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.

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What happens as the df of a dataset is increased?

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PSYC20009_2025_SM2 Supplementary or Special Exam: Personality and Social Psychology (PSYC20009_2025_SM2)- Requires Respondus LockDown Browser

What happens as the df of a dataset is increased?

查看解析

登录即可查看完整答案

类似问题

The degrees of freedom of a 4 x 5 table is:

​A researcher reports df = 18 for a repeated-measures t statistic. This research study used a total of n = 19 participants.

A repeated-measures study using a sample of n = 20 participants would produce a t statistic with df = ____.​

If the population variance is unknown, then a degree of freedom is lost in the calculation of sample variance.

In a contingency table, what does the degrees of freedom indicate?

Suppose that a study compares the means of two groups. There are 40 males in Group 1 and 35 females in Group 2. The degrees of freedom for this study when using the t-test for the difference between means is:

Based on the information in Question 1, what were the degrees of freedom (DF) for the interaction of color and style, C?

What concept do "degrees of freedom" represent in statistical analysis?

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A researcher reports df = 18 for a repeated-measures t statistic. This research study used a total of n = 19 participants.

A repeated-measures study using a sample of n = 20 participants would produce a t statistic with df = ____.