2. Greenhouse experiment. Consider a greenhouse experiment conducted to learn ab

Question

2. Greenhouse experiment. Consider a greenhouse experiment conducted to learn about the effect of drought stress on the growth of three types of plants (perennial ryegrass-PR, tall fescue=TF, and white clover=wc). The three plant types were assigned to 24 pots in a completely randomized fashion with 8 pots per plant type. Five plants of the assigned type were planted in each pot. For each plant type, 4 of the 8 pots were randomly selected to receive drought stress (restricted watering for 30 days) while the other 4 pots were given sufficient water every day for 30 days. At the end of 30 day period, the dry matter weight of plant leaves was determined for each pot. Data from 7 pots were excluded from analysis because the watering treatment that had been assigned to those pots had been mixed up in the midst of the study; i.c., these pots were drought stressed at first and then given sufficient water for the second half of the study or vice versa. Data are in grass.dat. Include in your answers any relevant software output that you have used (a) Are these data balanced or unbalanced? (b) How many treatments are there in this experiment? (c) Determine an Ismean for each level of the factor "plant type". Write down here the value for each of (d) Are there significant differences among the Ismeans computed in the previous part? Conduct one test to answer this question. Provide a test statistic, its degrees of freedom, a p-value and a conclusion statistic, its degrees of freedom, a p-value, and a conclusion. p-value(s) on which you based your answer, and clearly justify your answer. (e) Test for the presence of interaction between the two factors considered in this experiment. Provide a test (f Conclude whether drought stress has an effect on the growth of these three types of plants. Give the

Explanation / Answer

a)

Unbalanced design. A cross tabulation of factors will show where the unbalance
exists.

b) There are two treatment : planttype and watering

c)

Statistics

d)

One-way ANOVA: Weight versus planttype

Method

Equal variances were assumed for the analysis.

Factor Information

Analysis of Variance

Model Summary

Means

Pooled StDev = 1.29753

There is no significant difference in the means

e)

General Linear Model: Weight versus planttype, watering

Method

Factor Information

Analysis of Variance

Model Summary

Coefficients

Regression Equation

Fits and Diagnostics for Unusual Observations

The interaction is not significant.

f)

One-way ANOVA: Weight versus watering

Method

Equal variances were assumed for the analysis.

Factor Information

Analysis of Variance

Model Summary

Means

Pooled StDev = 0.973800

Drought stress has an effect on the growth

Variable planttype Mean Weight PR 2.329 TF 3.920 WC 2.880

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