Presented by Math 70 Statisticians: Libby Jones Nicole Miritello Carla Giugliano

1. The Skinny on High School Health Statistics Presented by Math 70 Statisticians: Libby Jones Nicole Miritello Carla Giugliano

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

3. 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:

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

13. Graph of Weight vs. Height and yhat

14. 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

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 154.96

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: Where: beta1 is for males beta1* is for females <=males <=females t = -.4316 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, 150.53)

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

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

26. Testing differences in meanweight across sexes: vs. t = -4.182 P > |t| = 0.000 Reject the Null

27. 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. 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.

30. 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 meanvision for 15 and 18 year olds: Females vs. t = -0.64 P > |t| = 0.522 Accept the Null

32. 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 meanvision 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