Assignment 4

One Way ANOVA

宋春林

Group 2; ID: 201328006310005

Data

随机在A、B、C三地抽取家蝇，测量翅膀长度，一共五十个样本，数字特征分别为μ1、μ2和μ3。问题：三地家蝇翅膀长度是否有差异？

H0假设：μ1=μ2=μ3，即三地家蝇翅膀长度无显著差异

Ha假设：μ1，μ2，μ3不完全相等，即三地家蝇翅膀长度至少有一个与其他样地有显著差异

α=0.05

R Script

# 输入数据
site1 <- c(45, 44, 43, 47, 48, 44, 46, 44, 40, 45, 42, 40, 43, 46, 47, 45, 46, 
    45, 43, 44)
site2 <- c(45, 48, 47, 43, 46, 47, 48, 46, 43, 49, 46, 43, 47, 46, 47, 46, 45, 
    46, 44, 45, 46, 44, 43, 42, 45)
site3 <- c(47, 48, 45, 46, 46, 44, 45, 48, 49, 50, 49, 48, 47, 44, 45, 46, 45, 
    43, 44, 45, 46, 43, 42)
fly.survey <- data.frame(length = c(site1, site2, site3), site = factor(c(rep("1", 
    20), rep("2", 25), rep("3", 23))))
# 检查数据
options(digits = 3)  # default value = 7
tapply(fly.survey$length, fly.survey$site, mean)

##    1    2    3 
## 44.4 45.5 45.9

tapply(fly.survey$length, fly.survey$site, var)

##    1    2    3 
## 4.56 3.26 4.48

boxplot(length ~ site, data = fly.survey, xlab = "Sites", ylab = "Length")

# Bartlett Test方差齐性检验（参数）
bartlett.test(length ~ site, data = fly.survey)

## 
##  Bartlett test of homogeneity of variances
## 
## data:  length by site
## Bartlett's K-squared = 0.764, df = 2, p-value = 0.6825

# 单因子方差分析One Way ANOVA
fit <- aov(length ~ site, data = fly.survey)
summary(fit)

##             Df Sum Sq Mean Sq F value Pr(>F)  
## site         2   26.3   13.15    3.24  0.045 *
## Residuals   65  263.4    4.05                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

plot(fit)

Conclusion Statement

单因子方差分析结果显示F value = 3.24 ，Pr(>F) = 0.045，因此拒绝H0假设，即认为三地家蝇翅膀长度在统计学上有显著差异。

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