Week 5 - ANOVA Discussion

Discussion Question

The R datasets library contains data on air quality in New York (airquality). Conduct a hypothesis test to evaluate if ozone levels are a function of month. NOTE: dichotomize month. If that test were significant, what else would be required? Post your hypothesis test and R code with your discussion.

Answer

This question confused me a little bit. My gut check says to do an ANOVA on the data (which I do in the R code below). The results from that show a P-value of 0.0776, which is low, but would not be significant with a significance level of 0.05. Generating a barplot of the means shows an upward trend, but a Chi-square test generates a P-value of 0.5142 which is not significant.

# Run an ANOVA on the data set
aq_aov = aov(Ozone~Month, data=airquality)
summary(aq_aov)

##              Df Sum Sq Mean Sq F value Pr(>F)  
## Month         1   3387    3387   3.171 0.0776 .
## Residuals   114 121756    1068                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 37 observations deleted due to missingness

aq_tab = model.tables(aq_aov, "means")

## Warning in replications(paste("~", xx), data = mf): non-factors ignored: Month

barplot(aq_tab$tables$Month)

chisq.test(aq_tab$tables$Month)

## 
##  Chi-squared test for given probabilities
## 
## data:  aq_tab$tables$Month
## X-squared = 3.2669, df = 4, p-value = 0.5142