Subject Mathematics Statistics-R Programming


Stink bugs are important agricultural pests of various crops.
Considerable investigative effort has been exerted to identify predators that can reduce their densities in fields and orchards.
An experiment with predator treatments was conducted to determine which predators were more effective at consuming stink bug eggs.
The assays were conducted in experimental arenas in a greenhouse over 48 h.
Each of seven predators was tested eight times by placing predators individually in arenas in the presence of a cluster of 28 stinkbug eggs that were on a naturally growing plant.
The response variable was proportional survival (of 28 eggs).
Predator-free controls were conducted simultaneously, but all seven of the predators reduced the egg survival significantly and so the control is not included in this analysis; this analysis compares predator types only.
For logistical reasons the replicates could not be run all on the same day so they were started on two different days (4 reps of each trial on each day) in two different weeks, and the two starting dates may contribute additional variation.
In the file the starting dates are listed as day “one” and day “two.” The study results can be found in “stinkbug_preds.csv”.
The treatments are indicated by the names of the predators.
We need to know whether the seven predators are equivalent predators and if they are different we would like to know how the predators rank (or should be grouped) in their capacity to consume eggs.

a. Methods: In a few sentences explain the design of the study and the steps of this linear model analysis (what you did with the data and why).

b. Results: In one paragraph explain whether predators differ in their effects on stinkbug eggs according to this experiment, and if so, which predators are different from which predators (i.e., how should they be ranked or grouped?). You should include statistics in the paragraph and a figure of the results (not the diagnostics) to help illustrate the findings.

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To examine this data, Factorial Analysis of Variance (ANOVA) is the most appropriate method. Here we have one dependent variable, survivability and two independent variables; predators and days. The Predator variable has 7 levels and day has 2 levels. So, a factorial design will be applied when there are at least two factor variables for its independent variables. In this data, we are interested in testing the effect of each treatment (predator) and also the effect of their combination on day1 and 2. For this type of 2 way data, a simple interaction plot displays the mean or median value for response variable for each combination of independent variables. When the main effects (treatment, day) are statistically significant, we conduct post-hoc test to see the significant difference between groups.

Null Hypothesis: There is no significant difference between means of the 7 treatments i.e. all 7 treatment means are equal.
Alternate Hypothesis: There is a significant difference between means of the 7 treatments i.e. all 7 treatment means are not equal....

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