level of significance and the ANOVA table shown below. One-way ANOVA: Drainage Source DF SS MS F P Channel 4 961.7896 240.4474 4.5623 0.0088 Error 20 1054.052 52.7026 Total 24 2015.8416 Is there enough evidence to conclude that there is a difference in the mean drainage times for the different channel designs?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Rapid drainage of floodwater is crucial to prevent damage during heavy rains. Several designs for a drainage canal were considered for a certain city. Each design was tested five times, to determine how long it took to drain the water reservoir. The following table presents the drainage times, in minutes.
| Channel Type | Drainage Time | ||||
|---|---|---|---|---|---|
|
1
|
41.5
|
43.2
|
50.2
|
41.2
|
24.2
|
|
2
|
38.8
|
48.2
|
51.0
|
38.1
|
25.2
|
|
3
|
32.7
|
33.5
|
35.0
|
22.7
|
24.7
|
|
4
|
26.5
|
30.7
|
33.1
|
23.8
|
26.7
|
|
5
|
45.1
|
47.3
|
48.4
|
37.1
|
40.0
|
Can you conclude that there is a difference in the
level of significance and the ANOVA table shown below.
| One-way ANOVA: Drainage | |||||
| Source | DF | SS | MS | F | P |
|---|---|---|---|---|---|
| Channel |
4
|
961.7896
|
240.4474
|
4.5623
|
0.0088
|
| Error |
20
|
1054.052
|
52.7026
|
||
| Total |
24
|
2015.8416
|
Is there enough evidence to conclude that there is a difference in the mean drainage times for the different channel designs?
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