Libby Jones Nicole Miritello Carla Giugliano

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The Skinny on High School Health Statistics. Libby Jones Nicole Miritello Carla Giugliano. Variables taken into consideration:. Height (inches). Weight (lbs). Gender. Age. Vision. Is the relationship between height and weight different across the sexes?

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Presentation Transcript

The Skinny on High School

Health Statistics

Libby Jones

Nicole Miritello

Carla Giugliano

Variables taken into consideration:

Height (inches)

Weight (lbs)

Gender

Age

Vision

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?

### What we hope to learn from our data:

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)

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)

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)

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)

Taking into account gender,

we now predict (weight)

with a 95% Confidence Interval of:

(148.07, 150.52)

Testing the mean weight

for females in high school:

vs.

t = 1.7024

P > t = 0.04

Reject the Null

Note: the sample mean is 143.39

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 154.96

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

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

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

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

For females:

vs.

t forage2 = 0.04

P > |t|= 0.97

Accept the Null

Test:

Where: beta1 is for males

beta1* is for females

<=males

<=females

t = -.4316

Accept the Null

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

Taking into account age, we now predict yhat with a 95% Confidence Interval of:

(148.06, 150.53)

Testing Variance

in weight across gender:

vs.

F(354,369) ~

0.79<1.03<1.24

Accept the Null

Testing differences in meanweight

across sexes:

vs.

t = -4.182

P > |t| = 0.000

Reject the Null

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.

ANOVA

Testing whether weight is dependent on age or not

F-statistic: 3.94

Probability > F: 0.01

Reject the Null

Testing Variance

in vision across gender:

vs.

F(354,369) ~(.813, 1.229)

2.0172 > 1.229

Reject the Null

Since variances are not equal, we cannot check for equality of mean vision across the sexes.

Testing Variance

in vision for 15 and 18 yr olds:

Females

vs.

F(97,41) ~(.0610<.862<1.733)

Accept the Null

Testing differences in meanvision

for 15 and 18 year olds:

Females

vs.

t = -0.64

P > |t| = 0.522

Accept the Null

Testing Variance

in vision for 15 and 18 yr olds:

Males

vs.

F(93,59) ~(0.636<1.553<1.612)

Accept the Null

Testing differences in meanvision

for 15 and 18 year olds:

Males

vs.

t = 0.42

P > |t| = 0.67

Accept the Null

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
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