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UNIV*6020 Data Analysis Assignment #2
Due: October 25, 2024

Experiment Description:

An experiment was conducted to evaluate the effects of irrigation frequency and fertilizer dosage on the growth of wheat (Triticum aestivum L.) seedlings in a split-plot experimental design, arranged as a randomized complete block with three replications (blocks). The main plots were used for four levels of irrigation frequency (daily, every 2 days, every 3 days, and every 4 days), with three fertilizer dosages (50 kg/ha, 100 kg/ha, 150 kg/ha) randomly allocated to the subplots of each main plot. The following data shows the height of wheat seedlings in cm.

Height of Wheat Seedlings (cm)
		Irrigation Frequency
Fertilizer Dosage	Block	Daily	Every 2 days	Every 3 days	Every 4 days
50 kg/ha	1	12.5	15.7	9.3	6.1
	2	13.9	17.0	8.8	7.5
	3	11.6	13.2	10.1	6.9
100 kg/ha	1	18.2	16.8	11.7	8.5
	2	19.6	20.3	13.5	9.8
	3	21.4	18.1	12.2	10.3
150 kg/ha	1	23.7	19.5	15.9	11.2
	2	25.8	22.0	17.1	12.4
	3	20.9	18.7	16.2	10.6

Data Analysis

Using the appropriate statistical model, determine whether irrigation frequency and fertilizer dosage affected the growth of wheat seedlings.

1. Start by entering the data into your program of choice (SAS or R).

2. Run a mixed model analysis to determine whether there are treatment effects and/or a block effect; be sure to include a test to determine whether the random effect(s) in your model are a significant source of variation in this trial?

3. Check the model assumptions and make any changes you feel are needed to ensure that the assumptions have been met.

4. Compare the least squares means (emmeans for R users) of treatments using a Tukey’s test In this part you need to do the pairwise comparisons and report the results. You may need to compare the main effects, or you might need to slice and look into the simple effects of variables based on the significance of interaction of variables. – remember to use your ANOVA as a guide.

Report Guidelines

A. Your report must include R or SAS syntax [as sas or R file] and its outputs [as pdf file]- (55%).

B. Your report must include two tables (15%):

Table 1: ANOVA results of wheat seedling height. This should include both fixed and random effects results. (8%)

Table 2: Presentation of means and their standard errors (or standard deviations) for each treatment group, along with the results of Tukey's multiple comparisons. Include letter codes to indicate significant differences between means (alphabetic code). (7%)

C. Your report should also include short or point-form answers to the following questions (30%)

1. Statistical Model:

What statistical model did you use? Write it out and clearly define each component, specifying whether each component was a FIXED or RANDOM effect. (10%)

2. ANOVA Summary:

Based on the ANOVA results (Table 1), write 2-3 sentences to summarize the main findings from your analysis. (5%)

3. Means Comparison Conclusions:

From the means comparison results (Table 2), what are three major conclusions you can draw from this study? (5%)

4. Residual Analysis:

Based on your residual analysis, explain whether you decided to modify the distribution of your data or change the link function between the linear predictor and the dependent variable. Why or why not? Provide a brief justification. (10%)

Your tables MUST follow the guidelines set out by the Can. J. Plant Sci., or Can. J. Anim. Sci. The tables should standalone, which means we should not need to read materials and methods OR results to understand what is being presented in the table.

CourseLink DropBox submission MUST include:

1. R or SAS syntax [as sas or R file] and its outputs [as pdf file]- (55% of total mark);

2. Two tables highlighted above (15% of total mark);

3. Answer to questions listed (30% of total mark).

Due: 11:59pm October 25, 2024

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UNIV*6020 Data Analysis Assignment #2 Due: October 25, 2024