9 ranking of wasting with a positive concentration index. It is not surprising that the top and bottom of the ranking for wasting did not coincide with those for stunting and underweight, as it is rare to observe children who are stunted, underweight _and_ wasted at the same time (cf. Figures 2 and 3) The overall concentration index rankings of all three categories are similar to some extent. Peru, Morocco, Nicaragua are found on the lower side of the spectrum and Egypt, Vietnam, Romania and Pakistan on the opposite side and the other countries somewhere in the middle.

# TESTS OF SIGNIFICANT DIFFERENCES BETWEEN CONCENTRATION INDICES

We now rank countries by inequality in a statistically more rigorous way. The standard errors of the concentration indices shown in Table 4 enable us to rank countries according to whether they have significantly more inequality than others. Tables 5-7 report the results of t- tests indicating the significance of the difference between the concentration indices of the column and row countries. Thus, for example, in Table 5, Bangladesh has a significantly less inequality in stunting than Brazil (hence the plus sign in front of the 4.05). Bangladesh also has less inequality in stunting than Cote d'Ivoire, but the difference in this case is not statistically significant. Bangladesh has _more_ inequality in stunting than Egypt, but the difference is again not statistically significant.

A glance across Tables 5-7 reveals one important point-in _the majority of cases, whatever the indicator, the differences in inequality between countries are not statistically significant._ Thus in only 44% of the 190 pairwise comparisons for stunting inequalities is the _t-_ ratio larger than 1.96 in absolute size, while the equivalent percentages for underweight and wasting are 42% and 23% respectively. This warns against reading too much into concentration index differences unless accompanied by statistical tests.

A Hasse diagram indicating the hierarchical order of countries makes it easier to grasp which inter-country differences _are_ significant. The principle of the chart is that the concentration indices of all countries on the same level are _not_ significantly different from one another, but _are_ significantly larger (or smaller) than those of all countries on a different level. However, with a large number of countries, a perfectly accurate chart would become extremely cumbersome and would make it harder-rather than easier-to grasp the essential results. The Hasse charts presented here are therefore _simplified_ Hasse charts, intended to convey the broad results of the various pairwise comparisons.

Figure 4. Simplified Hasse diagram for under-five stunting by equivalent consumption

|Bangladesh<br>Ghana<br>Guatemala|Indo|Egypt<br>nesia<br>Nepal<br>Pa|kistan<br>Ro|mania<br>Vietnam<br>Zambia|
|---|---|---|---|---|
|L<br>A<br>L<br>L<br>|~~~~~<br>|~~~~~~~~~~~~~~~------<br>|------I-<br>|<br>|
|r-------------r-------<br>**Brazil**<br>China<br>Cote d|-------T--<br>'lvoire|-----------------**----**---- ------ ----<br> <br>Guyana<br>Morocco|-----------T ----<br>Nicaragua|1--<br>----- T---~-~------1<br>Philippines<br>S Africa|
|||Per__-<br>**----**<br>-<br>----<br>**Peru**<br>**Rssia**|--||