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Learning Statistics with Python

bookAdvanced 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.


              
1234567891011

            
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)
copy
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SectionΒ 5. ChapterΒ 6

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bookAdvanced Confidence Interval Calculation with Python

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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.


              
1234567891011

            
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)
copy
Everything was clear?

How can we improve it?

Thanks for your feedback!

SectionΒ 5. ChapterΒ 6
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