Question

AaBbccI AaBbcel AaBbC AaBbCct AaB AaBbccl AaBbCcL AaBbc l Normal T No Spaci... Heading 1 Heading2 Title Subtitle Subtle Em... Emphas Styles 2.) An experiment was conducted to test the effects of nitrogen fertilizer on lettuce production. Five rates of ammonium nitrate were applied to four replicate plots in a completely randomized design. The data are the number of heads of lettuce harvested from the plot Treatment (lbs N/ Acre) 0 50 100 150 200 Heads of lettuce/plot 104 134 146 147 131 114 130 142 160 148 90 144 152 160 154 140 174 156 163 163 Write the linear statistical model for this study, and explain the model components State the assumptions necessary for an analysis of variance of the data. (Remember from AGRI 491G) Compute the analysis of variance for the data. Compute the least squares means and their standard errors for each nitrogen level. Compute the 95% confidence interval estimates of the nitrogen level means Test the hypothesis of no difference among the means of the nitrogen levels with the F test at the 0.05 level of significance. Write the normal equations for the data. This experiment was conducted in a completely randomized design with the field plots in a 4x 5 rectangular array of plots. Show a randomization design of the five nitrogen treatments to the 20 plots using a random permutation of the numbers 1 through 20. a. b. c. d. e. f. g. h.

Answer 1

a) The linear statistical model for this study can be expressed using the mathematical model that describes the relationship between the response and treatment for the one-way ANOVA is given by

$Y_{ij} = \mu + \tau _i +\epsilon _{ij}$

where

Yij represents the j-th observation (j=1,2,3,4) and on the i-th treatment (i = 1,2,3,4,5 levels) or are the number of heads of lettuce harvested from the plot.

mu is the common effect for the whole experiment

Tau_i represents the i-th treatment effect,

Eij represents the random error present in the j-th observation on the i-th treatment. They are assumed to be normally and independently distributed with mean zero and variance of sigma^2.

b) Assumptions for ANOVA

1. The experimental errors of your data are normally distributed

2. Equal variances between treatments: Homogeneity of variances Homoscedasticity

3. Independence of samples: Each sample is randomly selected and independent

c) Using Excel > DATA> one way ANOVA

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Row 1	4	448	112	445.3333
Row 2	4	582	145.5	395.6667
Row 3	4	596	149	38.66667
Row 4	4	630	157.5	51
Row 5	4	596	149	182
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	4994.8	4	1248.7	5.611294	0.005757	3.055568
Within Groups	3338	15	222.5333
Total	8332.8	19