Chi-square is used to look at the statistical significance of an association between a categorical outcome (such as wasted or not wasted) and a categorical determining variable (such as diarrhea in the last two weeks, no diarrhea). 

When running the cross-tab, an option is available to test the significance of the association using chi-square. 

According to SPSS User's Guide,  Chi-Square (Crosstabs) Tests the hypothesis that the row and column variables are independent, without indicating strength or direction of the relationship.

Pearson chi-square, likelihood-ratio chi-square, and linear-by-linear association chi-square are displayed. For 2x2 tables, Fisher's exact test is computed when a table that does not result from missing rows or columns in a larger table has a cell with an expected frequency of less than 5. Yates' corrected chi-square is computed for all other 2x2 tables.

ANOVA is used to see an association between a continuous outcome variable (such as mean HAZ score) and a categorical determining variable (such as iodized salt consumption). 

According to SPSS User's Guide, Analysis of Variance is a method of testing the null hypothesis that several group means are equal in the population, by comparing the sample variance estimated from the group means to that estimated within the groups.