Student Learning Objective: Write about Quantitative Patterns
Quantitative literacy is fundamentally an issue of literacy--of reading with comprehension and writing with precision and clarity. Literacy of any kind is a life-long project. Because robust QL entails a fluent and creative use of language, it is not possible to reduce its concepts into linguistic formulas. Nevertheless, this page suggests ways to foster the literacy piece of QL.
Activity or Assignment: Craft a paragraph that reports and interprets numerical findings. Specify the magnitude and the direction of the general pattern, and place it into a larger context. Select simple, plausible examples to support the major finding, and then provide a few exceptions. (See Miller, The Chicago Guide to Writing about Numbers, for more detail and examples.)
In order to write about patterns, you will probably need to...
Write about one number. Craft one exquisite sentence that conveys all the important context for a single number: who, what, where, when, unit of analysis. Include scale and system (metric or British) if necessary, and a compelling analogy or contextual statement if desired. Be precise so that you say what you mean.
Pay attention to grammar and mathematical vocabulary. The order of operations is not just a mathematical issue, but also an issue of grammar. Conjunctions such as "because" can imply causal relations. "Therefore" introduces a conclusion. "Per" implies division (35 miles per gallon means 35 miles/1 gallon). Choose verbs that convey direction and magnitude, such as "plummet" or "bounce."
Interpret charts and tables. Identify important comparisons, maximums, minimums, or trends in bar charts, line charts and tables. A good chart or table will make the author's argument clear, but you may be trying to read against the grain of the author's argument. Or you may find that the author has skewed the numbers (inadvertently or on purpose) through the
choice of axes or time frame.
Compare categories. Compare the variable in question in different countries or regions. Compare across gender, education, race or class. (Though we know that these categories are themselves historically contingent!) These categories are often expressed visually in a bar chart or in a table. The order in which the categories are presented visually can be changed to emphasize different trends or comparisons. Use analogies to summarize comparisons or trends. Compare to standard cutoffs or patterns.
Describe change over time. The historians' bread and butter. Compare the variable in question over time. With enough data, these variables are considered "continuous variables," and are often visually displayed as a histogram or a line chart. Here, the order is essential. The direction (increase or decrease), the magnitude (how much), and the time frame are essential. Use analogies to summarize patterns over time, including analogies to mathematical models (such as: linear, piecewise linear, nonlinear dynamic, exponential...). Compare to standard cutoffs or patterns.
Distinguish between correlation and causation. Correlation between two events does not imply causation. The direction of causality may not be what we first think. Or a third event may cause both of them. Or the correlation may be a coincidence. Humanists are adept at seeing multiple causes and can add a lot to this way of thinking.
Distinguish between mean, median and mode. Mean is the average number, median is the middle number, and mode is the most common number. A data set with a few major outliers can have a mean that is skewed, so reporting the median is often a good idea. And we should be skeptical of reports that offer only the mean or only the median.
Indicate variability. Variability helps us to understand how closely the data fit around the median. A common way to indicate variability is to report the standard deviation, expressed in the units of the measure in question, or report the Z-score. You can also use the "five number summary": report the minimum value, first quartile value (Q1), median, third quartile (Q3), and maximum value. Use analogies to describe the variability.
Distinguish between absolute change and relative change. Both measures are important, and we should be skeptical of reports that offer only the absolute or the relative change. A small absolute change may mean a very large relative change. Relative change can be expressed in percentages or ratios; percent change can be calculated for any amount of change, while ratios are particularly useful for doubling, tripling, or cutting in half. Be sure to include the magnitude, the direction, and the time frame for any change.
Distinguish between percentage change and change in percentage points. Both measures are important, and we should be skeptical of reports that only provide one. A small change in percentage points may mean a very large percent change. Be sure to include the magnitude, the direction, and the time frame for any change.
Activity or Assignment: Craft a paragraph that reports and interprets numerical findings. Specify the magnitude and the direction of the general pattern, and place it into a larger context. Select simple, plausible examples to support the major finding, and then provide a few exceptions. (See Miller, The Chicago Guide to Writing about Numbers, for more detail and examples.)
In order to write about patterns, you will probably need to...
Write about one number. Craft one exquisite sentence that conveys all the important context for a single number: who, what, where, when, unit of analysis. Include scale and system (metric or British) if necessary, and a compelling analogy or contextual statement if desired. Be precise so that you say what you mean.
Pay attention to grammar and mathematical vocabulary. The order of operations is not just a mathematical issue, but also an issue of grammar. Conjunctions such as "because" can imply causal relations. "Therefore" introduces a conclusion. "Per" implies division (35 miles per gallon means 35 miles/1 gallon). Choose verbs that convey direction and magnitude, such as "plummet" or "bounce."
Interpret charts and tables. Identify important comparisons, maximums, minimums, or trends in bar charts, line charts and tables. A good chart or table will make the author's argument clear, but you may be trying to read against the grain of the author's argument. Or you may find that the author has skewed the numbers (inadvertently or on purpose) through the
choice of axes or time frame.
Compare categories. Compare the variable in question in different countries or regions. Compare across gender, education, race or class. (Though we know that these categories are themselves historically contingent!) These categories are often expressed visually in a bar chart or in a table. The order in which the categories are presented visually can be changed to emphasize different trends or comparisons. Use analogies to summarize comparisons or trends. Compare to standard cutoffs or patterns.
Describe change over time. The historians' bread and butter. Compare the variable in question over time. With enough data, these variables are considered "continuous variables," and are often visually displayed as a histogram or a line chart. Here, the order is essential. The direction (increase or decrease), the magnitude (how much), and the time frame are essential. Use analogies to summarize patterns over time, including analogies to mathematical models (such as: linear, piecewise linear, nonlinear dynamic, exponential...). Compare to standard cutoffs or patterns.
Distinguish between correlation and causation. Correlation between two events does not imply causation. The direction of causality may not be what we first think. Or a third event may cause both of them. Or the correlation may be a coincidence. Humanists are adept at seeing multiple causes and can add a lot to this way of thinking.
Distinguish between mean, median and mode. Mean is the average number, median is the middle number, and mode is the most common number. A data set with a few major outliers can have a mean that is skewed, so reporting the median is often a good idea. And we should be skeptical of reports that offer only the mean or only the median.
Indicate variability. Variability helps us to understand how closely the data fit around the median. A common way to indicate variability is to report the standard deviation, expressed in the units of the measure in question, or report the Z-score. You can also use the "five number summary": report the minimum value, first quartile value (Q1), median, third quartile (Q3), and maximum value. Use analogies to describe the variability.
Distinguish between absolute change and relative change. Both measures are important, and we should be skeptical of reports that offer only the absolute or the relative change. A small absolute change may mean a very large relative change. Relative change can be expressed in percentages or ratios; percent change can be calculated for any amount of change, while ratios are particularly useful for doubling, tripling, or cutting in half. Be sure to include the magnitude, the direction, and the time frame for any change.
Distinguish between percentage change and change in percentage points. Both measures are important, and we should be skeptical of reports that only provide one. A small change in percentage points may mean a very large percent change. Be sure to include the magnitude, the direction, and the time frame for any change.
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