a. How are the quantitative traits (circumference, height) different from the di

Question

a. How are the quantitative traits (circumference, height) different from the discrete trait (gender)?

b. What effect does gender have on wrist circumference?

c. What effect does gender have on height?

d. How are height and wrist circumference related? e. Does being tall cause you to have a greater wrist circumference? Or does having a greater wrist circumference cause you to be taller?

1 individuali height wrist 2 $1.00 3 $2.00 4$3.00 5 $4.00 6 $8.00 7 $9.00 8 $13.00 9$15.00 10 $16.00 11 $17.00 12 $18.00 13 $20.00 14 $21.00 15 $25.00 16 $26.00 17 $5.00 18 $6.00 19$7.00 20 $10.00 21$11.00 22 $12.00 23 $19.00 24 $22.00 25 $23.00 26 $24.00 27 $27.00 28 average 170.9231 16.22692 29 stand dev 11.45748 1.415219 30 correlation 0.79792 Gender 168 160 157 175 163 155 173 170 167 167 165 170 160 162 142 168 185 185 190 188 178 181 173 184 178 180 14.8 F 14.9 F 15.4 F 15.2 F 15.5 F 14.2 F 15.2 f 15.2 F 15 f 15 f 16 f 15.9 F 15.7 F 15.6 F 14.8 F 15.9 M 16.5 M 17.5 M 19.6 m 18.1 m 17.1 m 18.7 m 16.5 M 17.5 m 18.1 m 18 M Height cnm 10 [$1.00, $10.60 ] ($10.60, $20.20] ($20.20, $29.80] wrist cmm 14 12 [14.2, 15.9 (15.9,17.6) (17.6, 19.3] (19.3, 21]

Explanation / Answer

a. Quantitative traits like height vary continuously i.e. they can have virtually infinite values possible whereas discrete/categorical traits have finite values/categories (2 in the case of gender).
Another difference is that the discrete traits are just labels, even if you interchange the labels the statistics will not change. For example if you switch male by female and vice versa then the statistical outcome will not change, its just that the male outcome will go to female and vice versa. Similarly instead of male and female if we put the labels red and green (or 1 and 0) then too the statistical answer won't change its just that it won't make sense biologically. In contrast if you interchange quantitative traits then the statistical output will change.

b. using the given data,
Average wrist size of females = 15.23 cm
Average wrist size of males = 17.59 cm
Hence we can say that males in general (not in every case) have greater wrist size than females.

c. using the given data,
Average female height = 163.6 cm
Average male height = 180.9 cm
Hence we can say that in general males have greater height than females.

d. The correlation coefficient between the height and wrist size is approx 0.8,hence we can say that height and wrist size are positively correlated.

e. By just looking at the correlation we cannot imply causation i.e. we cannot tell if height increases wrist size or wrist size increases height.
But if we think biologically then it is more logical that having a greater height results in requirement of stronger bones for supporting the skeleton and hence might result in increased wrist size.

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