# Can be several measurement in a repl considered as nested factor in Minitab analysis

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#### furanosa2000

Dear all,

I have a set of data of an experiment. In the experiment I have 3 factors and made 3 repetition, and on each repetition I took 10 measurement. Lets say the factors are A, B and C. I made 3 repetition which means I will have experiment A1, A2, A3, B1, B2, B3, C1, C2, C3. On each repetition, I took 11 measurement to the same unit experiment, which gave me A1a, A1b, ..., A1j etc.

I want to analyze using one way ANOVA whether there is differences between the factors. At first, I take means of each repetition and consider that as a single value and analyze it directly using one way ANOVA (so I only have 9 data). But then, I realize that each repetition has its own variability, which may affect the final decision whether the factors giving different effect. So I tried to analyze the data again, but this time using GLM and considered the 11 measurement nested within the repetition (giving total data to analyze of 198). I used the following model for the GLM: factor repetition(factor)

The ANOVA result of GLM is totally different from the one way ANOVA. When I used one way ANOVA the p value is 0.07, while when using the GLM model, the p value is <0.00. Does anyone have any idea whether we can consider several measurements as nested in the replicate?

For information I attach the data.

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#### Miner

##### Forum Moderator
Staff member
Re: Can be several measurement in a repl considered as nested factor in Minitab analy

• REPEAT - Multiple samples/measurements taken under the same experimental run (i.e., no experimental settings were changed during the collection of units)
• REPLICATE - Multiple experimental runs conducted under the same experimental settings, but at different times such that other experimental runs intervene (i.e., includes setup to setup variation)
Using these definitions, your experiment appears to have 3 replicates with 11 repeats per replicate. Is that correct?

Also, to clarify, you have a TIME column from 1 - 11. Does this simply mean that you took 11 consecutive samples in that order, or are you measuring 1 sample 11 times over some period of time (repeated measures)?

F

#### furanosa2000

Re: Can be several measurement in a repl considered as nested factor in Minitab analy

Hi Miner,

Yes, that is right. I did 3 replicates, and did 11 reading for the same sample. So I put the sample in an instrument, and the instrument read for 11 times in every minutes (repeated measures?).

I just have a discussion with my supervisor, and he suggested me to calculate the Standard Deviation for the 11 reads, and see whether the SD is higher or lower than the SD of the average of 3 replicates. I haven't done it yet, but it is most likely the SD for the 11 repeats will be lower than SD of the 3 replicates.

#### Miner

##### Forum Moderator
Staff member
Re: Can be several measurement in a repl considered as nested factor in Minitab analy

If your intent was to have multiple measurements for greater confidence in the results, it is not a repeated measures design. If your intent was to study changes OVER time then it is a repeated measures design.

The following is based on an assumption that you are NOT investigating the time element.

I would calculate the mean and standard deviation of the 11 repeats from each experiment. Analyze the means as one response and the standard deviations as another response. This is known as Taguchi Parameter Design. Factors may be classified into 4 categories 1) affects mean and variation, 2) affects variation only, 3) affects mean only, and 4) affects neither. You then select levels of factors to minimize variation first then levels of factors to shift the mean onto target.

The comparison of repeat variation to replicate variation is redundant if you proceed as above. The ANOVA of the standard deviations includes a significance test that the comparison does not.

F

#### furanosa2000

Re: Can be several measurement in a repl considered as nested factor in Minitab analy

Thank you so much for the explanation Miner..

Sorry for my very late respond. I have been busy with my experiments.

I have a follow up question to clarify. I found a statement from a book: "Practical Statistics for the Analytical Scientist: A Bench Guide" by S.L.R. Ellison, T.J. Farrant & V. Barwick (2009). I quote the text from page 118 as follow:

"Although perhaps as accurately considered as simple grouped data, the simplest example of a nested design is a set of replicate observations at each level of a single experimental factor, for example, replicate observations for each of several sets of extraction conditions or replicate observation on each of several days. Single factor nested design such as this can be analyzed using one-way ANOVA".

In my understanding from what the paragraph said is that the data from multiple measurement can be considered as nested within the treatment factor (is this correct?). So, I tried to analyze the data using both approach: 1) use all the multiple measurement data and consider it "nesting" within the factor (worksheet 1, analyzed using GLM; model: factor replicate(factor)), and 2) calculate the mean of each replicate and consider it as one response (worksheet 2, analyzed using regular one-way ANOVA). (attached Minitab file).

The first approach give p value <0.001 and the post hoc test using Tukey test that A>B=C, while using the second approach p value = 0.045, but Tukey test did not give any significant differences between the factors. Roughly, from the raw data, I expect the result from the first approach to be true, because in all the replicate of the response value for factor A never lower than factor B and C, while B and C are similar at some points.

So, if I use your approach the results should be the second approach, right?

Follwong the results above, what do you think about a low p-value (less than 0.05) but the post hoc test doesn't show any significant differences (like the results above) or the other way, a p-value higher than 0.05 but the post hoc test show there is a significant differences between the response? I often get this kind of results in my analysis.

Thank you very much for all your help.. very much appreciated..

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#### Miner

##### Forum Moderator
Staff member
Re: Can be several measurement in a repl considered as nested factor in Minitab analy

It took a while to register, but it finally did. You are on the right track.

If the tests are taken in different locations, but on the same part, this is a special type of design known as a Spatial Repeated Measures design. It is analyzed the same way as a Longitudinal (over time) Repeated Measures design except the different locations replace time.

If the tests are taken in the same location, or location does not apply, then analyze them as a nested design.

NOTE: The ANOVA results should be identical both ways. The spatial Repeated Measures adds some additional Post-hoc analysis to the ANOVA

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F

#### furanosa2000

Re: Can be several measurement in a repl considered as nested factor in Minitab analy

Hi Miner,

Thank you very much for your answer. Just to make sure, the first apporach Using GLM with replicate nested within the factors that I used is already correct?

what about the last question? about high p-value but post hoc test showed significant difference or low p-value but no significant differences detected using post hoc test. I just run another test and got p-value of 0.4 but the Fisher LSD test showed some significant differences of the response... (Or should I make a new thread for this? )

Thank you again so much..

#### Miner

##### Forum Moderator
Staff member
Re: Can be several measurement in a repl considered as nested factor in Minitab analy

I set the analysis up correctly in the attached file. Because the repeats are a random factor, you cannot run post-hoc tests, but the differences are visually apparent. The scatter plot shows an interesting artifact of your measurement device that you may want to investigate if you need to improve the R&R.

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#### furanosa2000

Re: Can be several measurement in a repl considered as nested factor in Minitab analy

Hi Miner,

Thanks for your answer. If we can not run the post hoc test, is there any way to check the statistically significant differences between the response? In this example I only have 3 factors, but in the following experiment I have 6 factors, and the differences are not visually apparent in the main factor plot. For example, i got a main factor plot where factor A is above the line, B below the line, C,D and E are almost touching the line and F just below the line. Without the post hoc test, can we group the factors?

#### Miner

##### Forum Moderator
Staff member
Re: Can be several measurement in a repl considered as nested factor in Minitab analy

Sorry for the delay, but this took some thought.

To be technically correct, you would have to manually calculate the post-hoc tests using the s = 0.0245309 from the GLM. You cannot get Minitab to perform these tests because it only provide the post-hoc test options for fixed factors and repeats are not fixed. If you specify them to be fixed in order to run the post-hoc tests, the GLM results will be incorrect.

However, in this instance you can use your results from the 1-Way ANOVA because the s = 0.02412, which is nearly the same as for the GLM. This may not always be the case, so do not assume that you can always do this.

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