Design based inference is a statistical methodology that aims to understand the effects of a certain treatment or intervention on a given population. This approach is often used in social science research, where the goal is to understand how a particular policy or program affects a group of individuals or a community.

One example of design based inference is a randomized controlled trial (RCT). In an RCT, a sample of individuals is selected and randomly assigned to either a treatment group or a control group. The treatment group receives the intervention being studied, while the control group does not. Researchers then compare the outcomes of the two groups to determine the effectiveness of the intervention.

For instance, imagine a study looking at the effects of a new parenting program on children’s academic performance. The researchers randomly assign a group of parents and their children to either the treatment group (which receives the parenting program) or the control group (which does not receive the program). The researchers then compare the academic performance of the two groups to see if the parenting program had a positive effect.

Another example of design based inference is a natural experiment. A natural experiment is a research design that uses a real-world event or policy change to study the effects of a certain intervention on a population. For instance, imagine a study looking at the effects of a minimum wage increase on employment rates. The researchers could compare employment rates in a state that increased its minimum wage with employment rates in a similar state that did not increase its minimum wage. By comparing the two states, the researchers can infer the effects of the minimum wage increase on employment rates.

In both examples, the goal of design based inference is to draw conclusions about the effects of a certain intervention on a population. This approach is often used in social science research because it allows researchers to directly measure the effects of a certain intervention on a group of individuals, rather than relying on self-reported data or other indirect measures. Additionally, the use of randomization or natural experiments helps to control for potential confounding variables and ensures that the results are representative of the overall population.