graphing relationships and describing patterns

two people that the book highlights about the invention of graphs to display data

willaim playfair and florence nightingale

line graph

visual representation of data using lines to connect data points to display trends changes over time

what should you consider when choosing the right graph to use

whether you are describing one variable or showing the relationship between two variables

graphs you can use when describing one variable

bar graphs, histograms, density plots, box plots

what does a graph that describes one variable tell us?

variation of data but don’t help us understand why the data varies or compare data

what should you do when graphing relationships between two variables?

identify variables to be graphed and the nature of the relationship you want to display

• what do they measure? how to measure it? are they interval, ordinal, or nominal?

• the higher level of measurement of variables, the more detail you can show on a graph

what are the IV’s values on a graph when it’s measured at the nominal level?

categories

when you graph relationship between two variables, they don’t show observation-level data but rather …

summary statistics that correspond to percentages in a cross-tabulation or mean values in a mean comparison table

summary statistics

measurements produced by summarizing data collected at a more granular level (ex: country data are usually aggregated from individual-level data)

what do we have the opportunity to do when the IV is measured at the interval-level?

plot individual-level data points on the graph

individual -level data points

specific data values or observations collected at the individual level represented as points (or other symbols) on a graph to show relationship between variables in a dataset

which graphs is suitable for showing variation over time?

line graphs and filled area graphs

• allow for visualization of changes and patterns over time, revealing trends, seasonality, and cyclical behavior

do you have to use the data exactly as you found it?

no! you can transform the variable as you see fit, like collapsing it to a lower level of measurement

line chart

graph that displays summary stats as points connected by straight lines; used to show trends and relationships between variables

what have bar charts been traditionally used for?

graphic accompaniment to cross-tabulation analyses and line charts have been used to visualize mean comparisons

what can line charts be used for outside of its traditional purpose?

display cross-tabulation and bar charts can be used to depict mean comparisons

direct relationship

relationship that runs in positive direction

• increase in independent variable is associated with increase in dependent variable

inverse relationship

relationship that runs in a negative direction

• increase in values on the IV is associated w/ a decreases in the DV

linear relationship

increase in IV is associated with a consistent increase or decrease in the DV

• can be positive or negative

positive linear relationship

• increase in IV occasions an increase in the DV

  • but as one continues to move along the IV, entering a different range of the independent variable continues to increase, the DV decreases

  • or a relationship that initially is positive or negative may flatten out, with an increase in the IV being associated with no change in the DV

negative linear relationship

• typical values of the DV decreases by the same amount for each unit change in the IV

  • bc ordinal-level independent variables don’t have equal unit differences, we generally only describe a relationship as linear when the independent variable is measured at the interval level

curvilinear relationship

relationship between IV and DV depends on which interval or range of the independent variable is being examined

• may change direction, from positive to negative or positive to negative

• or might remain positive or negative but change in strength or consistency, from strong to weak and vice versa

what is one of the most powerful and useful graphs?

scatterplots!

scatterplot

chart that shows a relationship between two interval-level variables; observed values are displayed as points on the chart

why are scatterplots extremely useful?

they display observation-level data, allows for trends, variability, and unusual observations

name two challenges for using scatterplots

• markers on the graph can become cluttered and crowded, obscuring the relationship between the variables

• scatterplot markers may overlap (overplotting)

  • can make it difficult to discern patterns or trends

two strategies for addressing scatterplot challenges

• simplest: reducing size of scatterplot markers, addresses clutter and overlapping

• use semi-transparent color for markers

  • transparency can effective represent the density of data points in a particular region on the scatterplot

name the three variations of traditional scatterplots

heatmaps, binned scatterplots, and jittering

heatmaps

visually represent data in a matrix form using color-coded cells

• color intensity or shading represents the magnitude or value of the data point

• darker colors or higher shading typically indicate a higher concentration of data points

• lighter colors or lower shading suggest a lower concentration

binned scatterplot

divides into a grid of hexagonal or rectangular bins

• each bin represents a specific range or interval of values for both variables

• one marker is used for each bin, but the marker sizes vary with the number of observations that fall into the range represented by the marker

• by aggregating the data into bins, it provides a clearer visualization of the overall density and distribution of data points

jittering

used to alleviate overplotting on a scatterplot

• introduces a small amount of random noise to the positions of the data points

• by introducing some random movement, the points are displaced from their original positions, creating a scattered appearance with fewer overlapping points

• can display individual data points while honoring the overall distribution and patterns

• if done with care and attention to detail, a researcher can use jittering to display relationships with one variable measured at the nominal or ordinal level on a scatterplot

what should you add if you graph involves multiple groups or categories?

legend or key, clarify the meaning of different symbols, colors, or patterns used to represent each group

something to avoid when making graphs

avoid distorting the relationship by using uneven or inappropriate scales

• if you’re graphing a transformed variable, like logged values, make that clear to the viewer

• ensure that the intervals on the axes are evenly spaced and clearly labeled

• conduct analysis and create graphs with integrity

suggestions for striking the right balance between good info and too much info

data-to-ink ratio, don’t chartjunk, and keep your audience in mind

data-to-ink ratio

• amount of information your graph conveys relative to the amount of ink (or toner) it takes to print your graph

  • minimizing non-essential elements, such as borders, gridlines, or decorative embellishments, allows for a cleaner and more efficient display of information

chartjunk

unnecessary or distracting elements in a visualization, such as excessive ornamentation, artistic effects, or other accessories that are not informative

keeping your audience in mind

if you’re creating a graph for a homework assignment, research paper, or academic presentation (oop that sounds like me), you should create academic-style graphs

academic-style graphs

style of graphs used in scholarly publications; limited embellishment, simple borders, grayscale colors, serious and austere

things to add to graphs to visualize data more effectively

• avoid unnecessary clutter, but make good use of the space

• use the graph to convey information: not too much information but not too little either

• can be helpful to include trend lines or regression lines to show trends, correlations, or patterns that may not be immediately apparent from the raw data points

• label interesting data points, like outlier observations, for case-level information

• show it to a classmate or friend