Our Normality: Tested and Explained
anderson-darling black belt data transformation hypothesis testing lean six sigma normal distribution normality test p-value process engineer process management six-sigma statistics the normal distribution curve
Almost all natural data on planet earth is normally distributed and most manufacturing process data is normally distributed too. What does this mean? Well, it simply means that the majority of statistical data tends to be concentrated at some center point and we find less and less data points as we move away from center.
Knowing if a data set is normally distributed is important because when it is normally distributed, we can easily test hypothesis and draw statistical conclusions. In the realm of manufacturing six-sigma, it means that you can improve your process by using various six-sigma tools such as T-tests, F-tests, ANOVA’s and Process Capability Studies without having to transform the data..
To be certain that your data is normally distributed, a statistical normality test should be conducted. Note that you want to check the normality of the data early-on in your project such that you can draw accurate statistical conclusions. The test to validate normality is called the Anderson-Darling Normality Test. You can find this test on-line using the R-Project.org or by using Minitab or Excel statistical software packages.
The key output of the Anderson-Darling Test is a P-value and if the P-value is greater than 0.05, then you can assume with 95% confidence that your data is normally distributed. When your data is normal, then you can confidently move forward with your six-sigma project.
If you conduct the normality test and find that your data is not normally distributed, then you need to determine why it is not a normal distribution. A good starting point is to look at the histogram of your data. What does it look like? Do you see uniform distribution? Or a bimodal distribution? Or a distribution that looks like half a bell curve? Or is it skewed or distorted? Histogram shapes that don't look like a bell curve could result in a low P-Value and hence fail the normality test.
After you look at the histogram, consider if the distribution shape makes logical sense. If you can’t explain it, then your population data may actually be normally distributed, In which case, you'll need to do some exploration to determine if you have a root-cause that is corrupting your data. For example, maybe you are simply lacking data points. If so, then go collect more samples. Or maybe you have machine operators who are running the process differently from each other and this is causing a bimodal distribution. Or possibly lab technicians are testing the samples differently. In these cases, you want to standardize the operating and testing procedures.
So if your data fails the normality test, always ask yourself; does it make sense? Should your data be normal with concentrated data around a center point and less data points further away from center? If logically speaking, your data should be normal, but it’s not, then dig deeper to solve your data problem.
If your data actually does represent a non-normal distribution, then it can be transformed into a useful format. However, this data transformation process requires statistical expertise. If you are not an expert, then buy your company’s black belt a cup of coffee and pick their brain to learn more about it. (Note that if your data is flawed and you transform it then you are compounding an error, and you will draw false conclusions in your project.)
Summary:
- Collect your data.
- Run the Anderson Darling Normality Test.
- If not normal, troubleshoot your data and transform it if necessary.
- If normal then move forward with your project.
A six-sigma process yields happy customers and high profits!
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.
CATEGORIES
All Categories 5 whys 5s 5s standardize 5s sustain 6m's ability accomplishment accomplishments accountability accuracy action action plans actions ada addiction addiction help admiration adverserial aerospace affordable agenda agriculture alcohol alcoholism amazon american disabilities act anderson-darling appreciation approachability approval art artisan assembly assembly line assessment assignments attention to details attribute gage r&r auto industry auto manufacturing auto production automobile manufacturing average avoidance best practices big bend black belt boss boulder city bourbon trail budget business business case business model business proposals candidate experience candidates capability capability study cape fear capital career cargo cash flow cell design cememt central limit theorem central tendancy ceo certification certification training challenges change change management changeover reduction chaos chemical child labor ci cnc cnc programming cogs communication communitiy company compassion compitition concrete conducting interviews conflict conflict management consistency constraints construction consumption continuous improvement corrective action correlation analysis cost savings costs course cp cp and cpk cpk cross-functional cross-training cross-training matrix crude culture current state current state map customer customer satisfaction customer service customer value customers cv daily goals dallas dam dashboard data data collection data transformation debt-free decision maker defects deliverables demand department design design of experiment design review design reviews develop development dfm diet difficulties direct labor discussion discussions diversity documentation doe drilling driving results drug use duluth dumping e learn e-learning eap ebit education effective effectiveness effectivity effects of change efficiency effort email empathy empirical rule employee employee assistance program employee development employee engagement employee recgonition employees encourage encouragement enforcement engagement engineer engineering equipment error proof excellence exercise expectations expertise experts facilitate facilitator factories factory family life farming feedback financial financials fishing fixed mindset flexibility flexible follow-up foolproof ford forecast fossil fuels fred jones freightliners friendships frontline leaders fun gage r&r gages gasoline gemba general motors goal alignment goals gold rush good conflict graphs great lakes great teams gross margins gross profits growth growth mindset guidance habits health healthy heavy equipment henry ford heritage hiring histogram history hoover dam housekeeping how to be a great teammate how to thrill customer human relations human resources hydro-electric hydro-electric power hypothesis testing ice breaker illinios river valley illinois illinois river immersion importing improve improvement industiral industrial industrial engineering industrial heritage industrial heritgage industrial history industry industry 4.0 inequity injury prevention innovation inspection instructions integrity internal promotion interview questions interview skills interview tips interviewing inventory investment iowa irresponsible jack daniels distillery tour job diversity job shop job shops jobs john deere kaizen kanban kappa kentucky knowledge lead leader leaders leadership leadership development leadership skills leading lean lean champion lean culture lean implementation lean journey lean kickoff lean launch lean manufacturing lean pilot project lean six sigma lean strategy lean tools lean vision learn learning leisure letter of commendation lifestyle logging logistics louisiana low prices lumber machine guarding machine speed machines maintenance making a pitch management management by walking around manager managers managing managing conflict managing the floor manpower manufactuing manufacturing manufacturing leaders manufacturing leadership manufacturing plants manufacturing results manufacturing supervisor manufacturing supervisor leadership manufacturing traning mardi gras marfa material mbwa mean measurement meditation meeting meetings mental health mental tension mentee mentor mentoring mentorship methods metrics midland milestones milk run mindset minnesota mississippi river model-t morale mother nature motivation muda multivariant analysis museum national park nature new hires new orleans new products night shift nimble business normal distribution normality test north carolina objectives office oil ojt okc oklahoma on line courses on time delivery on-site factories on-time delivery onboarding one-on-one online open-door operational excellence operator operators opex ore organization otd output overhead ownership p&l p-value packaging packaging material partner partnering partnership partnerships pdca pdca cycle peers performance performance management performance patterns performance review performance reviews perimian basis personal accountability personal growth personal grwoth personality petroleum pharmaceuticals pikes place pitch plan planner planning plant plant costs plastics point of use poka yoke poka-yoke policy port portland cement positive feedback positive interactions pou power plant pp ppk praise predictive maintenance presentation presentation anxiety presentations preventative maintenance prices prime costs principles printing private label problem solving problem statement problems procedure procedures process process capability process center process controls process engineer process management process variation product development product testing production production flow production supervisor productive conflict productivity products professionalism profit profits profressional development progress project project assumptions project charter project justification project management project objectives project timing projections projects promoted props provide qualifies quality quality control quality tool quick changeover r&d range rapid changeover recognition recognize recruiting recycling red tag referals refinery relationship reliability reputation resolving conflict resources respect responsibility responsible restore results resume resume screening resumes revenue rewards rigs risk management roi rolling-5 rolling-5 action plans root cause roots routine safety safety incentives sales sales tips sales volume salesperson sampling science scope screening screening applicants sculptures seattle self-promotion selling service set in order set up times set-in-order set-up reduction shadow board shadowing share shareholder shine shipbuilding shipping shopfloor single minute of exchange of die single-piece six-sigma skill development skills sleep slideshow smart goals sme smed social life solutions sort specifications specs speed to market staffing staffing model standard cost standard deviation standardize starved rock state-of-the-art statistics stats staycation steamship steel steel fabrication steel industry strategy stress stress management strong leader structure success sugar mill supervision supervisor supervisor development supervisor leadership supervisors supervsior supplier supply chain support support resources sustain systems t-test tactical takt tariffs teach teaching team team work team-based teammate teams teamwork technical tennesse whiskey tennessee texas the great depression the hoover dam the normal distribution curve timber time management time-series tools tourism toyota production system tpm tps training training methods travel troubleshooting trust turn around two sample t-test types of change understanding us manufacturing vacation validation value value stream value stream map value-driven values variance variances variation velocity vendor managed inventory video violations visual factory vmi voc volunteering vsm war on waste washington waste waste reduction waterway wellbeing wilmington nc work instructions work rules workforce workplace workplace conflict