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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
slide1

The Skinny on High School

Health Statistics

Libby Jones

Nicole Miritello

Carla Giugliano

slide2

Variables taken into consideration:

Height (inches)

Weight (lbs)

Gender

Age

Vision

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?

What we hope to learn from our data:

slide8

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)

slide9

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)

slide10

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)

slide11

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)

slide12

Taking into account gender,

we now predict (weight)

with a 95% Confidence Interval of:

(148.07, 150.52)

slide14

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

slide15

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

slide16

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

slide17

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

slide18

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

slide19

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

slide20

For females:

vs.

t forage2 = 0.04

P > |t|= 0.97

Accept the Null

slide21

Test:

Where: beta1 is for males

beta1* is for females

<=males

<=females

t = -.4316

Accept the Null

slide22

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

slide23
Taking into account age, we now predict yhat with a 95% Confidence Interval of:

(148.06, 150.53)

slide25

Testing Variance

in weight across gender:

vs.

F(354,369) ~

0.79<1.03<1.24

Accept the Null

slide26

Testing differences in meanweight

across sexes:

vs.

t = -4.182

P > |t| = 0.000

Reject the Null

slide27

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.

slide28

ANOVA

Testing whether weight is dependent on age or not

F-statistic: 3.94

Probability > F: 0.01

Reject the Null

slide29

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.

slide30

Testing Variance

in vision for 15 and 18 yr olds:

Females

vs.

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

Accept the Null

slide31

Testing differences in meanvision

for 15 and 18 year olds:

Females

vs.

t = -0.64

P > |t| = 0.522

Accept the Null

slide32

Testing Variance

in vision for 15 and 18 yr olds:

Males

vs.

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

Accept the Null

slide33

Testing differences in meanvision

for 15 and 18 year olds:

Males

vs.

t = 0.42

P > |t| = 0.67

Accept the Null

possible errors
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
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