Why t-distributions tend to be flatter and more spread out than normal distribution?

Answer 1

T-distributions tend to be flatter and more spread out than normal distributions due to their heavier tails. Unlike the normal distribution, which has thin tails, t-distributions account for uncertainty in sample variance estimation, making them more robust for smaller sample sizes. The additional variability inherent in t-distributions arises from the incorporation of the sample size through the degrees of freedom parameter. As the degrees of freedom decrease, the t-distribution becomes more spread out and flatter, reflecting increased uncertainty and variability in the estimates. This property makes t-distributions well-suited for inferential statistics, particularly when dealing with small sample sizes.

Answer 2

The shape of a t distribution changes with degrees of freedom (df). As the the df gets very large the shape of the t distribution will begin to look similar to that of a normal distribution. However, the t distribution has more variability than a normal distribution; especially when the df are small. When this is the case the t distribution will be flatter and more spread out than the normal distributions.