Learn Advanced Confidence Interval Calculation with Python

If working with a small distribution (size ≤ 30) that approximates the normal distribution, use t-statistics.

How to calculate the confidence interval?

st.t.interval(0.95, len(data) - 1, loc=data.mean(), scale=st.sem(data))

The t.interval() function from scipy.stats is used for the Student's T distribution.
0.95 represents the confidence level (also known as the alpha parameter).
len(data) - 1 is the degrees of freedom (df), which is the sample size minus one.
loc represents the mean of the sample data.
sem represents the standard error of the mean.

Degrees of Freedom

Degrees of freedom refer to the number of independent information elements used to estimate a parameter.

The formula for degrees of freedom is N - 1, where N is the sample size.

You can modify the alpha parameter to observe how it affects the confidence interval.


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import scipy.stats as st
import numpy as np

data = [104, 106, 106, 107, 107, 107, 108, 108, 108, 108, 108, 109, 109, 109, 110, 110, 111, 111, 112]
# Calculate the confidence interval
confidence = st.t.interval(0.95,
                           len(data)-1,
                           loc = np.mean(data),
                           scale = st.sem(data))

print(confidence)

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Section 5. Chapter 6

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