Problem 1.  Prairie junegrass has potential as a low input turf grass.  Seed production strategies need to be investigated to determine best management practices.  An experiment was conducted to investigate varieties, fertility, and the use of growth regulators.  Growth regulators in grasses tend to reduce plant height by influencing stem elongation.  The experiment was a split split plot treatment design in a randomized complete block with 4 replications (blocks).  Conduct your analysis and interpretation of the data twice, using Seed Yield (lbs/A) and Plant Height (inches) as separate responses.

 

Whole plots:  Fertility

1 = 30 lbs N applied in Fall

2 = 30 lbs N applied in Fall + 30 lbs N applied in Spring

3 = 60 lbs N applied in Fall

 

Subplots:  Growth regulator applications

1 = no Apogee growth regulator

2 = full rate (8 oz.)

3 = half rate (4 oz.)

 

Sub Sub plots:  3 prairie junegrass populations

1 = Site A

2 = Site B

3 = Site C

 

1. Write the linear additive model for the experiment.

 

2. Construct the ANOVA table, noting degrees of freedom, expected mean squares.

 

3. Calculate and add to your table the SS, MS, F tests, and p-values for the trial’s data.

 

4. Calculate the standard errors and the LSD’s for comparing fertilizer rates, growth regulator rates, varieties, and the variety* fertility interaction.

 

5. Briefly interpret the results, any interactions, and include appropriate graphs as a part of your discussion.

 

 

 

Problem 2:  A researcher was interested in the effect of harvesting pressure on long-term stand vigor in asparagus plots. This perennial crop begins producing shoots in spring, and new ones that emerge each week can be harvested for sale, or left to grow and rejuvenate the plants for the following year. An early stop date for harvesting would yield fewer shoots for sale, but later stop dates might endanger crop yields in subsequent years.

 

To study effect of harvesting duration on long-term stand vigor, investigators planted asparagus in multiple plots, and then randomized harvesting durations within four blocks of 4 plots each. Treatments were progressively longer harvesting intervals A–D, extending from first emergence to 1 June, 15 June, 1 July and 15 July, respectively. Stand vigor in each plot over consecutive harvest years after planting was assessed by yield of asparagus (oz) from spring up to 1 June. Thus, treatments were harvesting durations (4 levels) arranged in a RCB design, and yield on individual plots was measured repeatedly to evaluate vigor over consecutive years. A subset of the data from years 3–6 is in AsparagusData.xls.

 

Examine and analyze the results to determine how treatments affected vigor over years.

 

1. Produce a graph showing treatment means, by year. What do the patterns suggest?

 

1. Write a linear additive model for this experiment, and analyze the data as a classic split-plot-in time design. In an ANOVA table, show sources, degrees of freedom, E(MS) and the calculated SS, MS, F-tests and p-values. Discuss what your analysis suggests about the patterns seen in part a.

 

1. Evaluate graphically the assumptions required to accept the statistical conclusions from part b. Examine error variances among treatments and years, and pattern of serial autocorrelation among residuals with an ACF plot. If assumptions are suspect, suggest (but you need not demonstrate) how they might be remedied in further analyses.

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