The following contingency table reflects a sample of people who live and hike in an area known to have ticks with high Lyme's disease concentration. What graphs would best represent this data? Select all that apply.

Diagnosed with Lyme's Not diagnosed with Lyme's
Known to have been bitten by tick 7 123
Not known to be bitten by tick 5 345

Question

The following contingency table reflects a sample of people who live and hike in an area known to have ticks with high Lyme's disease concentration. What graphs would best represent this data? Select all that apply.

Diagnosed with Lyme's	Not diagnosed with Lyme's
Known to have been bitten by tick	7	123
Not known to be bitten by tick	5	345

BlackTom AI · Accepted Answer

A mosaic plot visually encodes the joint distribution of two categorical variables, so it is well suited here.

1. Relevant knowledge points and concepts
- Contingency tables summarize counts for two categorical variables (here: tick-bite status and Lyme diagnosis).
- Mosaic plots represent each cell as a rectangle whose area is proportional to the cell count (or proportion), making patterns and associations immediately visible.
- Clustered (grouped) bar graphs place bars for the categories of one variable side-by-side within levels of the other variable, enabling direct comparison of category proportions or counts across groups.
- Other common displays (histograms, line charts) are for quantitative or ordered data and are not appropriate for two nominal categorical variables.

2. Step-by-step reasoning process
- Start from the 2×2 table:
  Known bitten: Diagnosed = 7, Not diagnosed = 123 (row total = 130)
  Not known bitten: Diagnosed = 5, Not diagnosed = 345 (row total = 350)
  Column totals: Diagnosed = 12, Not diagnosed = 468. Grand total = 480.
- A mosaic plot will show two vertical bands (or two horizontal bands depending on orientation): the widths reflect one margin (e.g., bite vs no bite: 130/480 and 350/480) and the heights within each band reflect the conditional proportions (e.g., 7/130 vs 123/130). This makes the small proportion diagnosed among each bite-status visually obvious.
- A clustered bar graph grouped by bite-status with two bars per group (Diagnosed and Not diagnosed) allows direct side-by-side comparison of the diagnosed proportions: Diagnosed proportion among bitten = 7/130 = 5.38%; among not bitten = 5/350 = 1.43%. The clustered bars make this difference easy to read.

3. Intermediate calculations shown
- Row totals: 130 and 350.
- Column totals: 12 and 468.
- Grand total: 480.
- Proportions: overall diagnosed 12/480 = 2.50%; bitten diagnosed 7/130 ≈ 5.38%; not bitten diagnosed 5/350 ≈ 1.43%.

4. Why the correct answers are correct
- Mosaic plot: directly represents joint counts/proportions via area — ideal for contingency tables.
- Clustered bar graph: clearly compares diagnosis categories within each bite-status group — straightforward and interpretable.

5. Why other graph types are incorrect or less appropriate
- Histograms and line charts: for continuous/ordered data, not categorical contingency relationships.
- Pie charts: poor for comparing multiple groups and cross-classified proportions; they don’t show the two-way association cleanly.
- Stacked bar could show the same information but is less effective than clustered bars for comparing the diagnosed category within each bite-status (stacked bars emphasize total rather than side-by-side category comparisons).

6. Conclusion
The best representations are a Mosaic plot and a Clustered bar graph, matching the provided answer: Mosaic plot and Clustered bar graph.

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