56. Factorial designs have been used in forestry to assess the effects of various factors on the growth behavior of trees. In one such experiment, researchers thought that healthy spruce seedlings should bud sooner than diseased spruce seedlings

(“Practical Analysis of Factorial Experiments in Forestry,”

Canadian J. of Forestry, 1995: 446–461). In addition, before planting, seedlings were also exposed to three levels of pH to see whether this factor has an effect on virus uptake into the root system. The following table shows data from a 2  3 experiment to study both factors:

pH 3 5.5 7 Diseased 1.2, 1.4, .8, .6, 1.0, 1.0, 1.0, 1.2, .8, 1.0, 1.2, 1.4, 1.4 .8 1.2 Health Healthy 1.4, 1.6, 1.0, 1.2, 1.2, 1.4, 1.6, 1.6, 1.2, 1.4, 1.2, 1.2, 1.4 1.4 1.4 The response variable is an average rating of five buds from a seedling. The ratings are 0 (bud not broken), 1 (bud partially expanded), and 2 (bud fully expanded). Analyze this data.