Analysis of Data Part 2

Statistical Methods

For our data analysis, we used Statistical Package for Social Sciences (SPSS) 14.0 for Windows Integrated Student version.

Of Linearity and Homogeneity and Scatter Plots

To find out if an association exists between arm-span and height, and if yes, the degree of association, requires a correlational analysis. Because there is only one independent variable, and both independent and dependent variables (for the reason as to their selection, see post titled 'Analysis of Data Part 1') are scale data, and we're interested in their correlation, we've identified Pearson's Correlation Coefficient to be the most appropriate statistical test.


The coefficient of correlation only measures linear relationship. Thus, first we need to ascertain with a scatter diagram, whether arm-span and height are linearly related, and if a constant error variance exists.

We've plotted the scatter diagram of arm-span and height for the sample here. A copy is enclosed here as well.

The R square linear is 0.805. We interpret this to mean the goodness of fit of the line, ie 80.5% of the variation in height can be explained by the fitted line.

As a linear relationship exists between arm-span and height, we proceed to compute Pearson's correlation coefficient. This is the results from SPSS.

Since the p value (0.000) is less than 0.05, we reject the null hypothesis, and conclude there is a very strong, positive, and significant association between arm-span and height. [where r = 0.897, p < 0.05 and N = 30]

We are also interested to find out how the association looks when the sample is stratified by gender. Thus, we plotted the scatter diagram again, but setting gender as marker field. The scatter diagram of arm-span and height for females and males in the sample is available here. A copy is enclosed below as well.

R square linear of male and female samples is 0.759 and 0.638 respectively. In other words, 75.9% and 63.8% of the variation in height can be explained by the fitted line for male and female samples respectively. We take it that the fit lines for both genders are sufficiently linear and have homogeneous variance.


A linear relationship exists between arm-span and height for the two genders, so we proceed to compute Pearson's correlation coefficient. This is the results from SPSS.







For female Since the p value (0.000) is less than 0.05, we reject the null hypothesis, and conclude there is a very strong, positive, and significant association between arm-span and height for the women sampled. [ where r = 0.799, p < 0.05 and N = 23]


For male Since the p value (0.011) is less than 0.05, we reject the null hypothesis, and conclude there is a very strong, positive, and significant association between arm-span and height for the men sampled. [ where r = 0.871, p < 0.05 and N = 7 ]