KRIGOLSON TEACHING
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Paired Sample TTests

TTests are inferential statistical tests that allow you to draw conclusions about data. There are three types of ttests and they are used in very specific situations.

Paired (or dependent) sample t-tests are used when you want to compare two dependent, or related samples. For instance, if you measure fitness test scores for a single group of participants at two different points in time. Another dependent example would be having a single group of participants perform an experimental task in two different conditions. Another way to think of it would be that in paired, or dependent tests, all participants take part in all conditions - whether it is the same test separated by time or two conditions.

For example, as a researcher you have a new diet you want to put people on to see if it results in a loss in the amount of calories consumed on a daily basis. You measure the average daily calories consumed at the start and end of the diet. The data is HERE.

Load the data in R in a new variable called caloriedata. Note that the data has three columns, the first coding the subject number, the second coding the time point (1 = pretest, 2 = posttest), and the third the caloric intake measured at the time point. Let's give the columns in the table names:
names(caloriedata) = c('subject','time','calories')

The column for time is a factor, or independent variable. In R, you need to define factors as factors. Let's do this:

caloriedata$time = factor(caloriedata$time) 
Note, this was not necessary in Lesson 5A as there was only one set of data for one group.

​Also look at the subject column. You will note that the subject numbers 1 to 50 are repeated - that is a clear indicator this is a paired or dependent design.

Now, lets run a paired samples ttest to compare the average amount of calories consumed at the two time points.
analysis = t.test(caloriedata$calories ~ caloriedata$time, paired = TRUE)


Note the notation here, the code would translate to "Let's run a ttest where we examine caloriedata$calories as a function of caloriedata$time - by the way, its a paired/dependent samples ttest.

To see the results of the ttest, simple type:
print(analysis)

You should find that the result of the ttest is p = 0.02704.

Make sure you understand what degrees of freedom are. For a dependent samples ttest the degrees of freedom are: df = n -1.


Review. If you want to see the means of the data (or other descriptives) for the actual conditions - not the difference scores which are in the analysis results, you could do something like:
mean(caloriedata$calories[caloriedata$time == 1])

Assignment Question
The assignment questions for the sections 5A, 5B, and 5C can be found at the end of section 5C.
  • 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