Question

Congenital sensorineural deafness is the most common form of deafness in dogs and is often associated with congenital pigmentation deficiencies. A study of hearing impairment in dogs examined over 5000 dalmatians for both hearing impairment and iris color. The provided figure shows the SPSS output for a chi-square test on these data. SPSS Hearing EyeColor Crosstabulation EyeColor BrownBlue eyed eyedTotal Hearing Deaf Count Expected Count % within Eyecolor | 381.7 6.8% | 102 44.3 426.0 18.4% | 80% 179 1167 045.8 121.2 1167.0 20.7% | 32.3% | 21.9% 273 3740 Unilaterally impaired Count 988 Expected Count % within Eyecolor | Count Bilateral hearing Expected Count % within Eyecolor | Count 3467 3351.5 388.5 3740.0 72.5% | 49.3% | 70.1% 554 5333 Expected Count4779.0 554.0 5333.0 100.0% | 100.0% Tota 4779 % within EyeColor | 1000% | Chi-Square Tests Asymp. Sig. (2-sided Value df Pearson Chi-Square Likelihood Ratio Linear-by-Linear 153.138 133.597 2 153.052 5333 N of Valid Cases a 0 cells (.0%) have expected count less than 5, The minimum expected count is 44.25. Dogs with either one or both of their irises blue (a trait due to low iris pigmentation) were labeled blue-eyed. This is an example of a single sample classified according to two categorical variables, hearing impairment and iris color 801 o 70 60 。50 5 40 S 30 10- 0 Deaf Unilat. Bilat. Blue Deaf Unilat. Blat Brown Bar graph lI Select the statement that best describes the differences between the two distributions. O Both blue-eyed and brown-eyed dalmatians have the smallest proportion of deafness, a higher proportion of O O O unilaterally impaired hearing and the highest proportion of bilateral hearing impairment. This suggests that there is no relationship between hearing impairment and cye color Blue cyed dalmatians have a much higher proportion of deaf dogs and a lower proportion of bilaterally hearing dogs. This suggests a genetic link between eye color and hearing impairment. Blue-eyed dalmatians have a higher proportion of deaf dogs but a lower proportion of bilaterally hearing dogs. Therefore, the data do not suggest a genetic link between eye color and hearing impairment. Blue-eyed dalmatians have much higher proportions of both types of hearing impairment. Certainly there is a relationship between eye color and hearing impairment. (b) The expected cell counts satisfy the requirement for use of chi-square because, O all 6 expected counts are greater than 5 there are no zeros in the data. none of the expected counts is smaller than 1 all 6 column percents are greater than 5% O (c) Test the null hypothesis that there is no relationship between hearing impairment and iris color. Give the chi-square statistic and the P-value as reported in the SPSS output O2133.597, P 0.002 O 2153.138, P

Answer 1

Select the statement that best describes the difference between the two distributions
Blue-eyed dalmations have much higher proportion of deaf dogs and a lower proportion of bilaterally hearing dogs. This suggests a genetic link between eye colour and hearing impairment.

The expected cell counts satisfy the requirement for use of chi-square because
all 6 expected counts are greater than 5

c. test statistic

chi-square = 153.138, P<0.001

d. Which cells have the largest contribution to the chi-square statistic?

Blue-eyed deaf and blue-eyed bilaterally hearing

The calculation is shown below.

1 Observed frequen row Total 102 179 273 Brown eyed Blue eyed 324 988 3467 426 1167 3740 3 Deaf 4 Unilaterally impaired 5 Hearing 6 7 col total 8 9 Expected value formulas 10 11 Deaf 12 Unilaterally impaired(4779*1167)/5333 13 Hearing 4779 554 5333 Blue eyed (554*426)/5333 (554*1167)/5333 (554*3740)/5333 Brown eyed (4779*426)/5333 (4779*3740)/5333 15 16 Expected value 17 18 Deaf 19 Unilaterally impaired 20 Hearing 21 Brown eyed Blue eyed 381.75 1045.77 3351.48 0.00 44.25 121.23 388.52 0.00

3 chi stat Calculatiorn Brown eyed Blue eyed (O-E) (324-381.75)A2/381.75 (102-4425)12/44.25 (179-121.23)A2/121.23 5 Deat 26 Unilaterally impaired(988-1045.77)A2/1045.77 27 Hearing 8 9 0 chi stat Calculatiorn (3467-3351.48)42/3351.48 (273-388.52)A2/388.52 Brown eyed Blue eyed 31 2 Deaf 3 Unilaterally impaired 4 Hearing 35 8.74 3.19 3.98 75.35 27.53 34.35

are these difference consistent with your bar graph?
Yes