PUBH2007 Lecture Notes - Lecture 7: Randomized Experiment, Null Hypothesis, Sampling Distribution

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PUBH2007 LECTURE SEVEN
T distribution: What you use instead of Normal distributions if you have normally distributed data but
you don’t have the population SD
Use t distributions
Perform one-sample t procedures (CI and hypothesis test)
Perform two-sample t procedures (CI and hypothesis test)
Perform matched-pairs t procedures (CI and hypothesis test)
The t statistic does not have a Normal distribution
Its sampling distribution is called “tudet’s t-distribution with
n 1 degrees of freedo (denoted by d.f.), where n is the sample size
Lots of 'degrees of freedom' if no idea where he went on the path
Less uncertainty with the more points that you are certain of
As sample size increases, become more certain of the parameters that you are trying to estimate and
the statistics that you can calculate
T with d.f. = 10 has high centre of t distribution and low tails
T with d.f. =3 has low centre of t distribution and high tails
Represents less certainty in middle with fewer degrees of freedom
T distribution is symmetric and similar to Normal but with higher tails
Its shape depends on d.f.
If d.f. is large, e.g. n> 40, probabilities are almost the same as those for the Standard Normal
distribution.
Variable value = t statistic
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Document Summary

The t statistic does not have a normal distribution. Its sampling distribution is called tude(cid:374)t"s t-distribution with n 1 (cid:862)degrees of freedo(cid:373)(cid:863) (denoted by d. f. Lots of "degrees of freedom" if no idea where he went on the path. Less uncertainty with the more points that you are certain of. As sample size increases, become more certain of the parameters that you are trying to estimate and the statistics that you can calculate. = 10 has high centre of t distribution and low tails. =3 has low centre of t distribution and high tails. Represents less certainty in middle with fewer degrees of freedom. T distribution is symmetric and similar to normal but with higher tails. If d. f. is large, e. g. n> 40, probabilities are almost the same as those for the standard normal distribution. Probability = 0. 025 in each tail (from t quantiles: rcmdr) Use rcmdr to calculate p from t-statistic and d. f.

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