Lære Confidence Intervals

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Confidence intervals are a fundamental concept in statistics that help you understand the range within which a population parameter, such as the mean, is likely to fall. When you collect a sample and calculate its mean, you are estimating the true mean of the entire population. However, because different samples can yield different results, it is important to quantify the uncertainty around your estimate. This is where confidence intervals come in.

A confidence interval gives you a range of plausible values for the population parameter based on your sample data. The most common confidence level is 95%, which means that if you were to repeat the sampling process many times, about 95% of those intervals would contain the true population mean.

To calculate a confidence interval for the mean using Python, you typically follow these steps:

Collect your sample data and calculate the sample mean and standard error;
Choose a confidence level (such as 95%) and find the corresponding critical value from the appropriate distribution (z or t);
Compute the margin of error by multiplying the critical value by the standard error;
Construct the confidence interval by adding and subtracting the margin of error from the sample mean.

The scipy.stats library provides convenient functions to help you calculate confidence intervals, especially when working with sample data and assuming a normal (or approximately normal) distribution. When the population standard deviation is unknown and the sample size is small, you use the t-distribution. For larger samples or when the population standard deviation is known, the normal distribution (z) can be used.

Interpreting a confidence interval is just as important as calculating it. A 95% confidence interval for the mean does not mean there is a 95% chance that the true mean falls within the interval. Instead, it means that if you repeated the sampling process many times, 95% of the resulting intervals would contain the true mean.

Understanding confidence intervals allows you to make informed decisions based on data, recognizing the uncertainty inherent in any estimate.


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import numpy as np
from scipy import stats

# Sample data: heights of a group of people in centimeters
data = np.array([172, 168, 181, 175, 169, 170, 174, 177, 173, 176])

# Calculate sample mean and standard error
sample_mean = np.mean(data)
sample_std = np.std(data, ddof=1)
sample_size = len(data)
standard_error = sample_std / np.sqrt(sample_size)

# Set confidence level
confidence = 0.95

# Find the t-critical value for two-tailed interval
t_critical = stats.t.ppf((1 + confidence) / 2, df=sample_size - 1)

# Calculate the margin of error
margin_of_error = t_critical * standard_error

# Compute confidence interval
lower_bound = sample_mean - margin_of_error
upper_bound = sample_mean + margin_of_error

print(f"Sample mean: {sample_mean:.2f} cm")
print(f"95% confidence interval: ({lower_bound:.2f} cm, {upper_bound:.2f} cm)")

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Calculate the 95% confidence interval for the mean of a given dataset in the global scope.

Calculate the sample standard deviation (ensure you set ddof=1 for a sample).
Compute the standard error of the mean utilizing np.sqrt().
Use the t-distribution (stats.t.ppf) to find the critical value for a 95% confidence level. The degrees of freedom (df) should be the sample size minus one.
Calculate the lower and upper bounds of the confidence interval.
Assign the final bounds as a tuple to the interval variable.

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