Analysis and data
Analysis
Summary
John and Ian’s main interest was in the growth of the 12 different species of native flowers. There was great variety in the yields of the native flowers at the second harvest. Harvested yields for some species were very low because those species were dormant during the summer. However the mowing and nutrient treatments did influence yield for some species. The effects were different for different species of flowers. The treatments also had varying effects on the yield of the grasses.
Boxplots of yield in grams at the second harvest (n=16 for each boxplot).
Questions to consider
- Examine the boxplots shown above. Broadly, what kinds of analysis would you recommend for the various species?
- Choose a species for which there was variability in the dry weight. Provide a visual display to illustrate the variation in dry weights by treatment.
- Consider the assumptions required for analysing the Latin square design using a standard analysis of variance. For which species are these assumptions met? Produce a visual display to support your conclusions.
- Conduct a statistical analysis of the Latin square design (treatments, rows and columns) for one or more of the grass species. Write a brief summary of the results and include a visual display to illustrate the main findings.
- Investigate the effects of the mowing treatment and the nutrient treatment for native flower species that interests you. Write a brief summary of results and an explanation.
- Investigate the assumptions required for analysing the Latin square for three different species. What kind of strategies are appropriate in cases where the assumptions are not met? What kind of inferences can be made?
- For some species there is little variation in dry weight and only a small number of positive values observed. What kind of descriptive and inferential analyses would you consider for these species?
Data
Note that the data file only includes dry weight data from the second harvest. Although John’s primary interest was in the native flowers (species 3 to 14), he also recorded the dry weight of the three grasses (species 1, 2 and 15).
Definition of species and treatment variables in data file
| Species Number | Species name | Common name |
|---|---|---|
| 1 | Austrodanthonia caespitosa | Wallaby grass |
| 2 | Themeda triandra | Kangaroo grass |
| 3 | Wahlenbergia stricta | Australian bluebell |
| 4 | Pycnosorus chrysanthes | Golden billy buttons |
| 5 | Leucochrysum albicans | Hoary sunray |
| 6 | Helichrysum scorpiodes | Button everlasting |
| 7 | Bulbine bulbosa | Native lily |
| 8 | Linum marginale | Native flax |
| 9 | Arthropodium strictum | Chocolate lily |
| 10 | Chrysocephalum apiculatum | Common everlasting yellow buttons |
| 11 | Calocephalus citreus | Lemon beauty heads |
| 12 | Craspedia variabilis | Common billy-buttons |
| 13 | Velleia paradoxa | Spur velleia |
| 14 | Podolepis jaceoides | Showy copper-wire daisy |
| 15 | Microlaena stipoides | Weeping grass |
| Combined Nutrient and Mowing treatment | |
|---|---|
| 1 | Treatment A – high nutrients and annual mowing |
| 2 | Treatment B – high nutrients and biennial mowing |
| 3 | Treatment C – low nutrients and annual mowing |
| 4 | Treatment D – low nutrients and biennial mowing |
Definition of remaining variables in data file
| Row | Row in latin square |
|---|---|
| Column | Column in latin square |
| Weight | Dry weight in grams |
| Mowing | Mowing treatment: 1 = annual, 0 = biennial |
| Nutrient | Nutrient treatment: 1 = high nutrients, 0 = low nutrients |
| T1 | Treatment (Species 1) |
| R1 | Row in latin square (Species 1) |
| C1 | Column in latin square (Species 1) |
| W1 | Dry weight in grams of Species 1 |
| M1 | Mowing treatment (Species 1) |
| N1 | Nutrient treatment (Species 1) |
| T2 | Treatment (Species 2) |
| R2 | Row in latin square (Species 2) |
| C2 | Column in latin square (Species 2) |
| W2 | Dry weight in grams of Species 2 |
| M2 | Mowing treatment (Species 2) |
|---|---|
| N2 | Nutrient treatment (Species 2) |
| T8 | Treatment (Species 8) |
| R8 | Row in latin square (Species 8) |
| C8 | Column in latin square (Species 8) |
| W8 | Dry weight in grams of Species 8 |
| M8 | Mowing treatment (Species 8) |
| N8 | Nutrient treatment (Species 8) |
| T15 | Treatment (Species 15) |
| R15 | Row in latin square (Species 15) |
| C15 | Column in latin square (Species 15) |
| W15 | Dry weight in grams of Species 15 |
| M15 | Mowing treatment (Species 15) |
| N15 | Nutrient treatment (Species 15) |