Confidence intervals, t tests, P values
[Pages:42]Confidence intervals, t tests, P values
Joe Felsenstein Department of Genome Sciences and Department of Biology
Confidence intervals, t tests, P values ? p.1/31
Normality
Everybody believes in the normal approximation, the experimenters
because they think it is a mathematical theorem, the mathematicians
because they think it is an experimental fact!
G. Lippman
We can use the Gaussian (normal) distribution, assumed correct, and estimate the mean (which is the expectation). It turns out that, not surprisingly, the best estimate of the mean is the mean of the sample.
Confidence intervals, t tests, P values ? p.2/31
Normality
Everybody believes in the normal approximation, the experimenters
because they think it is a mathematical theorem, the mathematicians
because they think it is an experimental fact!
G. Lippman
We can use the Gaussian (normal) distribution, assumed correct, and estimate the mean (which is the expectation). It turns out that, not surprisingly, the best estimate of the mean is the mean of the sample.
(The median of the sample is a legitimate estimate too, but it is noisier).
Confidence intervals, t tests, P values ? p.2/31
Normality
Everybody believes in the normal approximation, the experimenters
because they think it is a mathematical theorem, the mathematicians
because they think it is an experimental fact!
G. Lippman
We can use the Gaussian (normal) distribution, assumed correct, and estimate the mean (which is the expectation). It turns out that, not surprisingly, the best estimate of the mean is the mean of the sample.
(The median of the sample is a legitimate estimate too, but it is noisier).
The sample mean is the optimal estimate as it is the Maximum Likelihood Estimate ? for which see later in the course.
Confidence intervals, t tests, P values ? p.2/31
Normality
Everybody believes in the normal approximation, the experimenters
because they think it is a mathematical theorem, the mathematicians
because they think it is an experimental fact!
G. Lippman
We can use the Gaussian (normal) distribution, assumed correct, and estimate the mean (which is the expectation). It turns out that, not surprisingly, the best estimate of the mean is the mean of the sample.
(The median of the sample is a legitimate estimate too, but it is noisier).
The sample mean is the optimal estimate as it is the Maximum Likelihood Estimate ? for which see later in the course. But how do we figure out how noisy the estimate is?
Confidence intervals, t tests, P values ? p.2/31
Normality
Everybody believes in the normal approximation, the experimenters
because they think it is a mathematical theorem, the mathematicians
because they think it is an experimental fact!
G. Lippman
We can use the Gaussian (normal) distribution, assumed correct, and estimate the mean (which is the expectation). It turns out that, not surprisingly, the best estimate of the mean is the mean of the sample.
(The median of the sample is a legitimate estimate too, but it is noisier).
The sample mean is the optimal estimate as it is the Maximum Likelihood Estimate ? for which see later in the course. But how do we figure out how noisy the estimate is?
Can we make an interval estimate?
Confidence intervals, t tests, P values ? p.2/31
A normal distribution (artist's conception)
how often
the true mean (expectation) true distribution
the measurement
Confidence intervals, t tests, P values ? p.3/31
Uncertainty of the mean
Let's go forward (distribution to data).
Confidence intervals, t tests, P values ? p.4/31
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