Power and Sample Size Calculations

Question One:

G-Power application downloaded.

Question Two:

Question Three:

Using RStudio to run a 2-Way ANOVA test.

Changing Treatment, Block, & Replication to Categorical Variable Status:

Power_Calculation <- Power_Calculation %>%
  mutate(Treatment = as.factor(Treatment),
         Replication = as.factor(Rep),
         Block = as.factor(Block))

Running 2-Way ANOVA :

To obtain the MSE, a 2-Way ANOVA needs to be ran. The MSE is calculated using the following equation:

MSE = [SS(Error) / (n-m)]

In this case the MSE would be calculated as follows:

MSE –> [(41.2)/(25 -3)] = 1.87

summary(aov(Y ~ Rep + Block*Treatment, data = Power_Calculation))

                Df Sum Sq Mean Sq F value Pr(>F)
Rep              1    1.0    1.04   0.028  0.870
Block            3   34.1   11.37   0.306  0.821
Treatment        2   69.1   34.54   0.928  0.424
Block:Treatment  6   41.2    6.87   0.185  0.975
Residuals       11  409.5   37.22               

Significance of Terms:

The terms are not significant due to the p-values of the F statistics all being greater than 0.05. Another sign that these terms are insignificant would be that the F-Values are close to 1.

Question Four:

Using G-Power to Compute the Power of the F-Test:

According to G-Power, the power of the F-test is 0.9533144.

Question Five:

Computing the Required Sample Size for 80% Power:

The required sample size to have 80% power would be 16.

Question Six:

When compared to the results I received on RStudio, I believe any differences present could be attributed to differences in rounding methods, as the calculations of SPSS seems to be more concise. I also noticed that the information SPSS is better labeled, and thus easier to identify and understand.