t-test or ANOVA to compare variance of several samples series

P

patric wessels

Dear all,

I have 2 series of 8 samples (each sample with 10 measured spots for thickness resulting in an average and variance/st.dev.). These two series are different with respect to sample preparation. I want to see if the sample preparation method leads to a difference with respect to the variation within the 10 measured spots.

Is it statistically allowed to compare the variance of several series using ANOVA or a t-test to see if the variation of these series are significantly different from eachother?

best regards,

Patric
 

Statistical Steven

Statistician
Leader
Super Moderator
patric wessels said:
Dear all,

I have 2 series of 8 samples (each sample with 10 measured spots for thickness resulting in an average and variance/st.dev.). These two series are different with respect to sample preparation. I want to see if the sample preparation method leads to a difference with respect to the variation within the 10 measured spots.

Is it statistically allowed to compare the variance of several series using ANOVA or a t-test to see if the variation of these series are significantly different from eachother?

best regards,

Patric

Patrick -

A t-test is just a one-way ANOVA with 2 treatments. I would analyze the data using a two-way ANOVA with sample prep and sample nested within sample prep. Additionally, I would use the 10 repeat measurements as my estimate of MSE in the model.
 
W

Winner

I agree with Steven. I will use ANOVA to test statistical difference in 8 samples.

I dont know what is the significance of 2 series for same sample though. If you had different sample preparator for 2 series in the same sample, the series might be statistically different too.

You can also try fitting a Regression Line and find which samples are away from the line to have a visual check.

Thanks,

Kumar
 
P

patric wessels

perhaps I should elaborate a bit about the samples: we produce a foil with a coating applied on it. The mentioned 10 measured spots are 10 points across the foil (as in our standard inspection), these data are called one sample with its average, stdev etc.

From our production plant I have these 2 series of 8 samples, each serie with a different sample preparation. It is impossible for me to differ the sample preparation on a same sample. Once prepared it is "finished". But wwe know that if samples are taken close from eachother (and we have a slow and stable process) they are very much alike.

I want to know if the variation in 1 sample depends on the sample preparation method.

So I think what Steven says makes sence.

I have attached (part of) my data.

Best regards,

Patric
 

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E

e-solver

patric wessels said:
perhaps I should elaborate a bit about the samples: we produce a foil with a coating applied on it. The mentioned 10 measured spots are 10 points across the foil (as in our standard inspection), these data are called one sample with its average, stdev etc.

From our production plant I have these 2 series of 8 samples, each serie with a different sample preparation. It is impossible for me to differ the sample preparation on a same sample. Once prepared it is "finished". But wwe know that if samples are taken close from eachother (and we have a slow and stable process) they are very much alike.

I want to know if the variation in 1 sample depends on the sample preparation method.

So I think what Steven says makes sence.

I have attached (part of) my data.

Best regards,

Patric

Do you mean to ask if the preparaton method can explain the variation in a sample since its not constant? Unless you can control the preparation or at least categorise it based on environmental elements like humidity or ambient temp etc then you just have to live with it, maybe some fractional factorial experiments can help you assess the interaction effect of preparation variation? I have some statistical process control charts on my website (95% complete) that I think would be of use...

R-chart: Calculates the upper and lower control limits for the variability in a process. The R-Chart is a control chart for processes where the variable can be measured rather than counted.

C-chart: Calculates the upper and lower control limits for the number of defects in a series of individual items. The c-Chart is a control chart for attributes. It is used when the quality characteristics of a process can be counted rather than measured.

P-chart: Calculates the upper and lower control limits for the number of defective items in a series of samples. Individual samples from the sample series, whose proportion of defective items (p) is above the upper control limit (UCL), can indicate that a process needs adjustment. The p-Chart is a control chart for attributes. It is used when the quality characteristic of a process is counted rather than measured.

We also do the X-chart. If you like give me the complete data set I will run it through for you. You really need to plot continuous processes over time to establish trends and measure variation that way instead of small isolated sample events to describe the difference. You cant really tell if the emultion used on the foil was chemically consistent for that sample and so on. None of this may be use to you, I guess I am just looking at it in another perspective. If so, sorry for my ramblings!


Andrew
B.Com (hons) M.Com (hons)
 
P

patric wessels

Andrew, thank you for your reply.

I don't want to explain the variance in my samples. What you descibe here, like using several control charts, is what I already do in order to control/analyse our process.

I only want to see if a different sample preparation and/or a heat treatment significantly influences the variance (better or worse, could be either of them).

So I need tot test the differences in variance between two (or more) data series (i.e. samples with different preparation/heat treatment).

Sorry if I wasn't clear in my question.

Best regards, Patric
 
E

e-solver

patric wessels said:
Andrew, thank you for your reply.

I don't want to explain the variance in my samples. What you descibe here, like using several control charts, is what I already do in order to control/analyse our process.

I only want to see if a different sample preparation and/or a heat treatment significantly influences the variance (better or worse, could be either of them).

So I need tot test the differences in variance between two (or more) data series (i.e. samples with different preparation/heat treatment).

Sorry if I wasn't clear in my question.

Best regards, Patric


Ah I see, then as an alternate (or perhaps in addition) you should look at using fractional factorial experiment designs. That way you can account for interaction effects etc...

Andrew
B.Com (hons) M.Com (hons)
 
D

Dave Strouse

Patrick -

I'm afraid you're being led off track unintentionally by our fellow forum members. By asking whether to use an ANOVA or a t-test they have missed your point of wanting to study variance.

If you want to analyze variance, you need to use a F test (if normal data) or Levines or Barletts test (there are others also), if non normal. BTW, you will likely need larger sample sizes to see differences unless there is a dramatic chang by method.

ANOVA or t-teat provides information on difference in means i.e. data center.
If you wish to understand difference in variance i.e spread of the data, you need a test akin to the ones I mentioned above.

I do hope that after you find the best preperation method, you will continue your search by analyzing with factorials or other means to acheive the best of the best.
 

Bev D

Heretical Statistician
Leader
Super Moderator
Ok - I LOOKED at the data in a graph. See attached.

There is significant within piece variation - larger than the difference between the preparations. BUT there is a statistically significant difference between the averages of the sample preps...assuming that the two preps are independent and no spurious association cause is at work - you would have to replicate the preperations to ensure that the difference is not coincidental to some other change that is time to time driven.

The largest component of variation is within piece. This 'could' be measurement error, but it may not be - only an MSA would tell you that. (NEVER assume - check it out if you haven't yet done so)

There is a slight difference in the overall variance within each preparation (the t test is done assuming unequal variances, but the VISUAL of the graph shows that this difference is very slight.)

There is a slight piece to piece variation within the two series that is driven by the first piece - I don't know if this first piece is positional or time based or you just sorted the data in some way such that the higher piece is first in the series...)

At this point I would ask if the Problem you see is the total variation in thickness across the foil? or if you just need to center teh thickness SO having the specification limits would be the best indication of your next steps.

I woudl not yet recommend jumping into fractional factorials as you may be able to detect the cause and solution a little faster with some simpler tools...

I encourage everyone to LOOK at the data first...or as Deming used to say (with some editorial license!): "plot the bloody dots"
 

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