Graphical Representation: Graphics We Live By (Part VI: Conversion Rates in Power BI)

Graphical Representation Series

Introduction

Conversion rates record the percentage of users, customers and other entities who completed a desired action within a set of steps, typically as part of a process. Conversion rates are a way to evaluate the performance of digital marketing processes in respect to marketing campaigns, website traffic and other similar actions. 

In data visualizations the conversion rates can be displayed occasionally alone over a time unit (e.g. months, weeks, quarters), though they make sense only in the context of some numbers that reveal the magnitude, either the conversions or the total number of users (as one value can be calculated then based on the other). Thus, it is needed to display two data series with different scales if one considers the conversion rates, respectively display the conversions and the total number of users on the same scale. 

For the first approach, one can use (1) a table or heatmap, if the number of values is small (see A, B) or the data can be easily aggregated (see L); (2) a visual with dual axis where the values are displayed as columns, lines or even areas (see E, I, J, K); (3) two different visuals where the X axis represents the time unit (see H); (4) a visual that can handle by default data series with different axis - a scatter chart (see F). For the second approach, one has a wider set of display methods (see C, D, G), though there are other challenges involved.

Conversion Rates in Power BI

Tables/Heatmaps

When the number of values is small, as in the current case, a table with the unaltered values can occasionally be the best approach in terms of clarity, understandability, explicitness, or economy of space. The table can display additional statistics including ranking or moving averages. Moreover, the values contained can be represented as colors or color saturation, with different smooth color gradients for each important column, which allows to easily identify high/low values, respectively values from the same row with different orders of magnitude (see the values for September).

In Power BI, a simple table (see A) allows to display the values as they are, though it doesn't allow to display totals. Conversely, a matrix table (see B) allows to display the totals, though one needs to use measures to calculate the values, and to use sparklines, even if in this case the values displayed are meaningless except the totals. Probably, a better approach would be to display the totals with sparklines in an additional table (see L), which is based on a matrix table. Sparklines better use the space and can be represented inline in tables, though each sparkline follows its own scale of values (which can be advantageous or disadvantageous upon case).

Column/Bar Charts 

Column or bar charts are usually the easiest way to encode values as they represent magnitude by their length and are thus easy to decode. To use a single axis one is forced to use the conversions against the totals, and this may work in many cases. Unfortunately, in this case the number of conversions is small compared with the number of "actions", which makes it challenging to make inferences on conversion rates' approximate values. Independently of this, it's probably a good idea to show a visual with the conversion rates anyway (or use dual axes).

In Power BI, besides the standard column/bar chart visuals (see G), one can use also the Tornado visual from Microsoft (see C), which needs to be added manually and is less customizable than the former. It allows to display two data series in mirror and is thus more appropriate for bipartite data (e.g. males vs females), though it allows to display the data labels clearly for both series, and thus more convenient in certain cases. 

Dual Axes 

A dual-axis chart is usually used to represent the relationship between two variables with different amplitude or scale, encoding more information in a smaller place than two separate visuals would do. The primary disadvantage of such representations is that they take more time and effort to decode, not all users being accustomed with them. However, once the audience is used to interpreting such charts, they can prove to be very useful.

One can use columns/bars, lines and even areas to encode the values, though the standard visuals might not support all the combinations. Power BI provides dual axis support for the line chart, the area chart, the line and staked/clustered column charts (see I), respectively the Power KPI chart (see E). Alternatively, custom visuals from ZoomCharts and other similar vendors could offer more flexibility.  For example, ZoomCharts's Drill Down Combo PRO allows to mix  columns/bars, lines, and areas with or without smooth lines (see J, K).

Currently, Power BI standard visuals don't allow column/bar charts on both axes concomitantly. In general, using the same encoding on both sides of the axes might not be a good idea because audience's tendency is to compare the values on the same axis as the encoding looks the same. For example, if the values on both sides are encoded as column lengths (see J), the audience may start comparing the length without considering that the scales are different. One needs to translate first the scale equivalence (e.g. 1:3) and might be a good idea to reflect this (e.g. in subtitle or annotation). Therefore, the combination column and line (see I) or column and area (see K) might work better. In the end, the choice depends on the audience or one's feeling what may work. 

Radar Chart

Radar charts are seldom an ideal solution for visualizing data, though they can be used occasionally for displaying categorical-like data, in this case monthly based data series. The main advantage of radar charts is that they allow to compare areas overlapping of two or more series when their overlap is not too cluttered. Encoding values as areas is in general not recommended, as areas are more difficult to decode, though in this case the area is a secondary outcome which allows upon case some comparisons.

Scatter Chart

Scatter charts (and bubble charts) allow by design to represent the relationship between two variables with different amplitude or scale, while allowing to infer further information - the type of relationship, respectively how strong the relationship between the variables is. However, each month needs to be considered here as a category, which makes color decoding more challenging, though labels can facilitate the process, even if they might overlap. 

Using Distinct Visuals

As soon as one uses distinct visuals to represent each data series, the power of comparison decreases based on the appropriateness of the visuals used. Conversely, one can use the most appropriate visual for each data series. For example, a waterfall chart can be used for conversions, and a line chart for conversion rates (see H). When the time axis scales similarly across both charts, one can remove it.

The Data

The data comes from a chart with dual axes similar to the visual considered in (J). Here's is the Power Query script used to create the table used for the above charts:

let
    Source = #table({"Sorting", "Month" ,"Conversions", "Conversion Rate"}
, {
{1,"Jul",8,0.04},
{2,"Aug",280,0.16},
{3,"Sep",100,0.13},
{4,"Oct",280,0.14},
{5,"Nov",90,0.04},
{6,"Dec",85,0.035},
{7,"Jan",70,0.045},
{8,"Feb",30,0.015},
{9,"Mar",70,0.04},
{10,"Apr",185,0.11},
{11,"May",25,0.035},
{12,"Jun",195,0.04}
}
),
    #"Changed Types" = Table.TransformColumnTypes(Source,{{"Sorting", Int64.Type}, {"Conversions", Int64.Type}, {"Conversion Rate", Number.Type}})
in
    #"Changed Types"

Conclusion

Upon case, depending also on the bigger picture, each of the above visuals can be used. I would go with (H) or an alternative of it (e.g. column chart instead of waterfall chart) because it shows the values for both data series. If the values aren't important and the audience is comfortable with dual axes, then probably I would go with (K) or (I), with a plus for (I) because the line encodes the conversion rates better than an area. 

Happy (de)coding!

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Graphical Representation: Axes (Just the Quotes)

"The ratio chart not only correctly represents relative changes but also indicates absolute amounts at the same time. Because of its distinctive structure, it is referred to as a semilogarithmic chart. The vertical axis is ruled logarithmically and the horizontal axis arithmetically. The continued narrowing of the spacings of the scale divisions on the vertical axis is characteristic of logarithmic rulings; the equal intervals on the horizontal axis are indicative of arithmetic rulings." (Anna C Rogers, "Graphic Charts Handbook", 1961)

"As a general rule, plotted points and graph lines should be given more 'weight' than the axes. In this way the 'meat' will be easily distinguishable from the 'bones'. Furthermore, an illustration composed of lines of unequal weights is always more attractive than one in which all the lines are of uniform thickness. It may not always be possible to emphasise the data in this way however. In a scattergram, for example, the more plotted points there are, the smaller they may need to be and this will give them a lighter appearance. Similarly, the more curves there are on a graph, the thinner the lines may need to be. In both cases, the axes may look better if they are drawn with a somewhat bolder line so that they are easily distinguishable from the data." (Linda Reynolds & Doig Simmonds, "Presentation of Data in Science" 4th Ed, 1984)

"The frequency of labelled scale calibrations on the axes of a graph can significantly affect the accuracy with which it is interpreted. As little interpolation as possible should be required of the user, in order to minimise errors. If single units cannot be marked, it has been suggested that multiples of 2,5 or 10 should be used." (Linda Reynolds & Doig Simmonds, "Presentation of Data in Science" 4th Ed, 1984)

"The plotted points on a graph should always be made to stand out well. They are, after all, the most important feature of a graph, since any lines linking them are nearly always a matter of conjecture. These lines should stop just short of the plotted points so that the latter are emphasised by the space surrounding them. Where a point happens to fall on an axis line, the axis should be broken for a short distance on either side of the point." (Linda Reynolds & Doig Simmonds, "Presentation of Data in Science" 4th Ed, 1984)

"An axis is the ruler that establishes regular intervals for measuring information. Because it is such a widely accepted convention, it is often taken for granted and its importance overlooked. Axes may emphasize, diminish, distort, simplify, or clutter the information. They must be used carefully and accurately." (Mary H Briscoe, "Preparing Scientific Illustrations: A guide to better posters, presentations, and publications" 2nd ed., 1995)

"Graphic misrepresentation is a frequent misuse in presentations to the nonprofessional. The granddaddy of all graphical offenses is to omit the zero on the vertical axis. As a consequence, the chart is often interpreted as if its bottom axis were zero, even though it may be far removed. This can lead to attention-getting headlines about 'a soar' or 'a dramatic rise (or fall)'. A modest, and possibly insignificant, change is amplified into a disastrous or inspirational trend." (Herbert F Spirer et al, "Misused Statistics" 2nd Ed, 1998)

"If you want to show the growth of numbers which tend to grow by percentages, plot them on a logarithmic vertical scale. When plotted against a logarithmic vertical axis, equal percentage changes take up equal distances on the vertical axis. Thus, a constant annual percentage rate of change will plot as a straight line. The vertical scale on a logarithmic chart does not start at zero, as it shows the ratio of values (in this case, land values), and dividing by zero is impossible." (Herbert F Spirer et al, "Misused Statistics" 2nd Ed, 1998)

"The visual representation of a scale - an axis with ticks - looks like a ladder. Scales are the types of functions we use to map varsets to dimensions. At first glance, it would seem that constructing a scale is simply a matter of selecting a range for our numbers and intervals to mark ticks. There is more involved, however. Scales measure the contents of a frame. They determine how we perceive the size, shape, and location of graphics. Choosing a scale (even a default decimal interval scale) requires us to think about what we are measuring and the meaning of our measurements. Ultimately, that choice determines how we interpret a graphic." (Leland Wilkinson, "The Grammar of Graphics" 2nd Ed., 2005)

"Arbitrary category sequence and misplaced pie chart emphasis lead to general confusion and weaken messages. Although this can be used for quite deliberate and targeted deceit, manipulation of the category axis only really comes into its own with techniques that bend the relationship between the data and the optics in a more calculated way. Many of these techniques are just twins of similar ruses on the value axis. but are none the less powerful for that." (Nicholas Strange, "Smoke and Mirrors: How to bend facts and figures to your advantage", 2007)

"We tend automatically to think of all the categories represented on the horizontal axis of a column Chart as being equally important. They vary of course on the value axis. Otherwise, there would be little point in the chart, but there is somehow this feeling that they are in other respects similar members of a group. This convention can be put to good use to manipulate the message of the most boring bar or column chart." (Nicholas Strange, "Smoke and Mirrors: How to bend facts and figures to your advantage", 2007)

"One of the easiest ways to display data badly is to display as little information as possible. This includes not labelling axes and titles adequately, and not giving units. In addition, information that is displayed can be obscured by including unnecessary and distracting details." (Jenny Freeman et al, "How to Display Data", 2008)

"Histograms are often mistaken for bar charts but there are important differences. Histograms show distribution through the frequency of quantitative values (y axis) against defined intervals of quantitative values(x axis). By contrast, bar charts facilitate comparison of categorical values. One of the distinguishing features of a histogram is the lack of gaps between the bars [...]" (Andy Kirk, "Data Visualization: A successful design process", 2012)