Print the dataframe

print(df)

##    OBS ID    Y TIME
## 1    1  1 26.5    0
## 2    2  1 14.8    1
## 3    3  1 19.5    4
## 4    4  1 21.0    6
## 5    5  2 25.8    0
## 6    6  2 23.0    1
## 7    7  2 19.1    4
## 8    8  2 23.2    6
## 9    9  3 20.4    0
## 10  10  3  2.8    1
## 11  11  3  3.2    4
## 12  12  3  9.4    6

#Summary Statistics by Time

library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

df_summary<-df%>%
  group_by(TIME)%>%
  summarize(mean_Y=mean(Y))
print(df_summary)

## # A tibble: 4 × 2
##    TIME mean_Y
##   <int>  <dbl>
## 1     0   24.2
## 2     1   13.5
## 3     4   13.9
## 4     6   17.9

#Summary Statistics by ID

df_summary_2<-df%>%
  group_by(ID)%>%
  summarize(mean_Y=mean(Y))
print(df_summary_2)

## # A tibble: 3 × 2
##      ID mean_Y
##   <int>  <dbl>
## 1     1  20.4 
## 2     2  22.8 
## 3     3   8.95

library(dplyr)

# Summarize the data to get the mean of 'Y' for each 'ID'
df_summary_2 <- df %>%
  group_by(ID) %>%
  summarize(mean_Y = mean(Y))

# Create a boxplot of the mean_Y values
boxplot(Y ~ ID, data = df, main = "Boxplot of Mean Y by ID", ylab = "Mean Y",col=c('red','green','black'))

#Conduct Normality test

# Conduct Shapiro-Wilk test for normality for each group defined by ID
shapiro_results <- by(df$Y, df$ID, shapiro.test)

# Output the results
print(shapiro_results)

## df$ID: 1
## 
##  Shapiro-Wilk normality test
## 
## data:  dd[x, ]
## W = 0.98569, p-value = 0.9345
## 
## ------------------------------------------------------------ 
## df$ID: 2
## 
##  Shapiro-Wilk normality test
## 
## data:  dd[x, ]
## W = 0.93983, p-value = 0.6533
## 
## ------------------------------------------------------------ 
## df$ID: 3
## 
##  Shapiro-Wilk normality test
## 
## data:  dd[x, ]
## W = 0.85228, p-value = 0.2336

##Variance test

# Conduct Bartlett's test for homogeneity of variances for each group defined by ID
# Conduct Bartlett's test for homogeneity of variances
variance_results <- bartlett.test(Y ~ ID, data = df)

# Output the results
print(variance_results)

## 
##  Bartlett test of homogeneity of variances
## 
## data:  Y by ID
## Bartlett's K-squared = 2.8185, df = 2, p-value = 0.2443

#Conduct Anova

model=lm(Y~factor(TIME),data=df)
summary_model=summary(model)
summary_model

## 
## Call:
## lm(formula = Y ~ factor(TIME), data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -10.733  -4.992   1.917   5.208   9.467 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     24.233      4.617   5.249 0.000775 ***
## factor(TIME)1  -10.700      6.529  -1.639 0.139883    
## factor(TIME)4  -10.300      6.529  -1.578 0.153319    
## factor(TIME)6   -6.367      6.529  -0.975 0.358058    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 7.996 on 8 degrees of freedom
## Multiple R-squared:  0.3023, Adjusted R-squared:  0.04066 
## F-statistic: 1.155 on 3 and 8 DF,  p-value: 0.3847

# Perform one-way ANOVA
anova_result <- aov(Y ~ factor(TIME), data = df)

# Print the ANOVA summary
sanova<-summary(anova_result)
sanova

##              Df Sum Sq Mean Sq F value Pr(>F)
## factor(TIME)  3  221.6   73.88   1.155  0.385
## Residuals     8  511.5   63.94

Anova-one way

Hassan N

2024-06-03

One way Anova

Data in a string format

Read the data into a dataframe

Print the dataframe