Introduction:
The researcher intends to explore the effect of possible factors for the organization of effective mid-day meal interventions. In order to conduct this study, the most appropriate research method would be the ex-post facto method.

Explanation:

1. Ex-post facto method:
The ex-post facto method is a type of research design that is used to explore the relationship between variables when the researcher has no control over the independent variable. In this method, the researcher observes and analyzes the effect of independent variables that have already occurred or have been manipulated by some other factors. It is a non-experimental method where the researcher cannot manipulate the variables but only observe and analyze the existing data.

2. Factors for effective mid-day meal interventions:
In this study, the researcher aims to explore the factors that contribute to the organization of effective mid-day meal interventions. These factors may include variables such as the quality of food provided, the nutritional content of the meals, the involvement of the community and parents, the infrastructure of the kitchen facilities, the training and qualifications of the staff, etc.

3. Lack of control over independent variables:
The researcher cannot manipulate these factors as they have already been implemented or are influenced by external factors. For example, the researcher cannot control the quality of food provided in the past or the involvement of the community and parents in the past interventions. Therefore, an experimental method would not be appropriate for this study.

4. Observing and analyzing existing data:
In the ex-post facto method, the researcher collects and analyzes existing data to establish relationships between the independent and dependent variables. In this study, the researcher can collect data from previous mid-day meal interventions and analyze the factors that contributed to their effectiveness. This method allows the researcher to explore the effect of the factors without manipulating them.

Conclusion:
Given the nature of the study and the lack of control over the independent variables, the most appropriate research method for exploring the effect of possible factors for the organization of effective mid-day meal interventions is the ex-post facto method. This method allows the researcher to observe and analyze existing data to establish relationships between the variables.