Making Quantitative Comparisons (15-20 minutes)

Making a comparison between numbers is often a version of amplification. But it is worthy of some further comment beyond what was described in the previous lesson due to some technical considerations about quantification.

Comparison is really the bread and butter of communicating something about data. It is hard to know if something is meaningful unless you have something to compare it against:

• How large or small is the value?
• How fast or slow was the pace of change over time?
• Is it below or above an important standard or cutoff (e.g., poverty line)?

Here are a few calculations you can do to make comparisons between numbers (adapted from Jane E. Miller’s The Chicago Guide for Writing About Numbers, chapter 5 on quantitative comparisons):

1. Rank: A comparison relative to other values, to include percentile when there are a lot of values
   1. Example: “the least expensive car”
   2. Example: “test score was in the 67th percentile”
2. Difference: Subtracting a reference value from number of interest.
   1. Example: “So far in 2019, MLB teams hit 797 more home runs this year compared to 2018”).
3. Ratio: Dividing a number by the reference value.
   1. Example: “I doubled my take-home pay per week with my new job, making $600 per week instead of $300 [Number of interest = $600, reference value = $300]”
   2. Example: “I now make 80% of what I did a year ago at this new job because my industry sucks and has the power to do this…I now make $40,000 instead of $50,000 per year [number of interest = $40k, reference value = $50k].
4. Percentage difference: Divide difference of a number and reference value by reference value and multiply by 100. See this on ways people sometimes confuse percentage change, percentage points, and percentile.
   1. Example: “so far in 2019, MLB teams hit 797 more home runs this year compared to 2018, a 14% increase” [number of interest = 6,382, reference value = 5,585])
5. z-score: Subtract the mean from the number of interest and divide by the standard deviation. A positive score is above the mean, a negative score is below the mean. Only use when distribution is approximately normal (i.e., “bell shaped”). Helps when comparing two values that come from very different distributions.
   1. Example: For instance, if you are comparing a 6-month-old baby that was 2.5cm shorter than the average to a 6-year-old 2.5cm shorter than the average, because variation within distributions are way different for these age-ranges, a z-score can be useful.
   2. Example: If someone is looking at different groupings of hockey players based on their contract value to think about contract value compared to production as a hockey player, a z-score could be helpful if the distributions for each grouping are very different.

Everything but z-score involves some basic arithmetic, but even a z-score is pretty simple if you know what a standard deviation is (which you do! and if you don’t, you will just need a few moments to remember after glancing at an example or definition or going through this again: March 15, 2022 Lesson Plan – Data and Writing Toward Social Change, Spring 2022 (cuny.edu)

There are some minor mathematical issues to keep in mind before choosing.

For example:

If you have a variable where values below zero are possible, then rank and difference work but ratios do not because values can be positive or negative.

If you have an ordinal variable, only rank would make sense.

If you a nominal variable (e.g., gender, name, race), differences cannot be quantified or ranked (you can convert nominal variables into discrete variables through some filtering and cleaning by counting them but nominal variables as is are not numeric in ways that can be calculated).

 

Rhetoric and Comparing Numbers

From a rhetorical perspective, once you have a valid way to compare mathematically, it doesn’t really matter how you choose to compare values. What matters is what your goal is as a writer and what sorts of interests your audience has.

Some tips:

• Always report value to set context and provide data for other calculations, then present one or two types of comparisons to give a more complete sense of the relationship
• To help readers interpret both value and difference, mention the highest and lowest possible values and observed  range in the data
• Value is also important for putting a ratio in context…always give values for percentage change and difference as well.
• Specify type of measure: Honda Civics most frequently stolen but Corvette stolen at highest rate.

 

Ways of Writing with Data: Examples, Amplification, Quantitative Comparisons (30 minutes)

Let’s stretch you out as quantitative writers. To be a flexible writer is to be a good writer–there really are not inflexible good writers. Remember: at some point, you will want something to stand out. Thus, moves of emphasis and explanation can be helpful.

From your in-progress draft or from something you totally invent from your analysis of your data set and/or secondary sources you are using, do the following:

-Revise a current or write a new sentence or series of sentences that uses an example to help readers understand something about your data analysis or the data analysis of another source. Go here for a refresher on the kinds of examples you could use and why you might use them.

-Take that same sentence or sentences and apply each of the 5 methods of amplification to it. You can rewrite each sentence with one or more methods or rewrite things 5 times (once for each method)–or some combination of these two approaches. Here is a review of the methods of amplifications.

-Let’s try quantitative comparison next. Consider the kinds of data you have or your secondary source has and try to do at least two kinds of quantitative comparison.

Post it all to this Google Doc.

 

As you finish up, be ready to share the following:

• Which sentence(s) you are most proud of and why
• Any questions you have about writing with data using these moves
• Any thoughts on why and when you might use any of these moves

After about 20 minutes, I want to see what you shared.

 

Fast Feedback (10-20 minutes)

Create two sentences:

1. Your argument so far of your Data-Driven Argument (your argument can and probably will change as you get to the final draft!).
2. One question you have about your project (e.g., somewhere you are stuck, a few options you are weighing, something technical you are not sure about).

Get into one of the Voice Channels for today if we have time with one other person.

If we don’t have time, share both sentences in the chat.

Depending if voice channels or just text channel for today, you will provide a response that asks a question of #1 and/or offers a possible direction for #2.

 

Next Time

-Turn in Data-Driven Argument by 11:59pm on Thursday, March 31

-Have an in-progress draft ready by class time on March 31 for an activity