We then subtracted the two correlation matrices from each other to obtain the matrix A and computed the Frobenius norm defined as A F = ∑ i ∑ j a i j 2 which serves as a distance measurement between the two correlation matrices.
The fundamental concept is that if the errors in the forecasts produced by different methods are unbiased and have a low degree of correlation with each other, the random errors from the individual forecasts will tend to offset each other, with the result that a composite of the forecasts will have lower errors than any individual forecast.
When two vectors are close to the correlation circle, they can be: (1) close to each other, meaning a positive correlation (2) orthogonal from each other, meaning that they are not correlated and (3) on the opposite side from the centre, meaning a significant negative correlation.
Items were also considered for deletion if they: (1) caused a significant increase in scale alpha values if they were deleted (item-total statistics), or (2) were highly correlated (>.70 from item-to-item correlations) with each other [ 22].
Pairs from southern population had generally higher correlations between each other than with individuals from the northern populations PT14-PT211) and hierarchical clustering based on these results identified two groups that correspond to the northern and southern populations.
When the various parameters were compared with each other, all motility parameters correlated significantly with each other (correlation coefficients varied from 0.44 to 0.81), similarly the plasma membrane integrity tests showed significant correlations between each other (0.37 – 0.37).
However, the resulting correlations deviate considerably from each other, mainly because they did not take into account the various interacting mechanisms.
A follow-up hierarchical regression analysis was performed to investigate whether the correlations differed significantly from each other.
Green, J. A. Testing whether correlation matrices are different from each other.
As for the cross-trait familial correlations computed for the four familial dyads (Table 5), results showed that within GLU-SBP (P < 0.001), GLU-WC (P = 0.027), GLU-TG (P = 0.049), HDL-WC (P = 0.010), SBP-WC (P = 0.017), and SBP-TG (P = 0.046), the specific familial correlations are significantly different from each other.
Generally, PM10, SO2, and NO2 were relatively highly correlated with each other (Pearson correlation coefficients ranged from 0.64 to 0.73).
