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Trellis How-To¶

This walkthrough repeats one surface across three values of a third factor, and checks the one shared scale that makes the three panels comparable.

Every chart in this family is drawn from a fitted model, so the walkthrough starts by building one. The same experiment is used on all ten chart walkthroughs, so once you have the regression sheet you can work through any of the others without setting the data up again.

The data is on this page rather than in a file to download. Press Copy for Excel, then paste it into a blank worksheet.

The data¶

A three factor experiment on a bonding process, run twice through. Temp is in degrees C, Press in psi and Time in seconds, and the response Strength is the peel strength of the finished bond. Each of the eight factor combinations was run twice, giving 16 runs.

Temp	Press	Time	Strength
180	40	10	49.5
220	40	10	65.4
180	60	10	61.8
220	60	10	66.8
180	40	20	52.3
220	40	20	70.7
180	60	20	60.7
220	60	20	70.0
180	40	10	50.6
220	40	10	66.4
180	60	10	61.2
220	60	10	67.2
180	40	20	51.4
220	40	20	67.1
180	60	20	61.9
220	60	20	71.6

Each factor takes exactly two values, so this is a full factorial of the three at two levels each, replicated once. That matters for more than one chart: a factor with exactly two observed values is the only kind that can carry a Cube Plot axis, and a design with centre points would have failed that test.

Steps¶

Put the data in Excel

Press Copy for Excel above the table. In Excel, open a blank worksheet, click cell A1, and press Ctrl+V. You should have headers in row 1 and the 16 runs in rows 2 through 17.
Make a design sheet to hold it

From the Excel ribbon: QXL DOE New > Create Design > Special > Create Custom Design.

On the first page set the number of factors to 3 and the number of runs to 16. On the second page set the number of outputs to 1. That gives you an empty design sheet of the right shape, which is how data collected outside Quantum XL gets analysed.
Fill in the design sheet

Copy the four columns of data into the three factor columns and the one output column. Name the factors Temp, Press and Time, and the output Strength, so the names on your charts match the ones quoted below.
Check the model holds the three two-factor interactions

The charts below assume a model of the three main effects plus AB, AC and BC. Add any that are missing with QXL DOE New > Modify Design > Inputs > Add/Remove Interactions.
Run the regression

QXL DOE New > Analyze Design > Run Regression. A worksheet called Regression is added after the design sheet. Every chart in this family reads that sheet.
Draw the trellis

QXL DOE New > Charts > Analysis > Trellis.

In the Outputs tree tick Strength Y-Hat. In Chart type leave Surface selected. In Primary factors set Horizontal axis (X) to Temp and Series axis (Y) to Press. In Panel variables set the First panel variable to Time and leave its From and to at 10 and 20 and its Slices at 3. Leave Add a second panel variable unchecked. Press Create.

Check the fit first¶

Before drawing anything, check the coefficient table on the Regression sheet against this. If these numbers match, every chart number quoted further down will match too; if they do not, the design was not entered the way this walkthrough assumes and nothing below will line up.

Term	Coefficient	Standard error	t	p
Constant	62.1625	0.2912	213.477	0.000000
Temp (A)	5.9875	0.2912	20.562	0.000000
Press (B)	2.9875	0.2912	10.260	0.000003
Time (C)	1.0500	0.2912	3.606	0.005696
AB	-2.2375	0.2912	-7.684	0.000030
AC	0.6500	0.2912	2.232	0.052506
BC	-0.1500	0.2912	-0.515	0.618877

The fitted equation is

Strength = 62.1625 + 5.9875 A + 2.9875 B + 1.0500 C - 2.2375 AB + 0.6500 AC - 0.1500 BC

in coded units, where each factor runs from -1 at its low value to +1 at its high value.

Every standard error is the same 0.2912. That is not a coincidence and it is a useful sign that the design was entered correctly: on a balanced full factorial every coded column is orthogonal to every other and carries the same amount of information, so every coefficient is estimated equally precisely.

What you should see¶

One worksheet holding three panels in a single row, each a surface of Strength over Temp and Press, and each with a band label above it naming the value of Time it is held at.

Panel	Band label	Time held at
left	Time (C) = 10	10
middle	Time (C) = 15	15
right	Time (C) = 20	20

Three slices give three evenly spaced values across the range you typed. From 10 to 20 in three slices is 10, 15 and 20. The last one is written as the to value exactly rather than reached by adding steps, so it is 20 and not 19.999999.

One panel variable gives one row of panels. Ticking Add a second panel variable would turn the row into a grid, with the first variable across the columns and the second down the rows.

The shared scale is the point of the chart¶

All three panels are drawn against one height axis, computed from all three together.

	Value
Lowest prediction anywhere in the trellis	50.4000
Highest prediction anywhere in the trellis	70.4500
Height axis, rounded out from that range	50 to 75

The lowest point sits in the Time 10 panel and the highest in the Time 20 panel, and neither panel is scaled to its own contents. That is what a trellis does that no other chart in this family does. A surface grid gives every cell its own axis, so two cells cannot be compared by eye; a trellis gives every panel the same one, so the rise from the left panel to the right one is visible as a rise rather than being flattened away by rescaling.

You can check this, and the check is more interesting than it first looks. Compare the same corner in the left and right panels:

Temp	Press	Time 10 panel	Time 20 panel	Rise
180	40	50.4000	51.5000	1.1000
220	40	65.5500	69.2500	3.7000
180	60	61.1500	61.6500	0.5000
220	60	67.3500	70.4500	3.1000

No corner rises by the same amount, and not one of them rises by 2.1000, which is twice Time's coefficient of 1.0500 and the figure you might expect. The four rises average to exactly 2.1000, and that average is what the coefficient reports. They differ from each other because AC and BC also move with Time, so how much Time does depends on where Temp and Press are.

A trellis is the chart that makes that visible, and it is visible only because the three panels share one scale.

Things to try next¶

Change the chart type. Set Chart type to Contour or Interaction and the same three panels are drawn as contours or as interaction charts. The panels change; the slicing and the shared scale do not.
Ask for more panels. Set Slices to 5 and you get panels at 10, 12.5, 15, 17.5 and 20. Above 16 panels a prompt warns that many can be slow to draw and asks whether to continue.
Use one slice. Set Slices to 1 and you get a single panel at Time 10, the From value, not the middle of the range.