Week 3: 29 Sept – Understatnding T-test I

Understatnding T-test

We had already explored T-Test and its role in understanding the statistical significance of a distributions mean. For a t-test to have a menaingful result, the distrivutions must satisfy the following conditions:

    • The data sets must be normally distributed, i.e, the shape must resemble a bell curve to an extent
    • are independent and continuous, i.e., the measurement scale for data should follow a continuous pattern.
    • Variance of data in both sample groups is similar, i.e., samples have almost equal standard deviation

Today, we will deep dive into these to understands why these conditions are necessary. But first, le us understand what a T-Distribution is

T Distribution

  • The t-distribution, also known as the Student’s t-distribution, is a probability distribution that is similar in shape to the standard normal distribution (bell-shaped curve).
  • The key feature of the t-distribution is that it has heavier tails compared to the normal distribution. The shape of the t-distribution depends on a parameter called degrees of freedom (df).
  • As the sample size increases, the t-distribution approaches the standard normal distribution.
  • In hypothesis testing with the t-test, the t-distribution is used as a reference distribution to determine the critical values for a specified level of significance (alpha) and degrees of freedom.


Normal distribution (z-distribution) is essentially a special case of t distribution. But whats important for us are certain properties that are common to both but is more prominent in the normal ditribution



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