Connecting lines and paired graphs

Why a line

Measure the blood pressure of eight people, give them a drug, measure again. Draw two bars of the mean, before and after, and the bars say the average fell by eight. They do not say whether everyone fell by eight, or whether two people fell by forty and the rest did not move. Those are different drugs.

The data know the difference, because each row is one person. A paired test uses that: it works on each person’s own change, and that is why a paired t test can find an effect that an unpaired test on the same numbers misses. A graph of paired data should show the same thing the test sees. The way to do it is to draw each person’s points and join them with a line, bar to bar. Parallel lines that all slope down are a consistent effect; lines that cross every which way are noise around a mean.

Dioptra draws these lines on any bar graph, dot plot, box plot or violin: connecting lines are an option of the graph, not a separate kind of graph.

A worked example

Paste eight subjects measured at baseline, week 4 and week 8 into a column table. The first row becomes the column titles. The third subject missed the week-4 visit, so that cell is empty.

Baseline	Week 4	Week 8
131	124	118
118	116	105
142		127
109	104	101
125	117	112
137	126	119
114	112	104
128	119	116

Run Analyze → Repeated-measures one-way ANOVA (or a paired t test on two columns, a Wilcoxon test or a Friedman test). The results sheet’s toolbar button reads Graph with connecting lines: these analyses default to the paired graph. Click it.

You get bars of the mean with SEM error bars, every subject’s points on the bar centres, a thin grey line per subject, and the significance brackets from the analysis. Now open the Connecting lines section of the inspector:

• Off / Subjects / Mean / Median / Both chooses what is joined. Subjects joins the values of each row. Mean and Median join the summary of each bar instead. Both draws the subject lines and the line of the graph’s summary (the mean, or the median when Bars and points → Summary says median). In the picture above it is Both.
• Missing says what an empty cell does. Gap (the default) breaks that subject’s line there; Join across connects the values on either side. Subject 3 above has a baseline and a week-8 value only, so with Gap it draws no line at all: there is no pair of neighbouring visits to join. A line from baseline straight to week 8 would hide that the week-4 value was never measured; choose Join across when that is what you want.
• Subject lines: style (solid, dashed, dotted), width in points, opacity, and colour. Colour by is one colour for every line (Prism’s convention), the data set (each segment takes the colour of the bar it starts from), the subject (each row its own colour from a palette), or a grouping column (a column of the table that says, say, Male or Female for each row: lines take a colour per group, a legend appears, and that column is not drawn as a bar).
• Summary line: its own style, width and colour.

Everything is undoable, and the graph redraws as you change it. Click a subject line in the graph to select it: the inspector shows the same controls, and the status line names the row.

How lines are matched

Lines join the values in the same row, as Prism does. Row 5 in Baseline and row 5 in Week 8 are the same subject. If your data are in long format (one row per measurement), pivot them to wide first with Data → Transform… → Pivot long to wide.

Lines run in the order the categories appear on the axis, which is the order of the data sets in the table (or of the analysis’s chosen data sets). Reorder the columns to reorder the lines.

Lines meet the points

When points are jittered sideways so they do not overlap, each line ends at its own point’s jittered position, not at the bar centre, so lines and points always agree. With Bars and points → Jitter at 0 % the points sit on the centre line, the classic before–after look; the paired preset uses 0 %.

Every bar style

The same lines work whatever draws the categories. Switch the family in the toolbar and the connecting lines stay:

Subject lines are drawn on top of bars, boxes and violins and beneath the points; error bars and the summary line sit above the points. Horizontal (Bars and points → Orientation) turns the graph so the categories run down the left; the lines turn with it. Log axes work as usual, and a line that crosses a broken axis is cut at the break, as the axis is.

Grouped tables

In a grouped table each row is a group (Day 1, Day 7, Day 14) and each data set has subcolumns. For repeated measures, subcolumn 1 of every data set is subject 1, subcolumn 2 is subject 2, and so on. Direction chooses which way the lines run:

• Within groups (default): inside each group, from one data set’s bar to the next (Saline to Drug on Day 1). This is Prism’s before–after on a grouped graph.
• Across groups: along each data set, from group to group (Saline on Day 1, Day 7, Day 14), Prism’s “each replicate”. The summary line then takes each data set’s colour.

Stacked bars draw no connecting lines: a stacked bar has no single height per data set to join.

In the file

A graph with connecting lines is an ordinary column (or strip, box, violin) graph with an options.connecting block; the graph reference lists every field and the file format chapter says how graphs of the old Before–after family from Dioptra 0.2 are opened: as the dot plot that draws the same picture.

"options": {
  "jitter": 0,
  "connecting": { "connect": "both", "style": "solid", "colour_by": "single",
                  "opacity": 0.55, "missing": "gap" }
}