11.4. Incorporating the Data Design

When we create a visualization, it’s important to consider the data scope, especially the data design (see Chapter 2). Considering the question of how the data were collected can impact our plot choice and the comparisons we portray. These considerations include the time and place where the data were collected and the design used to select a sample. We look at a few examples of how the data scope can inform the visualizations we make.

11.4.1. Data Collected Over Time

When data are collected over time, we typically make a line plot that puts timestamps on the x-axis and a feature of interest on the y-axis to look for trends in time. As an example, let’s revisit the data on San Francisco housing prices. These data were collected from 2003 through 2008 and show the crash in 2008/2009 of the US housing bubble. Since time is a key aspect of the scope of these data, let’s visualize sale price as a time series. Our earlier explorations showed that sale price is highly skewed, so let’s work with percentiles rather than averages. We plot the median price (this is a form of smoothing we saw earlier in this chapter):

sfh_labels={'price':"Sale price (USD)", 'date':""}
medians = rel_percentiles.query('percentile == 50')
fig = px.line(medians, x='date', y='price',
              title='Median sale price',
              labels=sfh_labels,
              width=500, height=250)
margin(fig, t=30)

This plot shows the rise in prices from 2003 to 2007 and the fall in 2008. But we can show more information by plotting a few additional percentiles instead of just the median. Let’s draw separate lines for the 10th, 30th, 50th (median), 70th, and 90th percentile sale prices. When we examine prices over time, we typically need to adjust for inflation so that the comparisons are on the same footing. In addition to adjusting for inflation, let’s plot the prices relative to the starting price in 2003 for each of the percentiles. This means that all the lines start at y = 1 in 2003. (A value of 1.5 for the 90th percentile in 2006 indicates that the sale price is 1.5 times the 90th percentile in 2003.) This normalization lets us see how the housing crash affected home owners in the different parts of the market.

infl_2003 = [1, 2.66, 6.14, 9.57, 12.69, 17.01, 16.60]

fig = px.line(rel_percentiles, x='date', y='rel_price', 
              line_dash='percentile', color='percentile',
              color_discrete_sequence=plotly.express.colors.sequential.Magma,
              title='San Francisco sale prices, inflation-adjusted',
              labels=dict(date='',rel_price='Sale price relative to 2003'),
              width=600, height=350)
fig.update_layout(legend_title_text='Percentile')
margin(fig, t=30)

When we follow the 10th percentile line plot over time, we see that it increases quickly in 2005, stays high relative to its 2003 value for a few years, and then drops earlier and more quickly than the other percentiles. This tells us that the less expensive houses, such as starter homes, suffered greater volatility and lost much more value in the housing market crash. In contrast, higher-end homes were affected less by the crash; at the end of 2008, the 90th percentile home prices were still higher than the 2003 prices. Applying this bit of domain knowledge helps reveal trends in the data that we might otherwise miss, and shows how we can use the data design to improve a visualization.

The housing data are an example of observational data that form a complete census in a geographic region over a specific period of time. Next we consider another observational study where self-selection and the time period impact the visualization.

11.4.2. Observational Studies

We need to be particularly cautious with data that do not form a census or scientific sample. We should also take care with cross-sectional studies, whether from a census or scientific sample. For this example, we revisit the data from the Cherry Blossom 10-mile run. Earlier in this chapter, we made a smoothed curve to examine the relationship between race time and age. We reproduce this plot here to highlight a potential pitfall in interpretation:

times = (
    runners_over_17.assign(age_5yr=runners_over_17['age'] // 5 * 5)
    .groupby('age_5yr')['time'].mean().reset_index()
)

px.line(times, x='age_5yr', y='time',
        labels={'time':"Average race time (sec)", 'age_5yr':"Runner age (5-yr)"},
        markers=True, 
        width=350, height=250)

It’s tempting to look at this plot and conclude that, for instance, a runner at age 60 can typically expect to take an additional 600 seconds to finish the run than when they were 40. However, this is a cross-sectional study, not a longitudinal study. The study does not follow people over time; instead, it gets a snapshot of a cross section of people. The 60-year-old runners represented in the plot are different people than the 40-year-old runners. These two groups could be different in ways that affect the relationship between race time and age. As a group, the 60-year-olds in the race are likely to be fitter for their age than the 40-year-olds. In other words, the data design doesn’t let us make conclusions about individual runners. The visualization isn’t wrong, but we need to be careful about the conclusions we draw from it.

The design is even more complex because we have race results from many years. Each year forms a cohort, a group of racers, and from one year to the next, the cohort changes. We create a visualization that makes this message clear by comparing runners in different race years. Here, we’ve separately plotted lines for the runners in 1999, 2005, and 2010:

fig = px.line(few, x='age5', y='time', color='year',
              line_dash='year',
              labels={'year':'Race year'},
              width=450, height=250,
             )
fig.update_xaxes(range=[18, 75], title="Runner age (5-yr)")
fig.update_yaxes(range=[4500, 7500], title="Median race time (sec)")
margin(fig, t=30)

We see that the median race times in 2010 are higher at every age group than the times for the runners in 2005, and in turn, the times are higher for the runners in 2005 than for the runners in 1999. It’s interesting that race times have slowed over the years. This is quite likely due to the increased popularity of the race where there is higher participation from novice runners in more recent years. This example has shown how we need to be aware of the data scope when interpreting patterns. We also need to keep data scope in mind with scientific studies. This is the topic of the next section.

11.4.3. Unequal Sampling

In a scientific study, we must consider the sample design because it can impact our plots. Some samples draw individuals at unequal rates and this needs to be accounted for in our visualizations. We saw an example of a scientific study in Chapters 8 and 9: the Drug Abuse Warning Network (DAWN) survey. These data are from a complex randomized study of drug-related emergency room visits, and each record comes with its weight that we must use in order to accurately represent the emergency room visits in the population. The two bar plots that follow show the distribution of the type of ER visit. The one on the left doesn’t use the survey weights and the one on the right does:

fig1 = px.bar(x=types_ct, y=dawn_cts.values)
fig2 = px.bar(x=types_wt, y=dawn_wts.values)

fig = left_right(fig1, fig2)
fig.show()

In the unweighted bar plot, the “Other” category is as frequent as the “Adverse reaction” category. However, when weighted, “Other” drops to about two-thirds of “Adverse reaction.” Ignoring sampling weights can give a misleading presentation of a distribution. Whether for a histogram, bar plot, box plot, two-dimensional contour, or smooth curve, we need to use the weights to get a representative plot. Another aspect of the data scope that can impact our choice of plots is where the data are collected, which is the topic of the next section.

11.4.4. Geographic Data

When our data contains geographic information like latitude and longitude, we should consider making a map, in addition to the typical plots. For example, the following map shows the locations for US air quality sensors, which is the focus of the case study in Chapter 12:

fig = px.scatter_geo(aqs_sites, lat='lat', lon='lon',
               locationmode='USA-states', scope='usa',
               width=550, height=300)

fig.update_layout(geo = dict(landcolor = 'rgb(217, 217, 217)'))
fig.show()

Notice that there are many more points in California and the Eastern Seaboard. A simple histogram of air quality with data from all of these sensors would misrepresent the distribution of air quality in the US. To incorporate the spatial aspect into the distribution, we can add air quality measurements to the map with different color markers, and we can facet the histograms of air quality by location.

In addition to plotting features like bars, color, and line styles, we also have the option to add text with contextual information to make our plot more informative. This is the topic of the next section.