Mean bone density amongst two groups of 50 people each is compared with each other. The test of significance used would be –
**Question:** Mean bone density amongst two groups of 50 people each is compared with each other. The test of significance used would be -
A. **T-Test for Independent Samples**
B. **One-Way ANOVA**
C. **Chi-Square Test**
D. **Non-parametric Test (Mann-Whitney U or Kruskal-Wallis)**
**Correct Answer:** .
**Core Concept:** In medical research and statistical analysis, comparing the means of two independent groups is a common task. When dealing with continuous variables like bone density, we use appropriate tests to determine if the difference between the means is statistically significant.
**Why the Correct Answer is Right:**
A) T-Test for Independent Samples: This test is used when comparing the means of two independent groups (groups that have not been selected from the same population) with a normal distribution (Gaussian distribution) of the data. In this case, we are comparing the bone density means of two groups, which makes this test suitable.
**Why Each Wrong Option is Incorrect:**
B) One-Way ANOVA: This test is used when comparing the means of three or more independent groups or when comparing the means of two groups corrected for multiple comparisons. Since we are comparing only two groups, One-Way ANOVA is not applicable.
C) Chi-Square Test: This test is used to compare proportions or frequencies between two or more groups. It is not suitable for comparing means like bone densities.
D) Non-parametric Tests (Mann-Whitney U or Kruskal-Wallis): These tests are used when the data does not follow a normal distribution. Since we assume the data has a normal distribution (Gaussian distribution) as indicated by the question, non-parametric tests are not suitable.
**Core Concept:** In medical research, understanding the appropriate statistical test for comparing means of independent groups is crucial for making accurate conclusions.
**Clinical Pearl:** When comparing the means of two independent groups with normal distribution of data, choose the T-Test for Independent Samples.
**Explanation of Wrong Options:**
1. One-Way ANOVA: This test is not applicable when comparing only two groups, as it is designed for three or more groups.
2. Chi-Square Test: This test is used for comparing proportions, frequencies, or contingency tables, not for comparing means like in our case.
3. Non-parametric Tests (Mann-Whitney U or Kruskal-Wallis): These tests are used when the data does not follow a normal distribution. Since the question assumes a normal distribution, these tests are not suitable.
**Why the Correct Answer is Right:**
A) T-Test for Independent Samples: This test is appropriate when comparing the means of two independent groups with normal distribution of data. In this case, we need to determine if the difference in bone density between two groups is statistically significant, and a T-Test for Independent Samples is suitable for this purpose.