"single factor anova with blocks. the forest service conducted an experiment on the growth rate of eight provenances (trees growing at a particular place of origin) of gmelina arborea (the treatments) were compared with respect to the girth at breast-height (gbh) of the trees attained since 6 years of planting (the response variable). since planting location could be a factor in growth, they used three blocks as plot locations that represented different soils and gradients.

a. list the degrees of freedom for the provenances and the blocks.

The degrees of freedom, in statistics, it's an equation that represents how many values of all data have the freedom to variate. The main function of this statistical magnitude is to ensure statistical validity, because if there're too many values that can variate, would mean that all of them are too separated from each other, which probably will skew the analysis.

In addition, to calculate the degrees of freedom (df), we apply this simple equation: df = N - 1; where N is the sample selected for the study. So, the experiment conducted uses 8 provenances, therefore, they df would be 7 (df = 8-1).

On the other hand, in the study, there are 3 blocks, which means that the degrees of freedom is 2 (df = 3 - 1).

Moreover, the df is a tiny part of the statistical analysis, but it's pretty helpful because it can allow the analyst to determine a probability value, which is the expected result.