Calculate confidence Intervals using the t Distribution
This approach is used to calculate confidence Intervals for the small dataset where the n<=30 and for this, the user needs to call the t.interval() function from the scipy.stats library to get the confidence interval for a population means of the given dataset in python.
Syntax: st.t.interval(alpha, length, loc, scale))
Parameters:
- alpha: Probability that an RV will be drawn from the returned range.
- length: Length of the data set
- loc: location parameter
- scale: scale parameter
Example 1:
In this example, we will be using the data set of size(n=20) and will be calculating the 90% confidence Intervals using the t Distribution using the t.interval() function and passing the alpha parameter to 0.90 in the python.
Python
import numpy as np import scipy.stats as st # define sample data gfg_data = [1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 5, 5, 5, 6, 7, 8, 10] # create 90% confidence interval st.t.interval(alpha=0.90, df=len(gfg_data)-1, loc=np.mean(gfg_data), scale=st.sem(gfg_data)) |
Output:
(2.962098014195961, 4.837901985804038)
Example 2:
In this example, we will be using the data set of size(n=20) and will be calculating the 90% confidence Intervals using the t Distribution using the t.interval() function and passing the alpha parameter to 0.99 in the python.
Python
import numpy as np import scipy.stats as st # define sample data gfg_data = [1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 5, 5, 5, 6, 7, 8, 10] # create 99% confidence interval st.t.interval(alpha=0.99, df=len(gfg_data)-1, loc=np.mean(gfg_data), scale=st.sem(gfg_data)) |
Output:
(2.3481954013214263, 5.4518045986785735)
Interpretation from example 1 and example 2:
In the case of example 1, the calculated confident mean interval of the population with 90% is (2.96-4.83), and in example 2 when calculated the confident mean interval of the population with 99% is (2.34-5.45), it can be interpreted that the example 2 confident interval is wider than the example 1 confident interval with the 95% of the population, which means that there are 99% chances the confidence interval of [2.34, 5.45] contains the true population mean
How to Calculate Confidence Intervals in Python?
In this article, we will be looking at the different ways to calculate confidence intervals using various distributions in the Python programming language. Confidence interval for a mean is a range of values that is likely to contain a population mean with a certain level of confidence.
Formula:
Confidence Interval = x(+/-)t*(s/√n)
- x: sample mean
- t: t-value that corresponds to the confidence level
- s: sample standard deviation
- n: sample size