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Use Python to discover the t distribution and associated tests
The t distribution, also known as the student’s t distribution, is a probability distribution that arises when estimating the mean of a normally distributed population in situations when the sample size is small and the population standard deviation is unknown. It is similar to the normal distribution but has heavier tails, meaning it is more prone to producing values that fall far from its mean. The t distribution is crucial for data analysis, especially when dealing with small sample sizes.
The t distribution is characterised by its degrees of freedom, which typically depend on the sample size.
The Irish statistician William Sealy Gosset published “Biometrika” in 1908 under the pseudonym Student. This paper refers to the distribution as the “frequency distribution of standard deviations of samples drawn from a normal population”. This work became well known through the work of Ronald Fischer, who called the distribution “Student’s distribution” and represented the test value with the letter t.
Student’s t distribution is a probability distribution that generalises the standard normal distribution. Like the normal distribution, it is symmetrical around its mean, being zero, and bell shaped.