Three different varieties of tomato (Harvester, Ife No. 1 and Pusa Early Dwarf) and two different plant densities (10, 20 thousand plants per hectare) are being considered for a particular region. To determine the effects of the variety and the plant density on the yield, each combination of variety and plant density is tested on three different plots resulting in the data shown below. Source: Effects of plant density on Tomato Yields in Western Nigeria, Experimental Agriculture, 1976, 43-47.

You may copy the following code into R: df = data.frame( variety = as.factor(c(1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3)), density = as.factor(c(1,1,1,2,2,2,1,1,1,2,2,2,1,1,1,2,2,2)), yield = c(10.4,9.2,8.1,12.8,11.2,13.2,8,8.6,10.3,12.6,13.6,11.4,15.9,15.5,17.3,16.5,19.2,18.5) )

Perform a two-way ANOVA to test for significant main and interaction effects. Factor A is the variety of tomato, factor B is the plant density and the interaction refers to their combined effects.

1. Source	Sum of squares	Degree of freedom	Mean squares	F-ratio	P-value
   Factor AA (variety)
   Factor BB (density)
   Interaction
   Residuals
   Total

2. Interpret the results of each part of the ANOVA. Variety of tomato
   • The effects of the variety of tomatoes are statistically significant.
   • The effects of the variety of tomatoes are not statistically significant.
   Plant density
   • The effects of the plant density are not statistically significant.
   • The effects of the plant density are statistically significant.
   Interaction effects
   • The effects of the interaction are not statistically significant.
   • The effects of the interaction are statistically significant.