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Interest of variances of Health expectancies

Because estimates of Health expectanciesgif are means of random variables assumed to be independent, according to the central limit theorem, they tend to have normal distributions. So, the latter normal is often assumed. It permits to test if differences between two Sullivan indices are caused by random fluctuations or not.

Therefore, if it is wanted to test the hypothesis of equality of two health expectancies, tex2html_wrap_inline1524 and tex2html_wrap_inline1526 (for example, for males and females, or two different times, countries...), it is sufficient to compute the following Z-score:

  equation506

If the absolute value of the statistic Z is too large (in comparison with what a normal law should give), the hypothesis is rejected. Then, the two health expectancies can be considered as not equal.

Since, we have always:

  equation513

where tex2html_wrap_inline1530 and tex2html_wrap_inline1532 are the standard errors of tex2html_wrap_inline1524 and tex2html_wrap_inline1526 . Hence, the sum of the two standard errors (right hand of the previous equation) is used as denominator of equation 26. The level of significance for Z depends on the probability which is accepted for the case of a false conclusion of inequality.

For example, for p=0.05, the hypothesis is refused for:

displaymath1522

In general, see normal law distribution. Table 4 gives an example of such calculation of ratio Z. The differences between the two indicators DFLE does not seem to be the consequences of random fluctuations.

 

 
Age tex2html_wrap_inline1526 tex2html_wrap_inline1532 tex2html_wrap_inline1524 tex2html_wrap_inline1530 tex2html_wrap_inline1526 tex2html_wrap_inline1530 Z
tex2html_wrap_inline992 1991 1981 tex2html_wrap_inline1562 tex2html_wrap_inline1564
0 70.11 0.25 67.77 0.23 2.34 0.48 4.86 ***
5 65.69 0.25 63.48 0.23 2.30 0.48 4.54 ***
tex2html_wrap_inline1102 tex2html_wrap_inline1102 tex2html_wrap_inline1102 tex2html_wrap_inline1102 tex2html_wrap_inline1102 tex2html_wrap_inline1102 tex2html_wrap_inline1102 tex2html_wrap_inline1102 tex2html_wrap_inline1102
tex2html_wrap_inline1102 tex2html_wrap_inline1102 tex2html_wrap_inline1102 tex2html_wrap_inline1102 tex2html_wrap_inline1102 tex2html_wrap_inline1102 tex2html_wrap_inline1102 tex2html_wrap_inline1102 tex2html_wrap_inline1102
tex2html_wrap_inline1102 tex2html_wrap_inline1102 tex2html_wrap_inline1102 tex2html_wrap_inline1102 tex2html_wrap_inline1102 tex2html_wrap_inline1102 tex2html_wrap_inline1102 tex2html_wrap_inline1102 tex2html_wrap_inline1102
65 12.28 0.22 9.88 0.21 3.40 0.42 5.67 ***
70 8.39 0.21 6.86 0.20 1.93 0.41 4.73 ***
75 5.83 0.20 4.25 0.18 1.04 0.38 4.17 ***
80 3.39 0.18 2.34 0.16 1.96 0.34 3.04 ***
85 1.75 0.17 1.51 0.15 1.48 0.32 0.69 ***
***= probability of equality of the two indicators < 0.001.
Tableau 4: Comparisons of DFLE in 1981 (1) and in 1991(2), for females in France. Definition of health states are similar at the two dates.


next up previous
Next: Références Up: Annex: Variance of Sullivan Previous: Variance of

Eric Hauet
Fri Apr 25 22:40:35 DFT 1997