Scoring
This question is scored in three sections. Section 1 consists of part (a), section 2 consists of part (b-i), and section 3 consists of part (b-ii). Each section is scored as essentially correct (E), partially correct (P), or incorrect (I).
Section 1 is scored as follows:
Essentially correct (E) if the response includes the following three components:
1. Recognition that the medians or centers are almost the same for the three sites
2. Recognition that the variability (ranges, IQRs, spread) is different across the three sites
3. Context is included
Partially correct (P) if the response includes only two of the three components.
Incorrect (I) if the response includes at most one of the three components.
Notes:
- In all sections, comments about shape should be ignored because complete shape information is not obtainable from boxplots.
- Responses are not required to give numerical values. If responses provide numerical values, any reasonable approximation from the boxplots is acceptable.
- Because the boxplots are all symmetric, it is acceptable if the response discusses means instead of medians.
- Any discussion of chemical X and chemical Y is considered extraneous.
- Context is satisfied by any of the following references: site, chemical, weight, total weight, X, Y, or Z.
Section 2 is scored as follows:
Essentially correct (E) if the response includes the following three components:
1. Site III is chosen.
2. Sums of the minimum and maximum are computed for the three chemicals at each site.
3. A reasonable numerical justification is given involving sums of a statistical measure across the three chemicals to choose Site III.
Partially correct (P) if the response includes only two of the three components.
Incorrect (I) if the response includes at most one of the three components.
Notes:
- If the response computes only the sum of the minimums for Site I and the sum of the maximums for Site II and recognizes that this is sufficient, the response is scored E.
- If an alternative measure is used that involves sums of the three chemicals, such as the sum of the medians or the sums of the first quartiles and sums of the third quartiles, instead of the minimum and maximum sums, the second component is not satisfied, but the third component might be satisfied.
○ If the response explicitly or implicitly compares the alternate sum to the other two sites (for example, by indicating that the sum is the closest to 20.5 percent or by listing the sums for all three sites) the response is scored P.
○ If the response does not have an implicit or explicit comparison, the response is scored I.
- If either Site I or Site II is identified as the correct choice, no matter how that choice is justified, the response is scored I.
- The approximate sums of the medians are 27.5 for Site I, 16 for Site II, and 20 for Site III.
Section 3 is scored as follows:
Essentially correct (E) if the response chooses chemical Y AND gives a reasonable justification based on the fact that the distributions of chemical Y are distinctive across sites.
Partially correct (P) if the response chooses chemical Y AND provides justification based on the boxplots, but does not clearly explain that the distributions of chemical Y are distinctive across sites; OR
if the response correctly discusses that the distributions of chemical Y are distinctive across sites, but never explicitly chooses chemical Y as the best choice, for instance, by stating only that there is substantial overlap across sites for chemicals X and Z but no overlap for chemical Y.
Incorrect (I) if the response does not meet the criteria for E or P.
Notes:
- To justify that the distributions of chemical Y are distinctive across sites, the justification must address both location and variability of the boxplots; for example, by stating that the boxplots do not overlap for chemical Y.
- If the response chooses chemical X or Z OR chooses chemical Y with no reasonable justification, the response is scored I.
- The justification that the distributions of chemical Y are distinctive across sites:
○ The following are acceptable because both location and variability are addressed. Such responses are scored E.
- The boxplots for chemical Y do not overlap, or the boxplots for chemicals X and Z overlap.
- All values of Site I are high, all values of Site II are low, and all values of Site III are in the middle.
- The ranges never intersect.
- The boxplots share no data.
- Has completely different percentages at each site.
○ The following are incomplete justifications and are scored P.
- The boxplots vary.
- Chemical Y varies the most.
- Chemical Y has the greatest variation.
- The variation between/among sites is the largest.
- The boxplots are different.
- The medians/means differ.
- The medians/means are most variable.
- There is a difference in the percentages of chemical Y for each site.
- The distribution of percents differs the most among the sites.
4 Complete Response
Three sections essentially correct
3 Substantial Response
Two sections essentially correct and one section partially correct
2 Developing Response
Two sections essentially correct and no sections partially correct
OR
One section essentially correct and one or two sections partially correct
OR
Three sections partially correct
1 Minimal Response
One section essentially correct
OR
No sections essentially correct and two sections partially correct