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df <- read.csv("Cancer.csv")

1.a. Yes, breast has the highest median. It also has the greatest IQR, along with ovary. Ovary’s box appears to have values skewed downward, and stomach’s as well (though to a lesser extent).

boxplot(
df$Survival ~ df$Organ,
main="Survival Time by Organ",
ylab="Survival (days)",
xlab="Organ"
)

1.b. Reject the null hypothesis, each mean is different.

mean_by_organ <- tapply(df$Survival, df$Organ, mean, na.rm = TRUE)
print(mean_by_organ)
##    Breast  Bronchus     Colon     Ovary   Stomach 
## 1395.9091  211.5882  457.4118  884.3333  286.0000

1.c. Through calculation, every standard deviation is different.

stdev_by_organ <- tapply(df$Survival, df$Organ, function(x) sd(x, na.rm = TRUE))
print(stdev_by_organ)
##    Breast  Bronchus     Colon     Ovary   Stomach 
## 1238.9667  209.8586  427.1686 1098.5788  346.3096

1.d. 0.05

1.e-g. SSTO=37983905, MSTO=3332214

anova_result <- aov(Survival ~ Organ, data = df)
summary(anova_result)
##             Df   Sum Sq Mean Sq F value   Pr(>F)    
## Organ        4 11535761 2883940   6.433 0.000229 ***
## Residuals   59 26448144  448274                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

1.h. Reject the null hypothesis.

{knitr::opts_chunk$set(echo=TRUE)}