Understanding Student’s t-distribution

Last Updated on 13 September 2023

In the realm of Six Sigma, analyzing data is key to identifying process variations and making improvements. Student’s t-distribution, often referred to as t-distribution, is a probability distribution used to estimate the mean of a population when the sample size is small, and the population standard deviation is unknown. Developed by William Sealy Gosset, who published under the pseudonym “Student”, the t-distribution aids us in hypothesis testing and calculating confidence intervals.

Why is it important for Six Sigma?

In the world of Six Sigma, we often deal with real-world data that may not always be readily available or large enough. The t-distribution comes into play when sample sizes are small (less than 30) and the population standard deviation is unknown.

In these scenarios, a normal (Z) distribution would lead to inaccurate results in hypothesis testing and confidence intervals. The t-distribution, being more flexible and adaptable to small sample sizes, bridges this gap and ensures accurate decision-making based on the available data.

How to use the t-distribution?

Now that we understand the importance of the t-distribution, let’s see how to apply it step-by-step:

1. Formulate Hypotheses: Develop null (H0) and alternate (H1) hypotheses regarding the population mean.
2. Calculate t-score: Use the following formula to compute the t-score:t = (Sample Mean – Population Mean) / (Sample Standard Deviation / sqrt(sample size))
3. Determine Degrees of Freedom (DF): DF refers to the number of independent values in the data set. It is calculated as: DF = Sample size – 1
4. Look up t-value: Use a t-table or statistical software to find the critical t-value corresponding to the specified confidence level and DF.
5. Compare t-scores: Compare the calculated t-score to the critical t-value. If the t-score is greater than the critical t-value, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.