DistributioN Alexa Curcio Problem Would a restriction on height such as prohibiting males from marrying taller females affect the height of the entire population Outline Height Distribution ID: 139327
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Slide1
Height DistributioN
Alexa
CurcioSlide2
ProblemWould a restriction on height, such as prohibiting males from marrying taller females, affect the height of the entire population?Slide3
OutlineHeight Distribution Means and Standard Deviations in U.S.Other countries’ statistics
Affect of taboo
Setting
parameters & Assumptions
R code
Problems
Adding the taboo
Some more problemsSlide4
Height DistributionMales and females have different means, but the same standard deviation.
Separately, male and female height
each follow
a normal distribution
.
While it may seem that adding both male and female heights to one graph would create a bimodal graph, this is not the case.Slide5
United StatesAverage height for males: 69.2 inches: 5 ft 9.2 inchesAverage
height for females: 63.8
5 ft 3.8 inches
Standard Deviation for
males & females
is 2.8
inches.
Males are about 5 inches taller than females, both have the same standard
deviation.
*Information taken from National Health and Nutrition Examination Survey Slide6
Other countriesCertain cultures discourage males from marrying taller females. This is especially true for arranged marriages.India
Female: 5 ft 1 inch
Male: 5 ft 7 inches
Difference: 6 inches (greater than US)
Pakistan
Female: 5 ft 4 inches
Male: 5 ft 5 inches
Difference: 1 inch
Iran
Female: 5 ft 3 inches
Male: 5 ft 8 inches
Difference: 5 inches
Iraq
Female: 5 ft 1 inch
Male: 5 ft 5 inches
Difference 4 inchesSlide7
Trends?There were no specific trends for these countries with regards to the taboo.Reasons:
No specific law prohibiting a male from marrying a taller female.
Arranged marriages are part of a culture, not of the entire country
. (Height is also dependent on regional and environmental factors)
Difficult to find data for height of a culture.
ie
: Muslim
heights (Middle East, Africa, Asia)
Data is
inconclusive.Slide8
Parameters & Assumptions1. Difference in mean between male and female 2. Standard deviation for male and female
3. Height to assign to offspring
Female: average – 2.5 inches
Male: average + 2.5 inches
Or, make it more dependent on gender
(2/3father + 1/3mother)
4. What creates a stable distribution?
Have every pair have x children.
Record the mean and standard deviation of the new populationSlide9
Offspring calculationOne formula for calculating male and female children based on parents height:Female = (F+M)/2 -2.5
Male = (F+M)/2 +2.5
In order to calculate variance for sons and daughters, must assume the father and mother are independent.
The expected value is (F+M)/2 -2.5 or +2.5, and to find the variance, we find the variance of the expected value…Slide10
R codeCreate a generation of males and females that are standard normal.Take a sample from this normal distribution, 1 male and 1 female.
Have these two mate and have 2 children, male and
female.
Depending on whether the child is male or female, assign a height to the
child.
Repeat this for approximately 100
generations.
Find the standard deviation and mean for males and females separately.Slide11
ProblemsThe assumptions made in the original parameters. (Offspring Calculation)This method limits the amount of children per
couple.
Height is dependent on other factors:
Nutrition
Medical history
Genetics
Environment
EtcSlide12
Inserting the tabooConstruct R code which only allows males to marry females that are shorter.
To do this, insert the restriction within each while loop that will only accept male height greater than female height.
Look at this
effect
on the overall height distribution of the
population.
If there is no significant difference, create a bigger
constraint.
Will this create more or less diversity in height?Slide13
More problemsThere will still be people that disobey the restriction.Males are generally taller than females.
Immigrants
Now, most women choose a man that is taller than they are.
Will this information interfere with comparing data?Slide14
Next timeTake into consideration the other factors for the height. (More specifically, genetics)Create a different taboo and see its effect.
Demonstrate the difference in standard deviations and means for males and females
of different generations.