USING GGPLOT II
        • USING GGPLOT III
      • Correlation and Regression >
        • CORRELATION
        • REGRESSION
      • MULTIPLE REGRESSION >
        • MULTIPLE REGRESSION
      • Logic of NHST >
        • Sample Size and Variance
        • DISTRIBUTIONS
        • TESTING DISTRIBUTIONS
      • T-Tests >
        • Single Sample TTests
        • Paired Sample TTests
        • Independent Sample TTests
      • ANOVA >
        • ANOVA ASSUMPTIONS
        • ANOVA
      • POST HOC ANALYSIS >
        • POSTHOC ANALYSIS
      • NON PARAMETRIC STATISTICS >
        • WILCOXON TEST
        • WILCOXON SIGNED TEST
        • MULTIPLE GROUPS
      • FACTORIAL ANOVA
      • REPEATED MEASURES ANOVA >
        • RM ANOVA
        • TREND ANALYSIS
      • MIXED ANOVA
      • MULTIVARIATE ANOVA
      • THE NEW STATISTICS
      • BAYESIAN TTESTS
    • RESOURCES
    • R TIPS
  • Directed Studies
    • Advanced Topics in Motor Control A
    • Advanced Topics in Motor Control B
    • An Introduction to EEG
    • Advanced EEG and ERP Methods
    • Neural Correlates of Human Reward Processing
    • Independent Research Project
  • MATLAB
    • THE BASICS >
      • Hello World
      • BASIC MATHEMATICS
      • VARIABLES
      • Matrices
      • Writing Scripts
      • PATHS AND DIRECTORIES
      • USER INPUT
      • FOR LOOPS
      • WHILE LOOPS
      • IF STATEMENTS
      • RANDOM NUMBERS
    • STATISTICS >
      • LOADING DATA
      • DESCRIPTIVE STATISTICS
      • MAKING FUNCTIONS
      • BAR GRAPHS
      • LINE GRAPHS
      • TTESTS
    • EXPERIMENTS: THE BASICS >
      • DRAWING A CIRCLE
      • DRAWING MULTIPLE OBJECTS
      • DRAWING TEXT
      • DRAWING AN IMAGE
      • PLAYING A TONE
      • KEYBOARD INPUT
      • BUILDING A TRIAL
      • BUILDING TRIALS
      • NESTED LOOPS
      • RIGHT OR WRONG
      • SAVING DATA
    • EXPERIMENTS: ADVANCED >
      • STROOP
      • N BACK
      • Oddball
      • Animation
      • VIDEO
    • EEG and ERP Analysis >
      • ERP Analysis
  • RESOURCES
    • EXCEL
    • HOW TO READ A RESEARCH PAPER
    • HOW TO WRITE A RESEARCH PAPER
  • Workshops
    • Iowa State EEG Workshop 2018
  • Python
    • The Basics >
      • Setting Up Python
      • Hello, world!
      • Basic Math & Using Import
      • Variables
      • Matrices
      • Scripts
      • User Input
      • For Loops