Five laptop users were asked for the acceptability of four brands for daily use. The responses of acceptability (A) and rejection (R) are given below

Users Brands
Alpha Beta Delta Gamma
H1 A R A R
H2 R A A R
H3 R A R A
H4 A R R R
H5 A A R A

Test whether is any significance difference between brands with respect to acceptability, Use (Cochran Q test)

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Solution:

Lipstick Brands Users Ri Ri2
H1 H2 H3 H4 H5
Alpha A R R A A 3
Beta R A A R A 3
Gamma A A R R R 2
Delta R R A R A 2
Ci 2 2 2 1 3 ΣRi = ΣCj = 10 ΣRi2 = 26
Ci2 4 4 4 1 9 ΣCi2 = 22

Here,

Number of brands (k) = 4

Number of housewives (n) = 5

Problem to test:

H0: There is no significant difference between brands.

H1: There is at least one significant difference between brands.

Test Statistic:

\(Q = \frac{ (k-1) \left [ k \sum_{i=1}^k R_i^2 – (\sum_{i=1}^k R_i)^2 \right ] }{ k \sum_{j=1}^n C_j – \sum_{j=1}^n C_j^2}\)

\(= \frac{(4-1) (4 \times 26 – (10)^2)}{4 \times 10 – 22}\)

\(= \frac{12}{18}\)

= 0.666

Critical Value:

At 5% level of significance then critical value is X2(0.05, 3) = 7.81

Decision:

Q = 0.666 < X2(0.05, 3) = 7.81, accept H0 at 5% level of significance.

Conclusion:

There is no significant difference between brands according to acceptability.

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