Researchers record the yields of corn, in bushels per plot, for four different v
ID: 3292065 • Letter: R
Question
Researchers record the yields of corn, in bushels per plot, for four different varieties of corn, A, B, C, and D. In a controlled greenhouse experiment, the researchers randomly assign each variety to eight of 32 plots available for the study. The yields are listed here:
A
2.5
3.6
2.8
2.7
3.1
3.4
2.9
3.5
B
3.6
3.9
4.1
4.3
2.9
3.5
3.8
3.7
C
4.3
4.4
4.5
4.1
3.5
3.4
3.2
4.6
D
2.8
2.9
3.1
2.4
3.2
2.5
3.6
2.7
Perform an analysis of variance on these data, use Fisher’s Least Significant Difference to check mean differences if the overall F test is significant, and draw your conclusions. (alpha=0.05) Provide the necessary SPSS output and circle any results that you refer to.
What is the null hypotheses and the critical value?
A
2.5
3.6
2.8
2.7
3.1
3.4
2.9
3.5
B
3.6
3.9
4.1
4.3
2.9
3.5
3.8
3.7
C
4.3
4.4
4.5
4.1
3.5
3.4
3.2
4.6
D
2.8
2.9
3.1
2.4
3.2
2.5
3.6
2.7
Explanation / Answer
here we are interested in testing hypothesis that
H0: mean of all groups are same
H1: Not H0
One-way ANOVA: response versus factor
Source DF SS MS F P
factor 3 6.621 2.207 11.05 0.000
Error 28 5.594 0.200
Total 31 12.215
S = 0.4470 R-Sq = 54.20% R-Sq(adj) = 49.30%
Individual 95% CIs For Mean Based on
Pooled StDev
Level N Mean StDev --------+---------+---------+---------+-
1 8 3.0625 0.4033 (-----*------)
2 8 3.7250 0.4234 (-----*------)
3 8 4.0000 0.5503 (-----*-----)
4 8 2.9000 0.3928 (-----*-----)
--------+---------+---------+---------+-
3.00 3.50 4.00 4.50
Pooled StDev = 0.4470
here overall p-value is 0.000 < 0.05 =alpha that implies that the null hypothesis of eqality of means are rejected. and can comment that at 5% significance the means are not same .
so we procced to which factor is different from other.....
Fisher 95% Individual Confidence Intervals
All Pairwise Comparisons among Levels of factor
Simultaneous confidence level = 80.51%
factor = 1 subtracted from:
factor Lower Center Upper ---------+---------+---------+---------+
2 0.2047 0.6625 1.1203 (----*-----)
3 0.4797 0.9375 1.3953 (-----*----)
4 -0.6203 -0.1625 0.2953 (-----*-----)
---------+---------+---------+---------+
-0.80 0.00 0.80 1.60
factor = 2 subtracted from:
factor Lower Center Upper ---------+---------+---------+---------+
3 -0.1828 0.2750 0.7328 (----*-----)
4 -1.2828 -0.8250 -0.3672 (-----*----)
---------+---------+---------+---------+
-0.80 0.00 0.80 1.60
factor = 3 subtracted from:
factor Lower Center Upper ---------+---------+---------+---------+
4 -1.5578 -1.1000 -0.6422 (----*-----)
---------+---------+---------+---------+
-0.80 0.00 0.80 1.60
in above comparison we can note that the CI for A-D and B-C has 0 in the interval. that means these treatments are same of each other at 5% level and all other combinations are significantly differ.
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