Study questions

1. In your own words summarise what you understand by variance components at different layers of a hierarchical experiment and explain how they are calculated. Give an example of another study in which it may be necessary to calculate variance components.

2. Repeat the statistical analysis for Experiment 1 restricting the data to concentrations between 15 and 35% of sucrose. Are there now any differences in percentage germination among the sucrose concentrations? Fit a polynomial regression. What are your conclusions? What now is your recommendation for an optimum sucrose concentration for the second experiment?

3. Another way to calculate mean percentage germination would be to add up the gcs, add up the tcs and calculate the ratio for each slide. Do this and re-run the polynomial regression analysis? Does this change the results in terms of estimated optimum sucrose concentration? What do you conclude?

4. By calculating an LSD based on five fields of view per slide discuss what differences in interpretation will have occurred when comparing the percentage pollen germinations compared with the number used in the actual experiment. Suppose it is decided in advance that a significant difference of 12 percentage points in germination rate will be sufficient. Calculate the number of fields of view per slide that will be required.

5. Do you think that eight concentrations of sucrose needed to be tested in this experiment? By considering the distribution of results in this experiment, decide on a reduced list of concentrations that should be sufficient to meet the objectives. Based on your decision and using the estimates obtained for the variance components in this case study, calculate the LSD that will be obtained if 12 buds are used and 10 fields of view per bud. What is the total number of observations that will be needed for this alternative experiment and compare with the one executed? Which experiment is the more efficient?