Command of Evidence — Quantitative

Quantitative evidence questions ask you to connect a claim with numerical evidence. Before comparing values, identify what was measured, the units, the groups, and the time period. A table cell might report total visitors, visitors per event, or the percentage of visitors who returned. Those quantities answer different questions.

For a bar chart, read the category labels, vertical-axis units, and legend before comparing heights. For a line graph, identify what each point represents and follow one labeled series at a time. A rising line means the measured quantity rose; it does not automatically mean conditions improved. On tables, trace the row and column into their intersection. Then translate one value into a complete sentence.

• Check whether values are counts, averages, percentages, or changes.
• Read notes for denominators, sample definitions, and measurement periods.
• Use the axis scale and labels; visual steepness alone does not measure the size of an effect.

Before looking for an attractive number, identify the relationship the claim requires. X is larger than

Y requires a comparison of levels. X increased requires two observations of X. An intervention

helped X more than Y requires two changes, followed by a comparison of those changes.

Write a short prediction in words: The increase for unfamiliar works should exceed the increase for familiar works. This separates evidence that addresses the claim from facts that merely sound favorable. The highest final score may belong to the group that benefited less. When a choice offers several correct numbers, ask whether those numbers establish the requested relationship.

With multiple series, distinguish within-group change from a between-group difference. Follow each group across time first. Then compare the groups at matching times. If the claim concerns convergence, calculate or estimate the gap at the beginning and end.

Two groups can both improve while their gap widens, narrows, or stays constant. A group can also close a gap without catching up. Preserve the claim's exact scope: the gap narrowed does not mean the groups became equal. Do not compare one group at the beginning with a different group at the end unless the question specifically calls for that comparison.

A count answers How many? A rate or proportion answers How many relative to what? A large sample can produce more successes even when its success rate is lower. Before comparing a percentage, name its denominator: all applicants, admitted applicants, surveyed residents, or something else.

To compare litter density across differently sized areas, divide litter count by surveyed area. To compare success rates, divide successes by attempts. You usually need only simple arithmetic. The more important reading decision is choosing the denominator that matches the claim. Do not replace a measured rate with a total, or assume equal denominators when none are stated.

• Percentage = relevant part / relevant whole x 100.
• Rate per 100 units = count / units surveyed x 100.
• A percentage of a group does not tell you the group's size.

Absolute change is the ending value minus the starting value. Relative change compares that difference with the starting value. A gain of 40 members doubles a club that began with 40, but increases a club that began with 100 by only 40%.

When the values are already percentages, subtraction gives percentage points. A rise from 20% to 30% is 10 percentage points, or a 50% relative increase. Read words such as more, faster, and larger increase carefully to identify the intended quantity. Also check intermediate observations: equal endpoints do not prove a steady trend, and higher cumulative totals do not necessarily mean faster current output.

Sometimes the passage supplies a mechanism or prediction, and the display supplies the observations. Translate the explanation into an expected pattern before reading the choices. If shade helps seeds mainly by reducing drying, its benefit should be greater under dry conditions than under wet conditions.

Look for the comparison that distinguishes the proposed explanation from alternatives. Showing that shaded seeds germinated is weaker than showing how shade's benefit changes with water conditions. A choice can quote the graph perfectly and still fail to test the passage's explanation. Prefer the relevant pattern over the most impressive isolated value.

Numerical results can support a pattern, a prediction, or a causal explanation with different degrees of strength. Check how the evidence was obtained. Random assignment and comparable conditions can strengthen a causal interpretation. An observational comparison can support an association and sometimes contribute to a causal argument, but self-selection or another difference may also explain it.

Do not reject useful evidence merely because it is not conclusive. Instead, match the conclusion's strength to the design. Also preserve the measured outcome: higher completion does not automatically mean greater enjoyment, and a group average does not describe every individual. Unless uncertainty information is supplied, do not label a small difference statistically significant.

Hard quantitative questions may combine requirements: a gap shrinks while both groups improve, or a gain exceeds another gain without reducing a baseline outcome. Split the claim into separate checks. Every required condition must hold.

Distinguish false data from true but insufficient evidence. A fact about one group may not establish a two-group comparison. Also avoid inventing requirements: if the claim asks for a larger increase, the answer need not identify the highest final score.

• Name the baseline or comparison group.
• Test each required condition using the same units.
• Reject an option that establishes only part of the requested relationship.
• For weaken questions, identify the predicted pattern and look for a relevant contradiction or alternative explanation.

Keep these checks in mind

• What quantity and population does each value represent?
• Does the claim require levels, changes, rates, or changes in a gap?
• Does the evidence establish every part of the requested relationship?
• Does the conclusion stay within what was measured and how the data were collected?

Begin with four brief reasoning drills, then complete sixteen multiple-choice questions. Later items generally demand closer distinctions. Identify the evidence for each answer and the specific flaw in its nearest competitor.