Question

Q2) Solve using one way ANOVA
The following table gives the yield on 15 samples fields under three varieties of seeds A, B
and C.
(3 marks) (1 mark)
(6 mark)
A
B
C
20
18
25
21
20
28
23
17
22
16
25
28
20
15
32
Test at 5% level of significance whether the average yields of land under different varieties of seeds show significance differences.
(Table value of F at 5% level for v1= 2 and v2= 12 is 3.88)

Answer 1

We draw the conclusion that there was no statistically significant difference between the average yield of land under the various seed varieties.

• ANOVA is a statistical analysis technique that divides systematic components from random factors to account for the observed aggregate variability within a data set. The presented data set is statistically affected by the systematic factors but not by the random ones. The ANOVA test is used by analysts to evaluate the impact of independent factors on the dependent variable in a regression analysis.
• Up to 1918, when Ronald Fisher invented the analysis of variance method, statistical analysis was conducted using the t- and z-test procedures produced in the 20th century.
• Assuming the data were normally distributed and the variances in the three populations were homogeneous, we will do an ANOVA test. He input the data ranges, chose Grouped By: Rows, and set Alpha to 0.05 after selecting Anova: Single Factor. He picked an acceptable output choice and then clicked OK.
• The computed F value was 3.1. The computed likelihood of getting this outcome by chance (P-value) is 0.08215976, which is less than the specified critical value (F crit) of 3.8852. (8.21 percent to three significant figures). Since P > 0.05, we draw the conclusion that there was no statistically significant difference between the average yield of land under the various seed varieties.

Hence, we draw the conclusion that there was no statistically significant difference between the average yield of land under the various seed varieties.

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