In a comparison of visual acuity of deaf and hearing children, eye movement rate
ID: 3050913 • Letter: I
Question
In a comparison of visual acuity of deaf and hearing children, eye movement rates are taken on 9 deaf and 9 hearing children. A clinical psychologist believes that deaf children have greater visual acuity than hearing children. Test the psychologist's claim by using the data in the table. (The larger a child's eye movement rate, the more visual acuity the child possesses.) Let 0.05. 2.45 |3.14 323 |2.30 2.64 |1.95 |2.17 2.45 |1.75 Deaf children Hearing children 1.15 1.65 1.43 1.73 1.75 1.33 2.03 1.64 1.95 Ho: The visual acuity of the two groups is identical Ha: The visual acuity of the deaf children is greater than the visual acuity of the hearing children. a. Rank the combined data and calculate the Wilcoxon test statistic T. This is a rank sum test. b. Specify the critical region and make a decision about Ho. c. Even though the samples sizes do not exceed 10, conduct the approximate z-test. Use the formula that ignores the ties. Find the test statistic, the p-value and make a decision. Let alpha = 0.05.Explanation / Answer
we shall conduct the analysis using the open source statistical package R , the complete R snippet is as follows
deaf<- c(2.45,3.14,3.23,2.3,2.64,1.95,2.17,2.45)
hearing<- c(1.15,1.65,1.43,1.73,1.75,1.33,2.03,1.64)
wilcox.test(deaf,hearing)
The results of the test are
Wilcoxon rank sum test with continuity correction
data: deaf and hearing
W = 63, p-value = 0.001348
alternative hypothesis: true location shift is not equal to 0
as the p value is less than 0.05 , hence we can safely reject the null hypothesis H0 and conclude that the visual acuity of the deaf children is greater than that of the hearing children
here n = 8-1 = 7
the critical value is 2 using the wilcox table for alpha = 0.05