1. The Skinny on High School
Health Statistics
Libby Jones
Nicole Miritello
Carla Giugliano

2. Height (inches) Weight (lbs) Gender Age Vision
Variables taken into consideration:
Height (inches)
Weight (lbs)
Gender
Age
Vision

3. What we hope to learn from our data:
Is the relationship between height and weight different across the sexes?
Does adding age as an independent variable change the relationship between height and weight?
Can we prove, statistically that male height is different from female height in high schoolers? Is weight statistically different?
Is female weight more variable than male weight? Is male height more variable than female height?
Is there a statistical difference between male and female mean vision scores?

4. Normality of Height

5. Normality of Weight

6. Distribution of Age
n = 725

7. Scatter Plot of Weight vs. Height

8. Regression of Weight vs. Height
Males
n = 370
t-statistic for h = 9.55
p-value = 0.00
95% Confidence Interval: (3.88, 5.89)

9. Regression of Weight vs. Height
Females
n = 355
t-statistic for h = 8.24
p-value = 0.00
95% Confidence Interval: (3.99, 6.49)

10. Regression of Weight vs. Height
with a Dummy Variable for SEX
sex = 1 if male
sex = 0 if female
<= males
<= females
t-statistic for h = 12.58
p-value = 0.00
t-statistic for sex = -2.34
p-value = 0.02
95% Confidence Interval: (4.25, 5.82)
95% Confidence Interval: (-12.49, -1.10)

11. t-statistic for h*sex = -2.36
Regression of Weight vs. Height
with a Dummy Variable for sex in the slope
sex = 1 if male
sex = 0 if female
<= males
<= females
t-statistic for h = 12.33
p-value = 0.00
t-statistic for h*sex = -2.36
p-value = 0.02
95% Confidence Interval: (4.28, 5.91)
95% Confidence Interval: (-.19, -.02)

12. (148.07, 150.52) Taking into account gender, we now predict (weight)
with a 95% Confidence Interval of:
(148.07, )

13. Graph of Weight vs. Height and yhat

14. Testing the mean weight for females in high school:
vs.
t =
P > t = 0.04
Reject the Null
Note: the sample mean is

15. Testing the mean weight for males in high school:
vs.
t = -2.62
P > |t| = 0.01
Reject the Null
Note: the sample mean is

16. Testing the mean height for females in high school:
vs.
t = -8.52
P > |t|= 0.00
Reject the Null
Note: the sample height is 63.70

17. Testing the mean height for males in high school:
vs.
t = 7.69
P > t = 0.00
Reject the Null
Note: the sample height is 67.35

18. Regression of Weight vs. Height
with a Dummy Variable for AGE
Age1 = 15 yr olds Age2 = 16 yr olds Age3 = 17 yr olds Age4 = 18 yr olds
Males
<= Age1
<= Age2
<= Age3
<= Age4
t-stat for h= 9.15, Age2=-.30, Age3=.63, Age4=.25
p-value for h= 0.00, Age2=0.76, Age3=0.53, Age4=0.80

19. Regression of Weight vs. Height
with a Dummy Variable for AGE
Age1 = 15 yr olds Age2 = 16 yr olds Age3 = 17 yr olds Age4 = 18 yr olds
Females
<= Age1
<= Age2
<= Age3
<= Age4
t-stat for h= 8.13, Age2=1.22, Age3= 0.71, Age4= 1.63
p-value for h= 0.00, Age2= 0.23, Age3= 0.48, Age4= 0.10

20. For females:
vs.
t forage2 = 0.04
P > |t|= 0.97
Accept the Null

21. Test: t = -.4316 Accept the Null Where: beta1 is for males
beta1* is for females
<= males
<= females
t =
Accept the Null

22. Regression of Weight vs. Height, Sex, Age
Age1 = 15 yr olds Age2 = 16 yr olds Age3 = 17 yr olds Age4 = 18 yr olds
sex = 1 if male, sex = 0 if female
male
female
<= Age1
<= Age2
<= Age3
<= Age4
t-stat:
h= 12.15
Age2=0.66
Age3=1.00
Age4=1.30
Sex=-2.29
p-value:
h= 0.00
Age2=0.51
Age3=0.32
Age4=0.19
Sex=0.02

23. Taking into account age, we now predict yhat with a 95% Confidence Interval of:
(148.06, )

24. Graph of Weight vs. Height, Age, Sex and yhat

25. in weight across gender:
Testing Variance
in weight across gender:
vs.
F(354,369) ~
0.79<1.03<1.24
Accept the Null

26. Testing differences in mean weight across sexes:
vs.
t =
P > |t| = 0.000
Reject the Null

27. in height across gender:
Testing Variance
in height across gender:
vs.
F(354,369) ~
0.84>0.73
Reject the Null
Since variances are not equal, we cannot test for the equality of mean height across the sexes.

28. ANOVA Testing whether weight is dependent on age or not
F-statistic: 3.94
Probability > F: 0.01
Reject the Null

29. in vision across gender:
Testing Variance
in vision across gender:
vs.
F(354,369) ~(.813, 1.229)
> 1.229
Reject the Null
Since variances are not equal, we cannot check for equality of mean vision across the sexes.

30. in vision for 15 and 18 yr olds:
Testing Variance
in vision for 15 and 18 yr olds:
Females
vs.
F(97,41) ~(.0610<.862<1.733)
Accept the Null

31. Testing differences in mean vision for 15 and 18 year olds:
Females
vs.
t = -0.64
P > |t| = 0.522
Accept the Null

32. in vision for 15 and 18 yr olds:
Testing Variance
in vision for 15 and 18 yr olds:
Males
vs.
F(93,59) ~(0.636<1.553<1.612)
Accept the Null

33. Testing differences in mean vision for 15 and 18 year olds:
Males
vs.
t = 0.42
P > |t| = 0.67
Accept the Null

34. Possible Errors: R2  0.20 for all regressions
Weight dependent on other factors
Diet,exercise, genetics, abnormal health conditions, muscle to fat ratio, etc.
Age variable approximates mean age from grade level
Weight and height data may be overestimates due to method of collection
Almost half of data is for 16 year old students
Rounding errors in height and weight measurements
Scale only measured up to 300 lbs

35. Conclusions:
Sex is statistically significant in determining the relationship between height and weight
Age, as an independent variable, is statistically significant in determining the relationship between height and weight for both males and females
Mean female weight is less than mean male weight at the 95% level of significance
At the 95% level of significance, variance of weight in females does not differ from that of males
Male height is more variable than that of females at the 95% level of significance
Because variance in vision is not equal between males and females, we could not compare male and female mean vision scores by an unpaired t-test