Causality between two variables | Three conditions for a causality | Possible causality | ||
(Condition 1) Bivariate analysis: Crude covariational relationship | (Condition 2) Multivariate analysis: Covariational relationship through controlling for third variables | (Condition 3) Temporal precedence | ||
Causal path A: on mathematical proficiency | ||||
(Step 1) From not being stunted to attendance rate | Yes P=0.003* Mann-Whitney U test* | Yes P=0.041* Ordinal regression¶ | Yes While stunting is chronic undernutrition that occurs generally before 3 years of age,24 school attendance takes place after enrolment at 5 or 6 years of age at primary schools. Thus, clearly, school attendance follows becoming stunted. | Yes |
(Step 2) From attendance rate to mathematical proficiency | Yes P=0.013* Spearman’s correlation† | Yes P=0.014* Ordinal regression‡ | Yes Without attending schools, children cannot take mathematics examinations. Thus, clearly, mathematical proficiency follows attendance. | Yes |
Causal path B: on national language proficiency | ||||
(Step 1) From not being thin to attendance rate | No P=0.141 Mann-Whitney U test* | Yes P=0.020* Ordinal regression¶ | Not necessarily Thinness is acute undernutrition that can occur after attendance at school, too. Thus, school attendance does not necessarily follow becoming thin. | No |
(Step 2) From attendance rate to national language proficiency | No P=0.104 Spearman’s correlation (rs)† | No P=0.483 Ordinal regression§ | Yes Without attending schools, children cannot take national language examinations. Thus, national language proficiency follows attendance. | No |
*See figure 2.
†See figure 3.
‡Coefficient estimate for not being stunted in multiple regression model with attendance rate (%) and other all background variables as dependent and independent variables, respectively.
§Coefficient estimate for not being thin in multiple regression model with attendance rate (%) and other all background variables as dependent and independent variables, respectively.
¶See table 2.
** * P <0.05