Which statement about the scree plot and sample size is correct?

Which statement about the scree plot and sample size is correct?

• A. With more than 200 participants, the scree plot provides a fairly reliable criterion for extraction.
• B. The scree plot is always exact regardless of sample size.
• C. A scree plot cannot be used to decide the number of factors.
• D. Reliability depends only on the number of variables, not sample size.

Answer: (A)

The main idea here is that the reliability of using a scree plot to decide how many factors to extract depends on the amount of data you have. A scree plot shows the eigenvalues from a factor analysis, and you look for where the slope levels off (the elbow) to suggest how many factors to keep. When you have a larger sample, the estimated eigenvalues are more stable and the elbow becomes a clearer, more trustworthy cue. In practice, having more than about 200 participants is a commonly cited guideline that gives a fairly reliable basis for extracting factors, because it reduces sampling error that can blur or mislead the elbow point. If the sample size is small, those eigenvalue estimates wobble more from sample to sample, making the elbow harder to identify and the factor count less dependable. That’s why the statement claiming the scree plot is always exact irrespective of sample size is not correct. It’s also not right to say a scree plot cannot be used to decide the number of factors, since researchers do use it—often as part of a broader decision that includes other criteria. Finally, reliability isn’t determined only by the number of variables; how many participants you have matters too because more variables typically require more cases to stabilize the factor solution.

The main idea here is that the reliability of using a scree plot to decide how many factors to extract depends on the amount of data you have. A scree plot shows the eigenvalues from a factor analysis, and you look for where the slope levels off (the elbow) to suggest how many factors to keep. When you have a larger sample, the estimated eigenvalues are more stable and the elbow becomes a clearer, more trustworthy cue. In practice, having more than about 200 participants is a commonly cited guideline that gives a fairly reliable basis for extracting factors, because it reduces sampling error that can blur or mislead the elbow point.

If the sample size is small, those eigenvalue estimates wobble more from sample to sample, making the elbow harder to identify and the factor count less dependable. That’s why the statement claiming the scree plot is always exact irrespective of sample size is not correct. It’s also not right to say a scree plot cannot be used to decide the number of factors, since researchers do use it—often as part of a broader decision that includes other criteria. Finally, reliability isn’t determined only by the number of variables; how many participants you have matters too because more variables typically require more cases to stabilize the factor solution.