Recipe 4: Completely Randomized Block Designs from the literature

Recipe for Completely Randomized Block Designs from the literature

Wei Zou

RPI

Oct 15, 14; Version 1

1. Setting

System under test

The purpose of this recipe is to replicate the experiment from a paper written by Rufino et.al (“Effect of substitution of soybean meal for inactive dry yeast on diet digestibility, lamb's growth and meat quality”) and validate the results from the experiment. In this project, we test the effect of substitution of soybean meal for inactive dry yeast on nitrogen balance, a subset of the data used in the original study with 12 obs is used to conduct the analysis of variance.

#Set my working directory
setwd("C:\\Users\\wei\\Desktop")

#import the data
data1<- read.csv ("table.csv",header=TRUE,sep = ",", quote="\"", dec=".");
head(data1)

##   YieldSub Nbalance
## 1        0      6.0
## 2       33      7.5
## 3       67      3.6
## 4      100      2.9
## 5        0      6.1
## 6       33      7.4

attach(data1)

Factors and Levels

This sub-dataset has one factor with four levels, namely four different Yeast substitution rates: 0%, 33%, 67%, 100%.

YieldSub<-as.factor(YieldSub)
nlevels(YieldSub)

## [1] 4

Continuous variables (if any)

The continuous variable in this sub-dataset is the nitrogen balance level (in g/day)

Response variables

The response variable in this study is the nitrogen balance (in g/day)

The Data: How is it organized and what does it look like?

The original experiment was conducted at the Animal Laboratory of the Anaimal Science Department, Federal Universtiy of Vicosa, from December 2009 to March 2010. It contains two parts: in part 1, the researchers evaluated the apparent nutrient digestibility, pH and ruminal ammonia concentration; in part 2, the researchers “investigated the nutrient intake, growth performance and meat quality of lambs fed fiets containing replacement levels of foybean meal by inactive dry yeast”.Therefore we have one factor with four levels with many testing continuous response variables.

Randomization

According to the authors, this is a randomized block design with four treatments (four percentages of yeast substitution) and nine replicates.

2. (Experimental) Design

How will the experiment be organized and conducted to test the hypothesis?

In this sample recipe, the effect of yeast substitution on the mean nitrogen balance is studied. An anova is performed to verify if the variation in mean nitrogen balance is due to pure sample randomization or the yeast substitution has a contribution effect. Therefore; H0: The variation in nitrogen balance is due to sample randomization only. HA: The variation in nitrogen balance is due to something other than sample randomization (in this experiment we test the effect of substitution of soybean meal for inactive dry yeast)

What is the rationale for this design?

An anova was conducted as the designed experiment has one factor with multiple levels.

Randomize: What is the Randomization Scheme?

It is noted by the authors that this is a completely randomized design.

Replicate: Are there replicates and/or repeated measures?

The original experiment has nine replicates.

Block: Did you use blocking in the design?

yes, the researchers divided the study period into three periods of 21 days, after 15 days of adaptation.

3. (Statistical) Analysis

(Exploratory Data Analysis) Graphics and descriptive summary

The boxplot shows that the the nitrogen balance level varies a lot among the four groups (medians vary among the four substitutition rate), indicating that it is highly possible that the variation in nitrogen balance level can be explained by the variation in the Yeast substitution rate.

#bloxplots 
boxplot(Nbalance~YieldSub,names=c("0%","33%","67%","100%"))

Testing

According to the result of the one factor, multiple level analysis of variance, we reject the null hypothesis that the variation in nitrogen balance level is due to sample randomization only and the effect of Yeast substitution rate is shown to be statistically siginificant.

model1 = aov (Nbalance~YieldSub, data = data1)
anova(model1)

## Analysis of Variance Table
## 
## Response: Nbalance
##           Df Sum Sq Mean Sq F value Pr(>F)   
## YieldSub   1   22.0   22.00    18.9 0.0015 **
## Residuals 10   11.6    1.16                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Diagnostics/Model Adequacy Checking

The qqplot shows that the residuals generated from our anova generally follows a normal distribution, the dispersion along the qqline is largely due to the small sample size in the subsample. The “random” distribution of the residuals is hardly to tell due to the small sample size, however, at least the current doesn't show any trend.

#qqplot
qqnorm(residuals(model1),ylab="Nitrogen balance level (g/day)")
qqline(residuals(model1),ylab="Nitrogen balance level (g/day)")

#Fitted Y vs. Residuals
plot(fitted(model1), residuals(model1))

4. References to the literature

http://www.smallruminantresearch.com/article/S0921-4488(12)00422-1/abstract?cc=y