**Software for Exploratory Data Analysis and Statistical Modelling**, and kindly contributed to R-bloggers)

In a previous post we considered using **R** to fit one-way ANOVA models to data. In this post we consider a few additional ways that we can look at the analysis.

In the analysis we made use of the linear model function **lm** and the analysis could be conducted using the **aov** function. The code used to fit the model is very similar:

> plant.mod2 = aov(weight ~ group, data = plant.df) > summary(plant.mod2) Df Sum Sq Mean Sq F value Pr(>F) group 2 3.7663 1.8832 4.8461 0.01591 * Residuals 27 10.4921 0.3886 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

The output from using the **summary** function of the fitted model object shows the analysis of variance table with the p-value showing evidence of differences between the three groups. In **R** we can investigated the particular groups where there are differences using Tukey’s multiple comparisons:

> TukeyHSD(plant.mod2) Tukey multiple comparisons of means 95% family-wise confidence level Fit: aov(formula = weight ~ group, data = plant.df) $group diff lwr upr p adj Treatment 1-Control -0.371 -1.0622161 0.3202161 0.3908711 Treatment 2-Control 0.494 -0.1972161 1.1852161 0.1979960 Treatment 2-Treatment 1 0.865 0.1737839 1.5562161 0.0120064

The multiple comparison tests highlight that the difference is due to comparing treatments 1 and 2. These 95% confidence intervals for the differences shown above can be plotted:

plot(TukeyHSD(plant.mod2))

which gives

The post-hoc adjustments are recommended as we are testing after looking at the data rather than undertaking a pre-planned analysis.

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