Data Science Classroom Series – 10/Nov/2021

Students T distribution

  • We would be t-score and Students t-distribution if the population variance is unknown
  • The Students-t distribution is predominantly use for creating confidence intervals and testing hypothesis with normally distributed populations when its sample sizes are small.
  • This is particularly useful when we don’t have enough information or it is too costly to obtain it
  • All else equal, Student’s T distribution has fatter tails than the Normal distribution and a lower peak. This is to reflect higher level of uncertainity caused by small sample size Preview
  • Formula: Preview
  • Degrees of freedom: (n-1)
  • For calculation, we have t-table Refer Here
  • Lets find a confidence interval with 95% confidence for the dataset Refer Here
  • To calculate confidence interval when the population variance is unknown we use the following formula Preview
  • The result Preview
  • Now try to Calculate the CI Intervals with 90% and 99% confidence using Students T distribution Preview
  • Margin of Error and Confidence intervals with known & unknown population variances Preview
  • Generally t distribution based confidence intervals have larger range due to uncertainity.
  • Impact on the range Preview
  • CI interval range will be less when the
    • Sample size is more
    • Sample is not dispersed but rather concentrated => Standard deviation will be less

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