How to use confidence intervals

· Category: Data Science

Short answer

A confidence interval provides a range of plausible values for an unknown population parameter, reflecting the uncertainty inherent in sample estimates.

Steps

  1. Compute the sample estimate such as a mean or proportion.
  2. Determine the standard error of the estimate based on sample variability and size.
  3. Choose a confidence level such as 95 percent and find the corresponding critical value.
  4. Multiply the critical value by the standard error to obtain the margin of error.
  5. Add and subtract the margin of error from the estimate to form the interval.

Tips

  • Wider intervals indicate more uncertainty; larger samples yield narrower intervals.
  • Interpret a 95 percent interval as the range capturing the true parameter in 95 percent of repeated samples.
  • Use bootstrap confidence intervals when theoretical distributions are complex.
  • Display intervals graphically to compare estimates across groups.

Common issues

  • Interpreting the interval as the probability that the parameter lies within it.
  • Computing intervals based on biased point estimates.
  • Ignoring finite population correction when sampling a large fraction of the population.
  • Using normal approximations for small samples or rare events.

Example

import pandas as pd
import numpy as np

df = pd.DataFrame({'sales': [100, 150, 200, np.nan]})
df['sales'] = df['sales'].fillna(df['sales'].median())
print(df.describe())

This snippet creates a DataFrame, handles a missing value with the median, and prints summary statistics common in exploratory analysis.