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The t-Distribution
From [Blu4 page 358] and [JK10 page 476]
How the t-Distribution is similar to the Standard
Normal Distribution
 It is bell-shaped
 It is symmetric about the mean
 The mean, median, and mode are all equal
to 0
 The mean, median, and mode are all
located at the center of the distribution
 The curve never touches the x-axis.
How it differs from the Standard Normal
 It is not quite as peaked as the Normal
 There’s more thickness in the tails of the tDistribution
 The variance is greater than 1
It’s a family of distributions, a different distribution for each degrees of freedom number
The variance is greater than 1 but as the degrees of freedom increases, the variance approaches
1, and the t-Distribution approaches the standard Normal Distribution
[to be done later – good pictures in [JK10 page 476] and [Blu4 page 358]
Advanced - the formula
[To be obtained from Burington & May or other advanced text]
What is Degrees of Freedom, df?
[Blu4 page 358] The degrees of freedom are the number of values that are free to vary after a sample
statistic has been computed. Example: five values and the mean is 10. Four of the five values are free
to vary. Once four values have been chosen, the fifth value is locked in. [JK10 page 476] The sample
variance is the mean of the squared deviations,
∑(𝑥−𝑥̅ )2
but we are constrained by ∑(𝑥 − 𝑥̅ ) = 0, the
sum of the deviations must be zero. Only the first 𝑛 − 1 of these deviations has freedom of value.
Cases where 𝑑𝑓 = 1 or 𝑑𝑓 = 2 are special and ordinarily we won’t consider nor encounter such cases.
4/30/2017 4:30 AM