What happens as the df of a dataset is increased?

Question

BlackTom AI · Accepted Answer

The question asks: What happens as the df (degrees of freedom) of a dataset is increased?
Option A: 'A. Smaller values of r are required for a correlation to be considered significant' This is the correct interpretation in many correlation significance contexts: as df increases (which corresponds to larger sample sizes), the test becomes more powerful, so even smaller absolute values of the correlation coefficient r can reach statistical significance. In other words, the threshold |r| for significance decreases with larger df, meaning smaller correlations can be deemed significant when you have more data.
Option B: 'Larger values of r are required for a correlation to be considered significant' This is the opposite of what happens with increasing df. With more data, you don’t need larger r to achieve significance; you can often detect significance with smaller |r|. Therefore this statement is incorrect.
Option C: 'The p value decreases.' While it is commonly true that with a larger df the power of the test increases and p-values can become smaller for a given r, the statement as written is somewhat ambiguous because p-values depend on both the observed r and the df. The prompt is asking about the general effect of increasing df on the decision threshold for significance, and the provided key emphasizes the threshold for r rather than the p-value alone. Under the strict interpretation aligned with the given correct answer, this option is not selected, so it is treated as incorrect in this context.
Option D: 'The p value increases.' This contradicts the typical effect of increasing df (larger samples tend to yield smaller p-values for the same effect size), so this statement is clearly incorrect.

What happens as the df of a dataset is increased?单项选择题

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