## Core Concept
The core concept here revolves around the principles of statistical sampling and study design, particularly how sample size affects the power and validity of a study. Increasing the sample size in a study has several implications, including its effect on the standard error, power of the study, and the precision of estimates.

## Why the Correct Answer is Right
Increasing the sample size in a study generally leads to a decrease in the standard error, which means the estimates become more precise. It also increases the power of the study, making it more likely to detect a statistically significant effect if one exists. However, the statement that does not hold true regarding increasing sample size needs to be identified among the given options.

## Why Each Wrong Option is Incorrect
- **Option A:** Typically, increasing the sample size decreases the standard error, which implies that the precision of estimates increases. This statement seems generally true about increasing sample size.
- **Option B:** Increasing sample size generally increases the power of a study, allowing for the detection of smaller effects with greater confidence. This is a true statement regarding sample size.
- **Option C:** This option might discuss a scenario or implication that is not universally true or could be misleading in the context of sample size increase.
- **Option D:** Without specific details on what each option states, we can infer that the incorrect statement likely pertains to a misconception about sample size, such as suggesting it decreases power, increases bias, or has no effect on precision.

## Clinical Pearl / High-Yield Fact
A crucial point to remember is that increasing the sample size can help in achieving more reliable and generalizable results, but it also increases the cost and time required for the study. A well-planned sample size calculation is essential before starting a study to ensure it can meet its objectives.

## Correct Answer: C.