The article by Tae Kyun Kim from the Department of Anesthesia and Pain Medicine at Pusan National University School of Medicine, Busan, Korea, discusses the T test as a parametric statistical method. The key points include: 1. **Probability Distribution**: When samples are drawn from a population with mean μ and variance σ², the sample mean X̄ follows a normal distribution N(μ, σ²/n). Under the null hypothesis μ = μ₀, the standardized statistic z = (X̄ - μ₀) / (σ/√n) follows a standard normal distribution. If the population variance is unknown, the sample variance s² is used, and the statistic - (X̄ - μ₀) / (s/√n) follows a t-distribution with n-1 degrees of freedom. 2. **Types of T Tests**: - **Independent T Test**: Used to compare means between two independent groups. It is suitable when the two groups are not related. - **Paired T Test**: Used to compare means of paired data, such as before and after treatments on the same subjects. 3. **Assumptions**: - **Normality**: The samples should be normally distributed. - **Equal Variances**: The variances of the two groups should be equal. - ** Independence**: The samples should be independent. 4. **Statistical Inference**: - **Sampling Distribution**: The distribution of sample means from a population follows a normal distribution with mean μ and variance σ²/n. - **T Distribution**: When the population variance is unknown, the t-distribution is used, which is similar to the normal distribution but with heavier tails. 5. **Independent T Test**: - The t statistic for independent samples is calculated using the sample means, variances, and degrees of freedom. - If the population variances are equal, the pooled variance is used; otherwise, the Welch-Satterthwaite equation is used to adjust the degrees of freedom. 6. **Paired T Test**: - The t statistic for paired samples is calculated using the differences between paired observations and their variances. - The correlation coefficient between the paired variables affects the statistical power of the test. 7. **Conclusion**: - Researchers must ensure that their samples meet the assumptions of normality, equal variance, and independence to draw valid conclusions. - Nonparametric tests can be used if the assumptions are not met, but parametric methods are generally more powerful. The article emphasizes the importance of correctly applying statistical methods and ensuring that the assumptions are met to obtain reliable results.The article by Tae Kyun Kim from the Department of Anesthesia and Pain Medicine at Pusan National University School of Medicine, Busan, Korea, discusses the T test as a parametric statistical method. The key points include: 1. **Probability Distribution**: When samples are drawn from a population with mean μ and variance σ², the sample mean X̄ follows a normal distribution N(μ, σ²/n). Under the null hypothesis μ = μ₀, the standardized statistic z = (X̄ - μ₀) / (σ/√n) follows a standard normal distribution. If the population variance is unknown, the sample variance s² is used, and the statistic - (X̄ - μ₀) / (s/√n) follows a t-distribution with n-1 degrees of freedom. 2. **Types of T Tests**: - **Independent T Test**: Used to compare means between two independent groups. It is suitable when the two groups are not related. - **Paired T Test**: Used to compare means of paired data, such as before and after treatments on the same subjects. 3. **Assumptions**: - **Normality**: The samples should be normally distributed. - **Equal Variances**: The variances of the two groups should be equal. - ** Independence**: The samples should be independent. 4. **Statistical Inference**: - **Sampling Distribution**: The distribution of sample means from a population follows a normal distribution with mean μ and variance σ²/n. - **T Distribution**: When the population variance is unknown, the t-distribution is used, which is similar to the normal distribution but with heavier tails. 5. **Independent T Test**: - The t statistic for independent samples is calculated using the sample means, variances, and degrees of freedom. - If the population variances are equal, the pooled variance is used; otherwise, the Welch-Satterthwaite equation is used to adjust the degrees of freedom. 6. **Paired T Test**: - The t statistic for paired samples is calculated using the differences between paired observations and their variances. - The correlation coefficient between the paired variables affects the statistical power of the test. 7. **Conclusion**: - Researchers must ensure that their samples meet the assumptions of normality, equal variance, and independence to draw valid conclusions. - Nonparametric tests can be used if the assumptions are not met, but parametric methods are generally more powerful. The article emphasizes the importance of correctly applying statistical methods and ensuring that the assumptions are met to obtain reliable results.