Which Test, When? A Simple Guide to Picking the Right Statistics Tool for Six Sigma

Statistical questions on exams often feel like riddles because they dress a simple decision in formal language. The fastest way to stop guessing is to translate the prompt into one clear question, then pick the smallest, most direct test that answers it.

Translate the prompt into plain English first

When you see a question, underline these three things: the variable type (mean, proportion, variance), the number of groups (one, two, many), and the relationship scope (compare or relate). Translate those into a one-line instruction: “compare averages of two groups” or “compare proportions across groups” or “measure association between two numeric variables.” That one-line translation almost always points directly to the right test.

A compact decision map you can memorize

One numeric variable, compare to a target: single-sample test (is the average different from X?)

Two numeric groups, compare averages: two-sample t-test (paired if same subjects before/after)

More than two groups, compare averages: ANOVA (then post-hoc where necessary)

Comparing proportions (%): chi-square or two-proportion test

Relationship between two numeric variables: correlation/regression

Checking variability or spread: variance tests or simple capability metrics

Practical short-cuts that save time on test day

Numbers vs percentages: if the question is about percent defective or proportion, think proportions, not t-tests.

Paired vs independent: if the same units are measured twice (before/after), it’s paired. If samples are different groups, it’s independent.

Many groups: if the question mentions three or more treatments/groups, reach for ANOVA logic rather than multiple t-tests.

How to practice this so it sticks

Translation drill: read a question, write the one-line translation, then state the test, no calculation. Repeat 20 times.

Application drill: pick 5 questions and run the actual calculation or interpretation; review only those where your translation was wrong.

Five short translation practice items (reply with your 1-line translations; I’ll tell you if they’re correct)

-Did the new process reduce average cycle time?

-Did the proportion of defective units change after the process change?

-Are the average scores different across three training groups?

-Is there a relationship between hours studied and exam score?

-Has the variance in processing time increased after a change?

Reply with your one-line translation for any of the items above (e.g., "compare averages of two groups") and I’ll tell you whether that translation points to the right test.

Two tiny examples (translate, then test)

1) “Did the new process reduce average cycle time?” → translate: compare two averages → two-sample test (or paired if same lines before/after).

2) “Did the proportion of defective units change after the change?” → translate: compare two proportions → two-proportion test or chi-square.

One way to reduce second-guessing under time pressure

Give yourself one extra step during practice: before you touch a calculator, write the translation in 7 words or fewer. This habit prevents wasted time on the wrong calculation and is the single most efficient way to reduce errors.

Best, Ted

P.S. If you’d like to practice, reply with one of the five items above and your one-line translation; I’ll tell you whether you picked the right test.

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