What reasoning error is illustrated by the statement regarding test scores and the new principal?

The reasoning error known as Post Hoc, which stands for "post hoc, ergo propter hoc," suggests that because one event follows another, the first event must be the cause of the second. In your instance regarding test scores and the new principal, the statement likely implies a cause-and-effect relationship between the arrival of the new principal and changes in test scores without sufficient evidence to support that this change is indeed a direct result of the new principal's influence.

By attributing changes in test scores directly to the new principal merely because the principal started their position around the same time as the change, there's an assumption that the principal is responsible for that change. This reasoning does not consider other factors that could contribute to variations in test scores, such as external academic influences, changes in curriculum, or the varying capabilities of the students. Therefore, relying on such a connection illustrates the Post Hoc reasoning error, which oversimplifies complex arguments by attributing causation incorrectly.