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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Course Content

Learning Statistics with Python

1. Basic Concepts

Sample vs Population Types of Statistics Types of Data Mean Value Median Value Median Value of the Even Number of Values Mean or Median Mode Value Descriptive Statistics Quiz

2. Mean, Median and Mode with Python

Examine the Dataset Calculating Mean and Median Values with Python Statistics with pandas Calculate the Mean and Median Salary

3. Variance and Standard Deviation

Population Variance Sample Variance Calculate Variance with Python Standard Deviation Standard Deviation with Python Calculating Variance and Standard Deviation

4. Covariance vs Correlation

Covariance Correlation Covariance and Correlation Quiz Calculate Covariance and Correlation

5. Confidence Interval

6. Statistical Testing

What is t-test Hypotheses t-test Mathematically One-Tailed And Two-Tailed Test t-test Assumptions Performing a t-test in Python Conduct a t-test Paired t-test