2^3-1 Experiment

You have a fully saturated design. Remove the ABC interaction when you using “Analyze Factorial Design” within Minitab…you will see p-values BUT be aware you have confounding so the factors you find statistically significant may be the confounded factor or a combination.

@Peach

I did a quick analysis and found Factor C to be statistically significant with an alpha of 0.05. Either I didn’t fill out your randomized design correctly or ….

I always us an initial value of alpha of 0.15 or 0.25 to do an initial screening of which factors to remove and then use an alpha of 0.05 after the first analysis.

@cseider  I think you did not understand my question. Anyways thank you

@MBBinWI  Thank you for the answer. What i am still trying to get my head around is how can all the values be perfect output to the regression. Is it because of small number of runs, 4 runs? Is it common for small experiments to have perfect outputs like this?

Thank you Joel Smith. It make sense. This is what i thought of the perfect fit issue, lack of enough data points. Thank you again.
For your information. This was the first experiment we did so we did not want to do many runs. We are going to do more experiments considering what we learned from this.
Thank you

Thank you Robert. This is what we are planning to do. I am trying to figure out how to analyze the new design using minitab. It is not easy to analyze the new design in Minitab. I will post the results here..

Did you ever ran a food related experiment? We are doing one and there is high variability among the response (set of people rate the taste of food). We thought we did enough work to select the best people to rate the change in taste.

Let’s back up and revisit your description of your experiment.

In the initial post you gave the impression you had run 4 experiments and had exactly 4 results. Your most recent post suggests you’ve done something quite different.

You said “Did you ever ran a food related experiment? We are doing one and there is high variability among the response (set of people rate the taste of food). We thought we did enough work to select the best people to rate the change in taste.”

The answer is yes and the questions are:
1) If the measurements are ratings of taste what kinds of ratings are they?
2. What, exactly do the response values in your first post represent ? That is what is 1.7, 3.2, etc.?
3. If the four experiments represent food that is being rated then do you have the same group of people rating all four food types or do you have separate populations of people for each one of the food types (we’re assuming the experiments are actually receipe changes).

If you are using the same group of people to rate all four of the food types then you do not have independent measurements – you have repeated measures and that requires a very different approach to your analysis, and if the taste ratings are Likert scale (ratings from 1-5 or whatever) then you need to forget the averaging and use the raw rating numbers.

We are now about 4 “if’s” removed from what might actually have been done so rather than continue in this vein I’d appreciate it if (that’s 5) you could answer the above questions.

Given that it is Likert rating and given that the same people rated all 4 receipes there is a simple way to analyze this kind of data and you may find that you already have all of the measurements you need. However, before describing this I’d prefer to wait for your reply to my questions.

• This reply was modified 304 days ago by  Robert Butler.
• This reply was modified 304 days ago by  Robert Butler.
• This reply was modified 304 days ago by  Robert Butler.

Ok, thanks for the clarification.

On the first experiment – I trust that one of those two additional experiments is a genuine replicate of one of the original 4. If it isn’t it should be.

On the second experiment-assuming the tasters were blinded (the usual situation in tastes tests is to make sure the tasters do not have any visual cues so, since various types of rice do indeed look different, the taste test should have been run in a manner that kept the tasters from looking at what they were tasting – like running the test in a dark room).

The other issue with taste tests is the need for a washout period so I hope the testing was spread over several days. Assuming you ran the taste test correctly then what you have is 16 responses per taster. Three tasters is on the low side (we used to run a minimum of 6) but if the experiment is done and gone then you’ll have to use what you have.

As mentioned previously, the taste panel results are repeated measures and you will have to find out if Minitab can handle data of this type.

What isn’t clear to me is your statement “The experiment was 2^4-1, total 8 runs, with 4 blocks (blocks were different rice used, assumed to be an inert factor).” If I read this one way I get the impression that you ran 4 different rice types but if I read it another way I get two rice types. If you can clarify this point I may be able to offer some additional thoughts.

If you had run the two additional points at the same time as the original 4 then you would have had some assurance that the various unknown/uncontrolled factors exhibited the same behavior during the course of the experimental run. Since some time has passed since you ran the first 4 experiments you have zero assurance that those unknown/uncontrolled factors are going to behave/exist/interact in the same way they did for the initial run. A replicate of one of the original design points, when used in conjunction with the original point, will give you a measure of the “pure error” of the augmented research effort in the face of changing condtions of unknown and uncontrolled variables and thus will guard against a declaration of significance where none really exists.

For the taste test: The smallest unit of independence is the individual taster. Anything within a taster is a repeated measure. This is the same problem you have in medicine where you take a group of patients and test their responses to multiple forms of medication (say, for example 4 different types of medicine to address a particular medical condition). If you can get a copy of Regression Methods in Biostatistics by Vittinghoff, Glidden, Shiboski, and McCulloch through inter-library loan there is an excellent discussion (with example) of this issue on pages 254-259.

Since you ran 4 blocks on an 8 point fractionated design you have some additional issues. The principal block for that kind of fractionation is 1, ab, ac, bc, ad, bd, cd, and abcd. If the blocking was such that 1 and ab were with rice type I, ac and bc were with rice type II, ad and bd were with rice type III and cd and abcd were with rice type IV then you have perfect confounding of rice type with factors C and D – in other words you cannot tell if the cooking time was due to either of these factors or due to rice type. You will have a similar problem only with different factors if you blocked in some other fashion.

In order to assess the effect of rice type you will have to figure out your confounding pattern and run a repeated measures model on rice type and whatever two other factors (and their two way interaction)are clear of rice type.

As a stopgap you could follow the method described by Vittinghoff and set up a two way ANOVA with tasters and the 8 combinations with two measures per combination. This would deal with the repeat measures nature of the data and give you an assessment of differences between the 8 combinations but it would not address correlations between the rice type, the two factors clear of rice type, and cooking time or any of the taste ratings.