Comparing Groups

Learn comparing centers, comparing variability.

Lesson 3 of 32 parts Practice Flashcards

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Comparing Centers

Objective: Explain comparing centers, apply the stated method, and check its conditions.

Compare the same center measure in common units across groups. A mean difference describes location, not individual overlap or causality. Distribution shape, spread, sample size, and study design matter before drawing broader conclusions from the difference. A center difference alone does not describe overlap or establish causation.

Formulas

Difference of means = x̄A−x̄B

Worked examples

Try itGroup A has mean 13; Group B has mean 7. Find A’s mean minus B’s mean.Show answer

Step 1: Compare the same summary measure and units. Step 2: Compute (13)−7. Step 3: The difference is 6; equal or different centers alone do not describe spread.

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Comparing Centers

Objective: Explain comparing centers, apply the stated method, and check its conditions.

Formulas

Difference of means = x̄A−x̄B

Worked examples

Try itGroup A has mean 13; Group B has mean 7. Find A’s mean minus B’s mean.Show answer

Step 1: Compare the same summary measure and units. Step 2: Compute (13)−7. Step 3: The difference is 6; equal or different centers alone do not describe spread.

Comparing Variability

Objective: Explain comparing variability, apply the stated method, and check its conditions.

Compare the same spread measure in common units and with a defined ratio direction. An IQR ratio compares middle-half width, not total range or SD. Equal centers can coexist with substantially different variability; center and spread should be reported together. Do not substitute a range for an IQR in a same-measure comparison.

Formulas

Spread ratio = IQR(A)/IQR(B)

Worked examples

Try itGroup A has IQR=42; Group B has IQR=7. Find the ratio IQR(A)/IQR(B).Show answer

Step 1: Use matching spread measures. Step 2: Compute (42)/7. Step 3: The ratio is 6; Group A’s middle half is wider.

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