Treating incoming lots as populations, and sampling from them as though they are populations, assumes that each lot is an individual universe. ]]>

1. What makes the example in Figure 2 with 5,000 beads a universe?

2. Can you provide a real example of a known universe or tell me whether Deming’s example of a customer enumerating the percent defective of a lot he has purchased is a known universe?

Thank you.

]]>And what would be the universe for each situation (all or some of the data on the process behavior chart)?

]]>The editor removed the example for the fourth question, making the article more obscure.

The operational definition of homogeneity is a process behavior chart (a control chart).

When we place data on a process behavior chart we place two values in the same subgroup based on a judgment that those two values were obtained under essentially the same conditions.

When we place values on an X chart we have to use values that are logically comparable.

Both of these judgments use the context for the data as the basis for organizing the data.

Once we have a rational organization, any signals on the chart will be evidence of a lack of homogeneity.

It does not matter whether we are plotting all of the data generated by a process or only some of those data. As long as the organization of the data respects the structures within those data, the process behavior chart will work.

But I am probably misunderstanding the fourth: “Given a collection of observations, is it reasonable to assume that they came from one universe, or do they show evidence of having come from multiple universes, processes or populations?” ?

Would you help me understand it?

The answer starts with: “Descriptive statistics, probability models, and statistical inference all rely on homogeneity. An average is meaningless when the data comes from different universes.”

1. Is your definition of data homogeneity simply that data come from a single universe?

2. What is your definition of a universe (in terms that do not refer to homogeneity to avoid circularity)?

3. Would you provide an example of universes by stating the universe in the two cases below assuming the data show homogeneity through a control chart displaying stability:

a. all production output is displayed on the control chart

b. a sample of 25 (appropriate) rationale subgroups from the much larger production are displayed on the control chart?

Thank you for your help.

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