I need help solving this statistic problem by using the R software: Professor A1

Question

I need help solving this statistic problem by using the R software:

Professor A1 Dudeck of the Department of Ornamental Horticulture. University of Florida, conducted a study to evaluate the performance of several cool-season grasses for the winter over seeding of golf greens in North Florida. In the study, a golf ball was rolled an incline plane, to induce a constant initial velocity, and then the distance traveled by the ball on the green was measured. The distance can be influenced by the slope of the green, and so the study was conducted in four randomized complete blocks: each block contained three plots with similar slopes. In each case, the ball was rolled down the slope of the plot. Three cultivars (A, Pennfine rye grass; B. Dasher rye grass; C, Barry rye grass) were randomly assigned to the three plots in each block. For the five balls rolled down the ramp on each plot, the average distance (m) from the base of the ramp to the stopping points are as follows: Read the data into R as stacked (all the distances are typed in one column, coding for the varieties are typed in the second column, and the corresponding block numbers are typed in the third column. Formulate the null and the alternative hypothesis to test the grass variety on the mean distance traveled by the ball. Construct an ANOVA table for this set of data using randomized block design What is the p-value for testing the hypotheses in part (b) Is there a difference in mean distance traveled due to difference in the grass variety? Write your conclusion. Perform Tukey's test for multiple pair-wise comparisons to compare the means distance traveled between the three grass varieties. Write your conclusions for part (f).

Explanation / Answer

Your input data on kk=3 independent treatments:

Descriptive statistics of your kk=3 independent treatments:

One-way ANOVA of your kk=3 independent treatments:

Conclusion from Anova:

The p-value corresponing to the F-statistic of one-way ANOVA is higher than 0.05, suggesting that the treatments are not significantly different for that level of significance. The Tukey HSD test, as well as other multiple comparison tests like Scheffe or Bonferroni, might not narrow down which of the pairs of treatments are significantly different. Even though your data does not suggest the presence of significatly different treatment pairs in one-way ANOVA, we proceed witht he multiple conparison tests. In some instances, a Bonferroni test of a small set of pairs might show significance, even though 1-way ANOVA suggests that there is too much noise and randomness in your data.

Here result is insignificant that is all the treatment means are equal.

So here we don't need of tukeys test.

We use tukeys test when results are significant.

Treatment A B C Input Data 2.734
3.043
2.6
3.047 2.568
2.977
2.183
3.028 2.238
2.616
2.127
2.697

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