# Difference between replication and repeated measurements

The following quote is from Montgomery's Experimental Design:

There is an important distinction between replication and repeated measurements.

For example, suppose that a silicon wafer is etched in a single-wafer plasma etching process, and a critical dimension on this wafer is measured three times. These measurements are not replicates; they are a form of repeated measurements, and in this case, the observed variability in the three repeated measurements is a direct reflection of the inherent variability in the measurement system or gauge.

As another illustration, suppose that as part of an experiment in semiconductor manufacturing, four wafers are processed simultaneously in an oxidation furnace at a particular gas flow rate and time and then a measurement is taken on the oxide thickness of each wafer. Once again, the measurement on the four wafers are not replicates but repeated measurements. In this case they reflect differences among the wafers and other sources of variability within that particular furnace run.

Replication reflects sources of variability both between runs and (potentially) within runs.

1. I don't quite understand the difference between replication and repeated measurements. Wikipedia says:

The repeated measures design (also known as a within-subjects design) uses the same subjects with every condition of the research, including the control.

According to Wikipedia, the two examples are in Montgomery's book aren't repeated measurement experiments.

• In the first example, the wafer is used under only one condition, isn't it?

• In the second example, each wafer is used with only one condition: "processed simultaneously in an oxidation furnace at a particular gas flow rate and time", is it?

2. "Replication reflects sources of variability both between runs and (potentially) within runs". Then what is for repeated measurements?

• Simply put, replication involves same technique on different sample – user36297 Dec 17 '13 at 3:13

I don't think his second example is replication OR repeated measurements.

Any study involves multiple cases (subjects, people, silicon chips, whatever).

Repeated measures involves measuring the same cases multiple times. So, if you measured the chips, then did something to them, then measured them again, etc it would be repeated measures.

Replication involves running the same study on different subjects but identical conditions. So, if you did the study on n chips, then did it again on another n chips that would be replication.

• How about an almost-mnemonic: you can replicate conditions but not subjects, though you can repeat a measurement on the same subject. – Wayne Mar 5 '14 at 22:23

Unfortunately, terminology varies quite a bit and in confusing ways, especially between disciplines. There will be many people who will use different terms for the same thing, and/or the same terms for different things (this is a pet peeve of mine). I gather the book in question is this. This is design of experiments from the perspective of engineering (as opposed to the biomedical or the social science perspectives). The Wikipedia entry seems to be coming from the biomedical / social science perspective.

In engineering, an experimental run is typically thought of as having set up your equipment and run it. This produces, in a sense, one data point. Running your experiment again is a replication; it gets you a second data point. In a biomedical context, you run an experiment and get $N$ data. Someone else replicates your experiment on a new sample with another $N'$ data. These constitute different ways of thinking about what you call an "experimental run". Tragically, they are very confusing.

Montgomery is referring to multiple data from the same run as "repeated measurements". Again, this is common in engineering. A way to think about this from outside the engineering context is to think about a hierarchical analysis, where you are interested in estimating and drawing inferences about the level 2 units. That is, treatments are randomly assigned to doctors and every patient (on whom you take a measurement) is a repeated measurement with respect to the doctor. Within the same doctor, those measurements "reflect differences among the wafers [patients] and other sources of variability within that particular furnace run [doctor's care]".

• (+1) Montgomery is referring to multiple data from the same run as "repeated measures" -- the quote actually says "repeated measurements". Is this slight difference in wording important? – amoeba Mar 5 '14 at 21:24
• Thanks for the catch, @amoeba. I'm used to saying / thinking / typing "repeated measures". It was just a slip of the fingers. – gung - Reinstate Monica Mar 5 '14 at 21:26
• So just to be clear: Montgomery's "repeated measurements" of wafers are not "repeated measures" of wafers, right? I would say that your answer lacks this stated explicitly. You say that Montgomery's "repeated measurements" can be interpreted as repeated measures with respect to furnaces (fair enough), but furnaces are not the object of study in this quote; wafers are. – amoeba Mar 5 '14 at 21:30
• @amoeba, off the top of my head, I'm not sure what corresponds to what I would call "repeated measures" in the engineering perspective on DoE. I suppose you could say "Montgomery's 'repeated measurements' can be interpreted as repeated measures with respect to furnaces (fair enough), but furnaces are not the object of study in this quote; wafers are", but M's point is that the repeated measurements are information about "differences among the wafers and other sources of variability within that particular furnace run". Identifying sources of variability is the point of DoE in engineering. – gung - Reinstate Monica Mar 5 '14 at 22:06
• Imagine you manufacture gears to be used in a machine. The gears must be 3.000 cm in diameter. If they are too small, there will be play in the gears & they will wear out prematurely, shortening the life of the machine. If they are too large, they will cause the machine to seize up & explode, potentially causing other damage or injury. The idea is to identify sources of variability (& subsequently determine how to control them). This is different from biomedical experiments in which the idea is to find viable treatments. – gung - Reinstate Monica Mar 5 '14 at 22:09

What's going on here is the confusion in terminology. Here in the book, measurements refer to a single experimental trial observation, and the experiment calls for several observations to be made.

The term 'repeated measures' refers to measuring subjects in multiple conditions.

That is, in a within-subject design (aka crossed design, or repeated measures), you have, say, two conditions: a treatment and a control, and each subject goes through both conditions, usually in a counter-balanced way. This means that you have subjects act as their own control, and this design helps you deal with between-subject variability. One disadvantage of this research design is the problem of carryover effects, where the first condition that the subject goes through adversely influences the other condition.

In other words, don't confuse 'repeated measures' and multiple observations under the same experimental condition.

• (+1) Do you mean that by "repeated measurements" Montgomery did not mean "repeated measures"? I think it's exactly what you mean, and I agree, but I find that your wording could be a bit more explicit about that. – amoeba Mar 5 '14 at 21:20

http://blog.gembaacademy.com/2007/05/08/repetitions-versus-replications/ Repetitions versus Replications May 8, 2007 By Ron 6 Comments Many Six Sigma practitioners struggle to differentiate between a repetition and replication. Normally this confusion arises when dealing with Design of Experiments (DOE).

Let’s use an example to explain the difference.

Sallie wants to run a DOE in her paint booth. After some brainstorming and data analysis she decides to experiment with the “fluid flow” and “attack angle” of the paint gun. Since she has 2 factors and wants to test a “high” and “low” level for each factor she decides on a 2 factor, 2 level full factorial DOE. Here is what this basic design would look like.

Now then, Sallie decides to paint 6 parts during each run. Since there are 4 runs she needs at least 24 parts (6 x 4). These 6 parts per run are what we call repetitions. Here is what the design looks like with the 6 repetitions added to the design.

Finally, since this painting process is ultra critical to her company Sallie decides to do the entire experiment twice. This helps her add some statistical power and serves as a sort of confirmation. If she wanted to she could do the first 4 runs with the day shift staff and the second 4 runs with the night shift staff.

Completing the DOE a second time is what we call replication. You may also hear the term blocking used instead of replicating. Here is what the design looks like with the 6 repetitions and replication in place (in yellow).

So there you have it! That is the difference between repetition and replication.

Let me add an interesting factor, lot. In the above example, instead of making six tests with the same lot of paint (which, per above definitions means six repetitions per combination of conditions) she tests with six different paint lots per combination of conditions, which means also 24 total experiments; does this mean she is doing six replications per combination of conditions? Another example: A liquid pigment is measured for color intensity I. The lab method of analysis has two factors: suspension clarification time "T" and sample size W. Each factor has two levels, i.e, short and long T, and small and large W. That makes a 2x2 design. Testing the same lot sample under the four different conditions means there are 4 experiments in total, no repetitions. Testing the same lot twice each time means there would be two repetitions per condition, 8 experiments in total. But what if we test samples from six different lots per condition? Does this mean there are six replications per combination or conditions? The number of experiments would be 24. Now, we may want to make the method more precise and ask the lab technician to repeat the test twice (from the same sample) every time he makes a measurement, and report only the average per lot sample. I assume we could use the averages as a single result per lot sample, and for DoE, say a 2-way layout ANOVA with replications, each lot sample result is a replication. Please comment.