Transcript Height DistributioN

Alexa Curcio
Would a restriction on height, such as
prohibiting males from marrying
taller females, affect the height of the
entire population?
•Height
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 problems
•Males
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.
•Average
•
height for males: 69.2 inches:
5 ft 9.2 inches
•Average
•5
height for females: 63.8
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
•Certain
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 inches
•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.
•1.
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 population
•One
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…
•Create
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.
•The
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
•Etc
•Construct
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?
•There
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?
•Take
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.