Fully Factorial ANOVA

Fully Factorial ANOVA

1. Effect of >1 independent variable on the independent variable *Interaction between factors*

   • Two approaches when considering an interaction between factors of interest
   • Analysis Steps
     • 1. load the required libraries
     • 2. Load the Data
     • 3. Visualise the data
       • head(data)
       • str(data)
       • Visualise any initial patterns using BOX PLOTS
         • interaction plot
           • Generally, if lines are parallel it is unlikely to be a interaction, if lines are not parallel, indicates some sort of interaction
     • 4. Create the Model
       • y ~ a + b + a:b
         • y ~ a*b, data=Data(file)
           • a*b stand for 'fully factorial'
             • 3 factors the general form would be lm(y ~ a + b + c + a:b + a:c +b:c + a:b:c, data=Data) but lm(y ~ a*b*c, data=Data) would do the same thing.
     • 5. Check the assumptions
       • Normal distribution of residuals
         • Method 1. Quantile Plot
         • Method 2. Histogram - will studentised residuals (divided by the SD)
         • Method 3. Hypothesis test (Shapiro-Wilk normality test)
           • if p value above 0.05 , we can assume distribution is normal
       • Homoscedascity (homogenous or equal variances)
         • Method 1. Residuals vs fits plot
           • Looking for clustering or no structure on vertical y axis
         • Method 2. levene test
           • Since the p -value is >0.05, we accept the null hypothesis that the variances are equal.
         • Plot means
     • 6. Run the anova and any post-hoc tests if required
       • is there a signficant interaction?
         • Do the factors have an effect on their own?
           • Post-Hoc test (TukeyHSD)
             • Summary Table
     • 7. Plot the results
       • Plot of means +/- standard error or boxplots
     • 8. Write up
       • METHODS - The aim of the experiment was to determine the effects of chilling on two varieties of grass (Quebec and Mississippi) with respect to CO2 uptake. Plants were either chilled or left at room temperature overnight (n=25). Data was screened for homogeneity of variance and normality visually and statistically with both assumptions met (p>0.05). A two-factor, fully factorial anova was run using the grass type and chilling treatment as factors (α = 0.05).
       • Results: A two-way Fully Factorial ANOVA (a=0.05) showed there was no significant interaction between the grass type and chilling treatment (F_1,96=0.6168,p=0.43). Mean CO2 uptake was significantly higher in the Mississippi grass type than in the Quebec grass type (F_1,96=42.27,p<0.001). Chilling the plants significantly decreased the mean CO2 uptake (Figure 1;(F_1,96=30.42,p<0.001).
       • Discussion: Chilling affected both species by decreasing CO2 uptake. Therefore the grass types are equally sensitive to chilling. Overall the Mississippi grass type had higher CO2 uptake indicating that it has a higher photosynthetic efficiency in both chilled and non-chilled conditions. Future assessments would assess a broader range of temperatures to determine threshold tolerances for both grass species.