e-Statistics
e-Statistics
For Students
For Contributors
Data in Statistical Studies
Textbook Data Sets
Worksheet Data Sets
Data and Story Library
Exploratory Graphics
Stem and Leaf Plot
Histogram
Boxplot
Scatter Plot
QQ plot
Bar Graph
Descriptive Statistics
Summary Statistics
Frequency Table
Grouped Data
Transformed Data
Normal Distribution
Normal Density Function
Z-score
Critical Value
Central Limit Theorem
Discrete Distributions
Binomial Distribution
Frequency Function
Normal Approximation
Inference on Mean
t-Distribution
Confidence Interval
Hypothesis Test
Power of Test
One-sided CI
Comparison of Two Groups
Test for Independent Groups
Nonparametric Test
Test for Paired Data
Simple Linear Regression
Regression Line
R Square
Residual Plot
Inference on Parameters
Predicting Responses
One-Way ANOVA Model
F-Distribution
Analysis of Variance
Strip Chart
Multiple Comparisons
Multiple Linear Regression
Model Estimate and Residuals
Model Selection and F-test
Two-Way Additive Model
Test of Effect
Analysis of Variance
Inference on Variances
Testing a Standard Deviation
Test for Two Groups
Test for Homogeneity
Inference on Proportions
Testing a Proportion
Comparison of Two Proportions
Chi-square Test
Chi-square Distribution
Goodness of Fit
Test for Homogeneity
Logistic Regression
Inference on parameters
Adjusted log OR

One-Way ANOVA Model

When the effect of $ k$ different groups is of our interest, an experimental design of one-way layout (or one factor layout) can be considered. The groups are generally referred as “treatments” or “factor levels.” For example, a researcher wants to investigate the blood cholesterol of men in three different socioeconomic groups, say level 1, level 2 and level 3. In general the data set of the experiment can be presented in the following table.

Level Sample data Sample size
1 $ X_{11},\ldots,X_{1n_1}$ $ n_1$
$ \vdots$ $ \vdots$ $ \vdots$
k $ X_{k1},\ldots,X_{kn_k}$ $ n_k$

© TTU Mathematics