Comparing two samples

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Worksheet with answersDownload PDF

What this lesson covers

  • Compare shift, overlap and spread on the box plots.
  • Intervals that do not overlap support a claim.
  • Overlapping intervals leave the question open.
Key idea

What to compare

  • Centre: how far apart are the medians?
  • Spread: is one group more variable?
  • Overlap: how much do the boxes overlap?
Worked example

Using the intervals

  • Two groups give these intervals for the median.
GroupMedianInterval
A6460 to 68
B7269 to 75
Worked example

Reading the result

  • The intervals do not overlap.
  1. A: 60 to 68
  2. B: 69 to 75
  3. B tends to be higher in the population

Common mistakes

  • Claiming B is always higher.
    Say B tends to be higher, because individuals vary.
  • Claiming no difference when intervals overlap.
    Overlap means there is not enough evidence to decide.

Your turn

  • 1. Intervals are 58 to 66 and 63 to 71. What can you say?
Show answer

1. They overlap, so we cannot claim a difference between the population medians

Summary

What to take away

  • No overlap supports a claim.
  • Overlap means we cannot tell.

More in AS 91264

Sampling and the enquiry cycleNotesBox plots and informal confidence intervalsNotesComparing two samplesNotesMaking and justifying an inferenceNotes

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