Multiple Testing

Type I Error

Correcting Type 1 Errors

What is ANOVA?

Difference between ANOVA and T-Test

Example – Crop Yield from Different Fields Treated with Different Amount of Fertilizer

Why is ANOVA Needed?

Interaction Effect of the Nominal Variables

Comparison of Crop Yield

Introduction to ANOVA

Independent Samples

Type I Error

Multiple Tests for a Single Experiment

Statistical Corrections

Type 2 Error

Correcting for Multiple Testing

Measurement Variable in ANOVA

Scenario 2

Crop Yield from Different Fields

Make a Box Plot of the Data at the Various Water Depths

Multiple Comparisons

Multiple Comparison

Pairwise Comparisons

Summarize

Calculate a Standard Error

Create a Bar Plot

Bar Plot

Create the Bar Plot

Scale Y Continuous

Intro

Calculating Pooled Standard Error

Example of Computing the Pooled Error Term

Conclusion

Mean Squared Error

Mean Squared Error Formula

What is Error?

Final Sum of Squares Between Subjects

Finding Sample Means

Grand Mean

Square Each Deviation

Graphing Means

One-Way Analysis of Variance

Pairwise T-Test Function

Bonferroni Multiple Comparison Test

Calculate a Standard Error

Plot the Standard Errors

Letters of Significant Difference

Vertical Adjustment Function

Terminology in ANOVA

Mean Squares (MS) and Variance

Why do We Use Variance for Mean Values?

Calculating the Mean Square, Sum of Squares and Degrees of Freedom of the Treatment

Calculating the Mean Square, Sum of Squares and Degrees of Freedom of the Error

Calculating the Total Sum of Square and Total Degrees of Freedom

Calculating the F-Value

The Critical F-Value (Accept/Reject Decision)

A Great ANOVA Resource (Free Top 10 Topic Course)

A Great Free Resource (Free Top 10 Topic Course)

Why block in an ANOVA?

Crop Yield Example

Summary of ANOVA Model

Sum of Squares Total

Sum of squares error

Degrees of Freedom

Standard deviation

Some useful mathematical facts

Standard error of the sample mean

Variance

Summary of the t-test

Sampling Distribution

Introduction

What is One-Way ANOVA?

Formula for Overall Mean

Sample Variance Formula

Sum of Squares Error Formula

Sum of Squares Within Formula

One-Way ANOVA Table

Pooled Variance

F Distribution

P-Value

Introduction

Independent groups ANOVA

Computing the effect of individual differences

Computing the F-value

Degrees of freedom between treatments

Calculating person totals

Person totals

Running the calculations

Computing between-subject effects

Degrees of freedom for sum of squared error

Intro

Formula for the F-value

Denominator of F-value

Logic behind the partitioning of variance

Variance between individual score and grand mean

Grand mean

Partitioning Variance

Summary

Interpreting the F-value

Intro

The ANOVA Model

Example: Ratings of Chocolate Bars

Model Sum of Squares

Degrees of Freedom Formula

F-Tests

ANOVA Test Statistic Formula

ANOVA for More Than Three Groups

Interpreting a Significant F-Test

Credits & Thanks

Data setup

Adding the Analysis Toolpak

Selecting data range

Examining the output

Inserting a graph

Cleaning up the graph

Adding a y-axis label

Calculating standard error

Specifying custom error bars

Adding error bars

Finding the total degrees of freedom

Finding the number of observations in each group

Finding SSE

Finding the Mean Squares

Mean squared error

Finding the F test statistic

Degrees of freedom for F test

Denominator Degrees of Freedom