Comparing Heights and Weights

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Modelling procedures

The above scatter graph clearly demonstrates that the data is relatively normal, it also shows that there is possible a linear relationship between the two data items.

As the two variables are uncontrolled, both are random and independent, I am going to us the Product Moment Correlation Coefficient (Pmcc, rm) to test for correlation.

The measures found are shown below, with the calculations used in  and :

Using this value of rm I will now carry out an hypothesis test:

Ho:        ρ = 0                There is no correlation.

Ha:         ρ > 0                There is positive correlation between Height and Weight.

Using a 5% significance level the critical value is: 0.2353

0.5927878 > 0.2353        We reject Ho, there is positive correlation between height and weight.

Now there is much noise concerning girls who want to be over thin, and that boys want to look like hunks.  This may manifest itself in the value of rm for both populations, this I will now investigate.

Boys and Girls

Looking at the graph above it is obvious that the boys fit the straight line much more closely, where as the girls seem to be more scattered.  The measures are as follows, the calculations and the formulae are given in  and .

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Girls                                Boys

Ho: ρ = 0                        Ho: ρ = 0                No correlation

Ha: ρ > 0                         Ha: ρ > 0                There is positive correlation

Critical value for 25 on rm is: 0.3365

For the Boys we reject Ho, however for the girls we accept Ho.  This says something rather worrying, the boys accept that as they get bigger they get heavier, however for the girls it is different.  

Are the girls falling under pressure to change their body shape?

Are they always dieting?

Is there no link between height and weight at all

What factors do effect the weight of girls and women?

I am a little surprised by these results I must say, hence I would like to carry out a much larger survey, looking into ethnic background, access to fashion magazines, social background etc.