Conclusions
The t-distribution serves as a vital tool in statistics, particularly when estimating the significance of population parameters with small sample sizes or unknown variations. While sharing the bell-shaped and symmetric characteristics of the normal distribution, the t-distribution distinguishes itself with heavier tails, introducing a higher likelihood of extreme values. Understanding its properties and applications is essential for accurate statistical inference in scenarios where the assumptions of normality and known population standard deviation are not met.
Student’s t-distribution in Statistics
As we know normal distribution assumes two important characteristics about the dataset: a large sample size and knowledge of the population standard deviation. However, if we do not meet these two criteria, and we have a small sample size or an unknown population standard deviation, then we use the t-distribution.
Prerequisite – Normal distribution
Table of Content
- What is t-distribution?
- When to Use the t-Distribution?
- Mathematical Derivation of t-Distribution
- Significance of the t-Distribution
- Interpretation of t-Distribution
- Properties of the t-Distribution
- t-Distribution Table
- t-scores and p-values
- Limitations of Using a T-Distribution
- T- Distribution Applications
- Difference Between T-Distribution and Normal Distribution