Comparative Statistics Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Compare two groups on a test: Group A (n=30n=30): mean=75, SD=10. Group B (n=30n=30): mean=82, SD=8. Calculate the difference in means and comment on whether group B performs better.

Solution

  1. 1
    Difference in means: xห‰Bโˆ’xห‰A=82โˆ’75=7\bar{x}_B - \bar{x}_A = 82 - 75 = 7 points
  2. 2
    Group B's mean is 7 points higher
  3. 3
    But consider variability: SD_A=10 and SD_B=8; the groups overlap substantially
  4. 4
    Cohen's d (effect size): d=7(102+82)/2=782โ‰ˆ79.06โ‰ˆ0.77d = \frac{7}{\sqrt{(10^2+8^2)/2}} = \frac{7}{\sqrt{82}} \approx \frac{7}{9.06} \approx 0.77 โ€” medium-large effect

Answer

Group B scores 7 points higher on average with Cohen's d โ‰ˆ 0.77 (medium-large effect).
Comparing groups requires reporting both the difference in centers and the effect size (like Cohen's d). A 7-point difference might be meaningful or trivial depending on the variability. Effect size standardizes the difference for meaningful interpretation.

About Comparative Statistics

Comparative statistics involves using statistical measures to compare two or more groups, data sets, or distributions.

Learn more about Comparative Statistics โ†’

More Comparative Statistics Examples

Example 2 medium

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Example 3 easy

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Example 4 hard

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