Independence in data means which?

Independence in data means which?

• A. Observations are uncorrelated
• B. One data point does not influence another
• C. Observations come from the same population
• D. Observations are dependent

Answer: (B)

Independence means each observation is not related to or influenced by any other observation. In practice, the value of one data point should give you no information about the value of another; the data points are treated as separate draws from the same process. This is why the statement describing independence is the best fit: it directly captures that no observation affects another. The idea of being uncorrelated is weaker. Two observations can have zero linear correlation yet still be related in nonlinear ways, so they wouldn’t be truly independent. Saying observations come from the same population addresses where the data come from, not how they relate to each other. Independence concerns the relationship between observations themselves. Observations being dependent is the opposite of independence, meaning there is some connection or influence between them.

Independence means each observation is not related to or influenced by any other observation. In practice, the value of one data point should give you no information about the value of another; the data points are treated as separate draws from the same process.

This is why the statement describing independence is the best fit: it directly captures that no observation affects another.

The idea of being uncorrelated is weaker. Two observations can have zero linear correlation yet still be related in nonlinear ways, so they wouldn’t be truly independent.

Saying observations come from the same population addresses where the data come from, not how they relate to each other. Independence concerns the relationship between observations themselves.

Observations being dependent is the opposite of independence, meaning there is some connection or influence between them.