What are the four questions that should be asked to determine if a statistical generalization is a strong inductive argument?
The correct answer and explanation is:
To determine if a statistical generalization is a strong inductive argument, there are four key questions that should be asked:
- Is the sample size sufficiently large?
A sample must be large enough to represent the population accurately. If the sample size is too small, it may not capture the diversity of the population, leading to a weaker generalization. A larger sample typically reduces the risk of sampling error and increases the reliability of the conclusion drawn from it. - Is the sample representative of the population?
The sample should accurately reflect the characteristics of the population it is intended to represent. A non-representative sample (e.g., biased sample or one that excludes certain groups) will undermine the strength of the generalization. It’s important to ensure that the sample includes all relevant subgroups of the population. - Is there any significant variation within the population?
If the population being studied has significant variation in the characteristic being examined, the generalization may need to account for this variability. For instance, a statistical generalization about the average height of individuals in a country might not be valid if there are large regional differences in height that are not reflected in the sample. - Is there a clear and reasonable connection between the sample and the conclusion?
The connection between the sample’s findings and the broader conclusion should be reasonable and not based on overgeneralization. The conclusion should logically follow from the sample data, and any assumptions or extrapolations made should be supported by evidence.
These four questions help assess the strength of the inductive argument. A generalization will be stronger when the sample size is large, representative of the population, accounts for variability, and draws reasonable conclusions based on solid evidence. If any of these criteria are not met, the argument may be weak or unreliable.