Skip to main content

Table 2 Information content of seven cases

From: The information content of financial survey response data

 

A

B

C

D

E

F

G

\( {I}_Z=\frac{\rho^2\left(Z,X\right)}{\rho^2\left(Y,X\right)} \)

0.894427

0.864447

1.014439

1.22563

0.274983

?

?

\( \hat{\omega}\triangleq \frac{\frac{n}{\sigma^2}}{{\displaystyle {\sum}_{i=1}^{k-1}}\left(\frac{n}{p_i\left(1-{p}_i\right)}\right)}=\frac{1}{\sigma^2{\displaystyle {\sum}_{i=1}^{k-1}}\left(\frac{1}{p_i\left(1-{p}_i\right)}\right)} \)

0.144737

0.141026

0.166667

0.152778

0.141026

?

?

\( \mathrm{Info}\ \mathrm{per}\ \mathrm{observation}={\displaystyle \sum_{i=1}^{5-1}}\left(\frac{1}{p_i\left(1-{p}_i\right)}\right) \)

0.628099

0.644628

0.545455

0.595041

0.644628

0.628099

0.528926

\( \mathrm{F}\mathrm{I}={\displaystyle \sum_{i=1}^{5-1}}\left(\frac{n}{p_i\left(1-{p}_i\right)}\right) \)

6.909089

7.090908

6.000005

6.545451

7.090908

6.909089

5.818186