Agriculture and Food 7–12 · Years 11–12
Designing a fair plant trial: replication, randomisation and a test of significance
Plant/Animal production: Experimental analysis and research in plant/animal systems
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The idea
A difference between treatment means counts only when it is large compared with the variation between replicates, which replication and randomisation let the trial measure and a t-test judges.
What you need
- results from a class plant trial (for example the shade cloth or planting density trial)
- spreadsheet or calculator with statistical functions
- random number table or random number generator
- plan of the trial area
How to do it
- Draw the trial plan: divide the area into replicate groups of plots, each holding every treatment once, and randomise the treatments within each group with random numbers.
- After harvest, enter each plot's result and calculate the mean and sample standard deviation for each treatment.
- For two treatments, find the difference between them in each replicate group, then the mean and standard deviation of those differences and the paired t statistic, and compare it with the critical t value at 5% for n - 1 degrees of freedom, where n is the number of replicate groups (a paired test matches a layout in which each group holds both treatments).
- Use the simulation to repeat the same trial 1000 times with the learner's own mean difference and plot standard deviation, and with fewer replicate groups, to see how often a real difference would be detected.
- Write a recommendation that states the difference, its variability and whether it is significant.
What you should see
For example inputs A = 4.2, 3.8, 4.6, 4.0, 4.4 g and B = 2.9, 3.3, 2.7, 3.1, 3.0 g from five replicate groups (listed in group order), the means are 4.20 and 3.00 g and the standard deviations 0.316 and 0.224 g. The five differences within the groups have a mean of 1.20 g and a standard deviation of 0.529 g, so the paired t = 5.07 with 4 degrees of freedom, above the critical value 2.776, and the difference is significant at 5% (two-tailed p = 0.007). Treating the same values as two unrelated groups would give t = 6.93 with 8 degrees of freedom and p = 0.00012. Read those two results together, because in this example the unpaired test is the more sensitive of the two. The reason is in the numbers: s_d = 0.529 g is larger than sqrt(s_A^2 + s_B^2) = 0.387 g, which is what s_d would be if the pairing carried no shared group effect, and the correlation between the paired values is r = -0.92. In these five example groups the two treatments move in opposite directions, so the groups carry no common effect for the pairing to remove and the paired test pays four degrees of freedom for nothing. The paired test is still the right test here, because the analysis follows the layout the trial was planted in and not whichever test returns the smaller p value; but blocking buys sensitivity only when plots inside a group really are more alike than plots in different groups, which these values are not. Use the simulation to see the case blocking is for: raise the replicate group standard deviation and the unpaired share of 1000 trials significant at 5% falls while the paired share does not move, because the group effect cancels in the within-group differences. With larger plot variation or fewer replicate groups the same difference in means is detected in fewer trials by both tests. The learner knows it worked when the spreadsheet reproduces t = 5.07 and t = 6.93 for the example values, explains which of the two the layout calls for, and then gives the class trial's own t by the same steps.
What changes
This activity lists no variables to change, measure and keep the same.
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- If the treatment means differ, the treatment worked.
- One pot per treatment is enough if it is looked after carefully.
- Grouping all plants of one treatment together makes a trial fairer.
- Blocking a trial always makes a real difference easier to detect.
Safety card
Hazards
- none beyond normal classroom work
Controls
- no materials are handled in the analysis
Note
Analysis only: no chemicals, heat or animals.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
Sources
The pages the author read to write this activity.