A manufacturer wished to compare the effectiveness of four methods of treating r

Question

A manufacturer wished to compare the effectiveness of four methods of treating raw fabric to render it water repellant. Six types of fabric were used in the operation. A specimen of each type was divided into fourths, and each fourth was randomly assigned to one of the four methods. After treatment, each item was tested for water-repellency wand scored either 0 if unsatisfactory or 1 if satisfactory. The results are shown below.

Can you conclude (using Cochran’s test) that these data provide sufficient evidence to indicate a difference among the methods?

  

Data:           

2

Method Fabric A B C D 1 1 1 0 0

2

1 1 0 1 3 1 0 0 0 4 1 1 1 0 5 1 1 0 1 6 1 1 0 1

Explanation / Answer

Cochran's Q test is

H0: The methods are equally effective.

Ha: There is a difference in effectiveness among methods.

Step :1 Arrange the data in proper row and column. It is already arranged

Step :2 Compute the sum of each column and row

Sum for each column

G1 = 6 ; G2 = 3; G3 = 1; G4 = 3

sum of G = G* = 6 + 3 + 1 + 3 = 13

G*2 = 62 +32 +12 +32 = 55

Compute the sum of L *= L1 + L2 + L3 + L4 + L5 + L6 = (2+ 3 + 1+ 3 +3 +3)=15

sum of L*2 = 41

Step : 3 Number of condition k = 4

Step : 4 Cochran Statistic

Q = (k-1)[ k x G2 * - (G*)2 ] / ( k x L* - L*2]

Q = (4-1) [ 4 * 55 - 132] / (4 * 15 - 41) = 3 * 51/ 19 = 8.053

Step :5 see chi- square table for critica value for dF = 3 and alpha = 0.05

X2critical = 7,82

Step : 6

For the example data, we would decide to reject the null hypothesis, because the obtained Q value of 8.053 is larger than the critical Chi-square value of 7.82. and we can conclude that  these data provide sufficient evidence to indicate a difference among the methods.

Method Fabric A B C D Total(Li) Li^2 1 1 1 0 0 2 4 2 1 1 0 1 3 9 3 1 0 0 0 1 1 4 1 1 1 0 3 9 5 1 1 0 1 3 9 6 1 1 0 1 3 9 Total Gi 6 5 1 3

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.