Making a comparison between numbers is often a version of amplification. But it is worthy of some further comment beyond what was described on the previous page 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):
- Rank: A comparison relative to other values, to include percentile when there are a lot of values
- Example: “the least expensive car”
- Example: “test score was in the 67th percentile”
- Difference: Subtracting a reference value from number of interest.
- Example: “So far in 2019, MLB teams hit 797 more home runs this year compared to 2018”).
- Ratio: Dividing a number by the reference value.
- 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]”
- 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].
- 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.
- 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])
- 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.
- 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.
- 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: Distributions and Measures of Variability – ENG 4950: Data and Writing Toward Social Change, Spring 2021 (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.
Task
Using your data set or the the Airbnb data set we used in class, make as many of the types of comparisons from the above examples as you’d like to get practice with.
In a comment below, write out at least one comparison you made and explain how it might be an effective one to make.
After commenting below, click the button to continue:
In the data set I’m working with, I’m curious who the most valuable players are in the targets of the data set. The data set split up the entire population into various categories from refugees, to men to women to boys and girls to many other categories. I wonder what the most valuable is in the population and who received the highest funding for COVID-19 relief as there were researched disparities in the allocation of these resources.
In the Airbnb dataset, out of 3681 people 1522 prefer to have an entire home or apt for themselves which represents a total of 41.3% the customers whereas 58.7% prefer to have a private room. This comparison is important to make because it allows us to make judgements to whether people would most likely rent out a private room or an entire place. Having this comparison, there is a better idea about people’s preferences when looking at Airbnbs.
The highest amount of ratings for Airbnb is Great Bedroom in Manhattan with a total of 607 reviews. This is important to know because it can allow viewers to understand which Airbnb has the most ratings as well as whether this is a popular place that people frequently go to.
Out of the 19.6 million student in college during 2018, in the first two quarters alone, at least 5% of all students filed for government assistance with the cost of education. This figure dose not include the millions of other student that applied for private aid, like scholarships and grants.
It is known that pandemic affected the psychological side of individuals, either directly or indirectly. I compared and contrasted the frequency of the term “anxiety” between UK and US: on July 2019 Canada reported to search such term 91%, whereas in the US the same term was searched 89%. This shows us a slight difference between these 2 countries in terms of psychological symptoms and how to seek for help during quarantine.
The most important regression connected to the hypothesis included the graduation rate for economically disadvantaged students as the independent variable. The regression resulted in a strong positive correlation, with a correlation coefficient of 1.02 and an r square of .77. This means that 77% of the overall graduation rate variation can be described by the graduation rate for economically disadvantaged students. Finally, the p-value of 3.57 x 10-9 tells that the regression is significant, and the null hypothesis is to be rejected. The regression analysis showed a similar correlation coefficient with the other independent variables: male graduation rate, female graduation rate, non-ELL graduation rate, and non-economically disadvantaged students’ graduation rate. The main outlier was the regression run using the ELL graduation rate as the independent variable. The regression resulted in a correlation coefficient of -.37, which translates to an inverse relationship between the two variables. Moreover, the analysis resulted in a p-value of .07, which tells us that we fail to reject the null hypothesis. The null hypothesis states that there is no relationship between the two variables, and in this case, since the p-value is above .05, we accept it.
I use the Airbnb data set for this analysis, I pick the category “number of reviews,” I sort and filter this column to see which one of these Airbnb has the highest, the greatest amount of reviews by guests (in term of ranking). It turns out the Airbnb with ID 903972 has the largest amount of reviews which is 607 reviews, meaning this property may have a higher possibility, a higher chance to be rented compares to other properties. I think this is an effective one because it helps those guests especially who are new to get a better idea of what others/previous guests think about this property before they rent it. As always, before we want to buy something that we never used them before, we always want to look for the product’s reviews first to get to know more about it so we can make a good choice.
In 2016, 43,246 black people were arrested for robbery. In the same year, 34,138 white people were arrested for robbery. This data shows that black people were 26.7% more likely to be arrested for robbery than white people. I think this is an effective comparison to note because it raises questions about the systematic and structural forces of oppression that exist and the ways in which they are contributing to this. From there we can brainstorm potential solutions.
I used the Airbnb data set and sorted by the price column and sorted by largest to smallest. I found by comparison that one apartment is priced at 9999 which is 4999 higher than anything else. I think the fact that there is an outlier this high is completely odd compared to everything else and it would make sense as to why this apartment only has one review.
I used percentage difference and I think it helps out a lot. It shows how much of a difference between different temperatures of different years and I calculated by how much percent each year could rise or like a difference between a certain number of years. It’s effective too since it shows by how much percentage the temperature is increasing annually and I feel like percent’s can accurately display change and draw a reader in if it’s like a massive change in difference.
Inequality is prominent among Latin Americans and the Middle East, with the top 10th percentile of the income distribution having a hold of the 54% and 56% of the average nat. income respectively. In Africa, the 10th percentile have a hold of 50% of the national income.
Russia has an equally large disparity as the 10th percentile own up to 46% of the national income. India’s inequalities have been on the rise over the years with the 10 th percentile income share recording 30% ownership of the national income in the 80s but shooting the numbers to 56% in the past decade. Conversely, China has also grown within the same time from 28% to 41%.
Working women who were in full-time positions year-round the female employees made 82.3 cents to every dollar their male counterparts made in 2019 found on median earnings data resulting in women getting paid 17.7% less than men over all earning $10,157 less than men.
New York State total violent crime had decreased by 30% from 2001 to 2017. Texas’ total violent crime had been declining by the end of 2010. Subsequently, the crime rate has increased. In the same period, Texas’ total violent crime has not changed. This is an interesting comparison as it opens a discussion as to the causes of New York’s relatively better performance relative to violent crime. Whether these differences are due to demographic shifts, public policy or economics.
In the Airbnb case study, there are 1522 out of 3775 people who would like to live in an entire room or apartment; 2159 out of 3775 people who would like to live in a private room; 94 out of 3775 people who like to share a room with others. The statistic shows that approximately 97.5% people who would like to have live by themselves. It implies that privacy is an important factor for people in travel. In comparison, the rest of the 2.5% of people who choose to live in the shared room is seeking a lower price.