A civil engineer is interested in determining whether four different methods of

Question

A civil engineer is interested in determining whether four different methods of estimating flood flow frequency produce equivalent estimating of peak discharge when applied to the same watershed. Each procedure k 1 used of Peak discharge when applied to the same (in cubic feet per second, are shown in Table 2. Are these four methods are different? Write down your model, hypotheses and mode assumption. You must verify the model assumptions. If the model assumptions are violated, apply transformation on the original data. Repeat the procedures on the transformed data.

Explanation / Answer

Here there are 4 types of estimation methods.

And we have to test the hypothesis that,

H0 : mu1 = mu2 = mu3 = mu4

H1 : Atleast one of the mean is differ than 0

Assume alpha = level of significance = 5% = 0.05

This we can done using EXCEL.

steps :

Enter data in EXCEL sheet --> Data analysis --> Anova : Single Factor --> ok --> Input range : select all the data --> Grouped by : columns --> Alpha : 0.05 --> Output Range : select one empty cell --> ok

The test statistic F = 78.51409

P-value = 3.08E-11

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : Atleast one of the mean is differ than 0.

ANOVA assumptions :

To use the ANOVA test we made the following assumptions:

Anova: Single Factor SUMMARY Groups Count Sum Average Variance Column 1 6 4.26 0.71 0.43704 Column 2 6 15.7 2.616667 1.428347 Column 3 6 47.58 7.93 2.71284 Column 4 6 85.82 14.30333 6.782067 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 668.9573 3 222.9858 78.51409 3.08E-11 3.098391 Within Groups 56.80147 20 2.840073 Total 725.7588 23

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