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## Short Assignment Requirements

I want the assignment to be solved with R Programming

## Assignment Description

NAME: _________________________________

·         When performing hypothesis tests (ANOVA), make sure to include all 5 steps. Points will be deducted if all the steps are not included.

·      Assume

·         Use R or any other statistical software to complete the assignment. Do not submit any hand calculations.

·         Provide all necessary output with the important details highlighted. Please make every effort to explain in as much detail as possible (no more than 5 sentences per question).

·         DUE March 9th, 2017 at 11:59pm

1)      Jonathan Hnosko (MS, Food Science, 2007) developed an experiment to measure the effects of pressure and time on the growth of Listeria, a food borne pathogen. The experiment consisted of two factors: Pressure at 3 levels (400, 450 and 500) and Time at 5 levels (1, 2, 3, 4 and 5 days post inoculation). A common source of Listeria was plated on 45 agarous petri dishes and were then randomized to the 15 combinations of Pressure and Time, such that each combination has three replicates. Thus, the design is a completely randomized design with a two-way treatment structure and three replicates petri dishes per treatment combination. The log of the number of colony forming units (LogCFU) was recorded for each of the 45 petri dishes. The data for this experiment appear in the following table:

a.       List the factor/s and tell if they are fixed or random.

b.       Assess the assumptions of equal variances and normality.

c.       Assuming the assumptions were met, perform the relevant ANOVA.

i.            Test for significance of the interaction term (Use 5 step hypothesis test).

ii.            If the interaction is not significant, test the main effects (Use 5 step hypothesis test).

iii.            If the main effects are significant, use Tukey’s to get pairwise comparisons for the main effects.

d.       The estimated cell means are plotted with Pressure on the horizontal axis (plot a) or Time on the horizontal axis (plot b), with the remaining factor levels plotted within the graph.

i.            The following plot shows the estimated cell means for each level of Time with lines connected across the levels of Pressure. In a few sentences, describe what you see. (Be sure to describe the interaction and also the relationship between the different lines). Be sure to say how this relates to c(ii) and (iii)

ii.            Make a plot that shows the estimated cell means for each level of Pressure with lines connected across the levels of Time (Opposite of the graph above). In a few sentences, describe what you see. (Be sure to describe the interaction and also the relationship between the different lines). Be sure to say how this relates to c(ii) and (iii)

2)      Courtney Leisner (MS Botany, 2009) designed an experiment to explore the growth of the plant Bienertia Sinuspersici, a species with C4 photosynthesis that is salt tolerant. Four levels of salt concentration were of interest to the researcher: 0, 50, 100 and 200 mM NaCl. The experiment consisted of 16 tubes identically planted to the plant species and then randomly assigned to the four salt treatments (4 replicate tubes per treatment). The tubes were placed in individual hydroponic growth systems at the specified concentration of NaCl in the water and the plants were allowed to grow for 8 weeks. At the end of the growth period, the plants were harvested and the dry weight of the roots was measured. The following table presents the data from this experiment:

a.       List the factor/s and tell if they are fixed or random.

b.       Assess the assumptions of equal variances and normality.

c.       Assuming the assumptions of the ANOVA model were met, perform the relevant ANOVA. (Use 5 step hypothesis test).

d.       Perform pairwise comparisons for all mean and summarize findings in 2-3 sentences.

3)      4 laboratories are randomly selected from a large population, and each is asked to make 3 determinations of the percentage of methyl alcohol in specimens of a compound taken from a single batch. Based on the accompanying data, are differences among laboratories a source of variation in the percentage of methyl alcohol? Test this using the following dataset and procedure:

1:            85.06     85.25     84.87

2:            84.99     84.28     84.88

3:            84.48     84.72     85.10

4:            84.10     84.55     84.05

a.       List the factor/s and tell if they are fixed or random.

b.       Assess the assumptions of equal variances and normality.

c.       Assuming the assumptions of the ANOVA model were met, perform the relevant ANOVA. (Use 5 step hypothesis test).

4)      Consider a Completely Randomized design (CRD) with a single factor. Suppose the factor (treatments) has 4 levels (Level1, Level2, Level3, Level4) and that each level has 4 observations (replicates). Make up a dataset of response values, consisting of 4.4=16 total values to be placed one value per cell in the provided table (treatment levels are the columns and replicates are the rows) to illustrate described situations concerning the  and Limit yourself to using numbers 1 through 16 for the values to be entered in each cell. Only use the values you need, you do not need to use all 16 if they are not needed. If needed, you can re-use any value multiple times.

RECALL:

a.      and

 Treatments Replicates1234 Level1 Level2 Level3 Level4

b.      and

 Treatments Replicates1234 Level1 Level2 Level3 Level4

c.      and

 Treatments Replicates1234 Level1 Level2 Level3 Level4

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