Question

If anyone can "dumb this down for me I'd appreciate it. I'm really not good with statistics, I'm easily confused by all the terms and symbols so if someone is willing to explain a basic easy to understand example that would be much appreciated- What types of misconceptions and errors do your foresee occurring in a business setting if the normal distribution assumptions are not applied correctly? Please include a real-world business example in your response.

Answer 1

Misconception 1:
Something is “wrong” if the distribution is non-normal.

Often, distributions other than the normal are more appropriate for a given
set of data. In particular, when a naturally occurring boundary exists (e.g., zero,
with cycle time data), the assumption of normality may not be sensible because
the normal distribution has positive probability throughout the entire real number
line (i.e., from negative to positive infinity).
Some Six Sigma practitioners are encouraged to discover why the data are
nonnormal and to continue to look for explanations until normality is obtained.
This may be poor advice and frustrate the investigator because, despite best
efforts, the assumption of normality frequently cannot (reasonably) be obtained.
The misunderstanding may be due to an unwarranted inference from the
name of the distribution itself. Six Sigma practitioners, especially those new to
statistical theory, may believe that it is “normal” to see such a distribution in
practice. Though the normal distribution may be a reasonable assumption for
many processes, it is not reasonable for all processes.
Furthermore, practitioners are occasionally led to believe that an approximately
normal distribution implies that a process is in statistical control. Again, the
inference is not valid through control charting a practitioner can assess the
stability of a process.