Question

1. Crop yields per acre depend on many variables, but two obvious ones are fertilizer and weed control. In an effort to test the effects of various levels of fertilizer and of herbicide, researchers selected six plots of land and subdivided each into eight pieces. Each of the eight pieces of each plot was treated with one of the eight combinations of fertilizer (none, light, moderate, heavy) and herbicide (none, some). The per acre yields of each piece of land are recorded below:

In the data, levels of fertilizer are 1 (none), 2 (light), 3 (moderate), 4 (heavy) and levels of herbicide are 1 (none) and 2(some).

fert     herb   yield

1        1        64.40

1        1        61.20

1        1        58.34

1        1        59.72

1        1        62.84

1        1        62.59

2        1        59.09

2        1        62.59

2        1        63.71

2        1        64.01

2        1        66.50

2        1        60.11

3        1        64.40

3        1        66.98

3        1        63.78

3        1        66.52

3        1        65.17

3        1        62.33

4        1        54.69

4        1        64.27

4        1        64.40

4        1        63.56

4        1        65.77

4        1        66.07

1        2        57.50

1        2        59.38

1        2        61.04

1        2        61.54

1        2        61.06

1        2        61.64

2        2        66.67

2        2        63.62

2        2        66.20

2        2        65.59

2        2        62.85

2        2        66.07

3        2        70.37

3        2        62.72

3        2        67.85

3        2        63.74

3        2        64.88

3        2        63.96

4        2        61.83

4        2        64.20

4        2        65.94

4        2        67.56

4        2        60.28

4        2        67.75

Give a statement to be tested, identify the random variables involved and the assumptions you make about them, state the hypotheses to be tested, ask SPSS to run the analysis for you, including a post hoc, and then discuss the outcome. Describe the critical region(s) upon which you base your decisions. Include any SPSS output in your discussion.

Answer 1

The SPSS output is:

The random variable is various levels of fertilizer and of herbicide.

Assumptions for Two Way ANOVA

• The population must be close to a normal distribution.
• Samples must be independent.
• Population variances must be equal.
• Groups must have equal sample sizes.

There is a significant main effect of fertilizer. (F (3, 40) = 5.594, p < 0.05)

There is no significant main effect of herbs. (F (1, 40) = 1.330, p > 0.05)

There is no significant interaction effect. (F (3, 40) = 1.013, p > 0.05)

There is a significant mean difference between light and none fertilizer.

There is a significant mean difference between moderate and none fertilizer.

There is a significant mean difference between heavy and none fertilizer.