Twenty-five children are chosen randomly from a school playground. Their heights are measured in 2 consecutive months. What statistical test could be used to test the hypothesis that their heights are not different in consecutive months?
## **Core Concept**
The core concept being tested here is the comparison of measurements of the same subjects over two time points. This scenario describes a **paired data** or **repeated measures** design, where the same subjects are measured twice (in this case, the children's heights are measured in two consecutive months).
## **Why the Correct Answer is Right**
The correct answer, **. Paired t-test**, is appropriate for this scenario because it is used to compare the means of two related groups of samples. The paired t-test, also known as the dependent samples t-test, assesses whether the average difference between paired observations is significantly different from zero. In this context, it would evaluate if there's a significant difference in the heights of the children measured in two consecutive months.
## **Why Each Wrong Option is Incorrect**
- **Option A:** . **Independent t-test** - This test is used to compare the means of two independent groups, not suitable for paired or repeated measures data.
- **Option B:** . **ANOVA (Analysis of Variance)** - While ANOVA can compare means among three or more groups, it is not specifically designed for paired data or to compare only two related groups.
- **Option D:** . **Wilcoxon Rank-Sum Test** - This is a non-parametric test used to compare two independent samples, not paired data.
## **Clinical Pearl / High-Yield Fact**
A key point to remember is that when dealing with **paired data** (measurements from the same subjects over time or matched subjects), the appropriate statistical test to compare means is the **paired t-test**. This ensures that the analysis accounts for the dependency between the measurements.
## **Correct Answer: B. Paired t-test**