Q1_1a:A t-test or single factor ANOVA would be adequate for testing that the difference between control and impact sites is the same for before and after the proposed impact
Q1_1b:A categorical factor representing whether the observations were collected before or after the proposed impact and a numerical variable representing the difference in algae density between control and impact sites
Q1_1c:The difference in algae density between control and impact sites at a number of times before and after the proposed impact. Hence the different times are the 'replicates'
Q1_1d:Normality, homogeneity of variance and independent observations (keep in mind however, that the replicates are pseudoreplicates in this case).
Q1_3a:Boxplots suggested that the populations are likely to be unequally varied
Q1_4a:Transformation successful. Populations now appear normally distributed and equally varied.
Q1_6:The difference in kelp density between control and impact sites was found to be significantly greater after the proposed impact (power plant) than before. This suggests that the power station did have a significant detrimental impact of giant kelp plants.
Q2_1:The population mean kelp density is the same before and after.
q2_1a:3
Q2_1b:The population mean kelp density is the same for all times
q2_1b:6
Q2_1c:The population mean kelp density is the same for both control and impact sites within the times
q2_1c:6
Q2_1d:The population mean kelp density is the same for both before and after, control and impact site combinations. There is no interaction
q2_1d:6
Q2_3:BA:CI
Q2_4:Normality and homogeneity of variance (based on the overal residuals - TIME:CI) which can be tested using boxplots as usual. Boxplots suggest that variances not equal and that mean and variance are likely to be related. Log10 transformation corrected this. As the repeated factor CI has only two levels, compound symmetry is no longer relavent!
Q2_5:Control and impact sites within times - so more times OR more control and impact sites would be better.
Q2_6a:1
Q2_6b:0.12952
Q2_6c:1.2894
Q2_6d:0.2711
Q2_6e:18
Q2_6f:1.80814
Q2_6i:1
Q2_6j:5.7753
Q2_6k:556.98
Q2_6l:<0.001
Q2_6m:1
Q2_6n:1.8383
Q2_6o:177.29
Q2_6p:<0.001
Q2_6q:18
Q2_6r:0.0104
Q2_8:Reject the null hypothesis that there is no interaction between before-after and control-impact. Whist an the control site the density of kelp was greater after the 'impact' than before, at the impact site, the density of kelp was lower after the 'impact' than before.
Q2_9:Since the replicates for the test of interaction are the observations at control and impact sites within each time (that is the interaction between TIME and CI) increasing the number of times and or the number of control and impact sites would both increase power. Note that for such data to be analysed as a simple ANOVA as was done in Q1 above, the only option available to increase power is to increase the number of times.