The T-test & Tennis Balls
How to Use the Two Sample T-Test
Product manufacturing provides endless improvement opportunities. I thrived in my manufacturing career by aggressively pursuing operational improvements. I’m sure that you too are always working on a wide array of factory opportunities. These projects will range from quality improvements, cost reductions, process improvements, lean, six-sigma and product enhancement projects.
As Nike says, “Just Do It!” – right? Well, it’s not always so easy with manufacturing projects. In manufacturing, there is always a risk associated with any change because any change has the potential to adversely affect the products that you produce. A wise project manager will systemically, methodically and cautiously advance their project through to completion. They know that even when a project appears to be a slam-dunk, things can backfire and thus unfavorably impact products and customers. Sloppy project implementation can lead to a giant snowball of customer complaints.
How can you protect your product and ensure that your projects won’t inadvertently and unfavorably impact your customers? It’s easy, just use a two sample t-test when making any process, equipment or material changes. A t-test is a statistical tool that allows you to compare before and after samples of your product in order to ensure that changes won’t cause a degradation to product quality. In other words, a two sample t-test proactively confirms that a project’s implementation will not inadvertently degrade a product’s form, fit or function.
How does a two sample t-test work? Well, it starts by collecting baseline product samples from your process. Say that you found a lower cost supplier of a certain raw material that is used in your product. If you convert to this new raw material, your company will save millions of dollars. One of your initial steps is to then identify what quality characteristics this material change could affect and then start gathering test samples and data for evaluation.
For example, if your company makes tennis balls and you’re considering changing from natural rubber to synthetic rubber as the main component in the design, then you may be concerned that the tennis balls with the synthetic rubber won’t bounce the same as the tennis balls made with the natural rubber. Your plan would then be to measure any potential tennis ball performance differences between the two materials.
The standard performance test requires that the tennis ball samples be dropped from a height of 100 inches onto a concrete floor and then the bounce height measured with all measurements taken from the bottom of the ball at its peak height. Below describes the steps required as to how you can compare the two material factors head-to-head and determine whether or not the rubber compound affects bounce performance.
HOW TO USE THE TWO SAMPLE T-TEST
STEP 1: In our tennis ball example, you will want to take a 30-piece random sample from your standard tennis ball (the design with natural rubber).
STEP 2: Implement the new synthetic rubber on a trial run. This trial should represent a limited production run and the product should not be sold to customers. Collect 30 random samples from this trial run.
STEP 3: Conduct the bounce test on both sets of 30 samples and collect the data.
STEP 4: Enter the data into statistical software such as Minitab or a free online program such as R-Project
STEP 5: Run the Two Sample T-test to calculate the p-value of your study.
STEP 6: Interrupt your results. To keep things simple, consider this; if your p-value is less than 0.05, then you would say that the synthetic rubber is statistically different that the natural rubber when it comes to tennis ball bounce. If the p-value is greater than 0.05, then you could conclude that the two samples come from the same population of tennis balls, thus the rubber change isn’t creating a significant difference in bounce performance. In other words, the two sets of sample data are represented as two separate normal distribution curves, however both sample-set curves may or may not represent the exact same population distribution.
But how can you tell if the sample data represents the same population or not? Well, you can tell by the separation distance between the two sample curves. If the two sets of sample data are “too far apart” from each other, then the data sets represent two different populations. If the sample data sets are not too far apart from each other, then they are considered part of the same population. In statistical analysis, we use a 0.05 p-value (+/-) to determine if sample data represent the same or different populations.
I like to think of the two sample t-test like an amoeba. The amoeba may change shapes and become flatter or wider and even appear to be splitting into two forms, but it isn’t until the amoeba actually splits into two when we can confirm that yes, there are now two two single-celled organisms instead of just one. It is similar with sample data. Two sets of samples may appear to be different, but it isn’t until the p-value of a two sample t-test drops below 0.05 before we can say that yes, we have two separate populations instead of just one population. In our tennis ball example, it would mean that the tennis balls that are made with the synthetic rubber are statistically different and are not considered as a direct replacement for the natural rubber tennis balls.
The two sample t-test is a great tool for process engineers and project managers alike. It is the first quality indicator as to whether a project has the potential for success or not. Later in the project of course, short-term, and long-term process capability studies should be performed within the framework of a robust product validation process. These validations are longer term and more costly than a t-test. That is why I always recommend that a two-sample t-test be performed early-on in a project. It is a low cost means that yields directionally valid results.
Contact me through Tools for the Trenches if you would like more information about the two sample t-Test and its usefulness in manufacturing.
Stay connected with news and updates!
If you want some weekly T4T wisdom coming straight to your inbox for your reading pleasure - look no further! Join our mailing list to receive the latest blogs and updates.
Don't worry, your information will not be shared.
We hate SPAM. We will never sell your information, for any reason.
