T-distribution

• Student's t-distribution

  • A probability distribution that is used to estimate population parameters (n < 30) and/or the population variance is unknown.
  • It was developed by William Sealy Gosset. that used the pen name "Student."
• Degrees of Freedom

  • df = n-1
  • The number of degrees of freedom is one, less than the sample size
• As the sample size increases, the distribution becomes more normal.
• Properties of the t-distribution

  1. Symmetrical about 0.
  2. Bell-shaped like the normal distribution but has heavier tails.
  3. Mean, median, and mode are all equal to zero.
  4. The variance is always greater than one. (As the number of df increases and approaches infinity, the variance also approaches 1).
  5. As the df increases, the t-distribution curve looks more like a normal distribution. (STDev varies with the sample size, s >1)
  6. The STDev varies with the sample size (s > 1).
  7. Total area is 1 or 100%.
• Percentiles

  • The percentage of values in a set of data scores that fall below a given value.