Section 8.5 Standard Error
To quantify the width of the sampling distribution, one option is to compute its standard deviation -- the result is called the standard error.
$ standard_error = np.std(sample_means)
standard_error
np.float64(0.04626531069684985)
In this case, the standard error is about 0.045 kg -- so if we collect many samples, we expect the sample means to vary by about 0.045 kg, on average.
People often confuse standard error and standard deviation. Remember:
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Standard deviation quantifies variation in measurements.
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Standard error quantifies the precision of an estimate.
In this dataset, the standard deviation of penguin weights is about 0.38 kg for chinstrap penguins.
$ np.std(weights)
np.float64(0.3814986213564681)
The standard error of the average weight is about 0.046 kg.
$ np.std(sample_means)
np.float64(0.04626531069684985)
Standard deviation tells you how much penguins differ in weight. Standard error tells you how precise an estimate is. They are answers to different questions.
However, there is a relationship between them. If we know the standard deviation and sample size, we can approximate the standard error of the means like this:
def approximate_standard_error(sample):
n = len(sample)
return np.std(sample) / np.sqrt(n)
$ approximate_standard_error(weights)
np.float64(0.046263503290595163)
This result is close to what we got by resampling.
