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Hello everybody Welcome to our seminar today today we have fundamentals of raring part six correlation um you made it almost to the end of our um series on the fundamentals of ring and um you might remember me if you attended all of our seminars from the first part of this serious factors
Of ring but for those who are new to this series um let me briefly introduce myself my name is Floren file I’m your presenter today I’m working for Atlas material testing technology as yeah manager for our client education program and also as consultant for weing technology and also I’m representing
Atlas in several standardization um committees ISO um but also at asdm Dean in Germany yeah as you might recognize ni for my pronunciation um actually from Germany and as you might see also with the camera I don’t see it currently myself it’s already relatively dark so for me
It’s definitely good evening but we have attendees from Mostly the Americas today some from Europe actually but so for you it’s a good day good morning and actually because of that I’m turning off now my camera probably also because of a little bit of end Bend with at the end
Um um it’s a lot of internet traffic going on so and the important part is the slides I’m showing you today and um yeah my background is actually chemistry so I’m a chemist so and actually even polymer chemistry is my background so so um so I mean many instances are very
Close to our customers customers of Atlas material testing technology in regard to understanding what’s happening to the materials yeah just a little bit of housekeeping in the beginning um Everybody in the audience is muted but you can submit your question via the question bar on the go to webinar
Control panel today’s presentation and I will try my best should last about 55 minutes and um we hopefully we have time at the end to go through all the questions I will have an eye on the questions as we come in during the seminar and maybe answer them during the
Seminar but I will definitely have a time slot at the end for um answering the questions and even so um you have questions after the seminar you can always contact us um and ask you question related to correlation today but also to the other topics related to
Bevering and at the end of today’s presentation there’s also a short feedback survey popping up when when you close the go to webinar uh control bar and we would be happy if you could answer those to help you us to improve for future seminars yeah us is atlas material
Testing technology we are a global manufacturer of weing test instruments we also provide weing testing as a service outdor ring laboratory ring so we have test Laboratories in Mount Prospect close to Chicago in the United States and um in linen close to Frankfurt in Germany and um we also have
Atlas custen system very to larger scale solar simulation for wind tunnels but also for crash tests for example and we do Consulting we do client education and we are active in standardization and that’s actually mostly where I am active at Atlas material testing technology and by providing this support client
Education standard support Consulting support we hope we can support our customers globally and have a good relation to our customers globally and that’s why we spent all of these thought efforts in our client education program and we hope you like our client education program yeah you made it as mentioned
Already to the sixth part of the fundamentals of ring today we will talk about correlation correlation factors different type of correlation factors different type of Statistics or approaching correlation dealing with correlation and we will look go through some examples dealing with correlation yeah correlation in weing typically addresses the relationship
Between two tests or the performance of materials in two different test condition in two different test scenarios and typically you compare yeah change of material in different setups this can be artificial revering but this can all uh typically compared to Natural ring an environment which is close to
The end use environment of the materials to to be tested and correlation is des is describing the relation between the two different tested ups but you can also do correlation studies between different type of instrument different light sources different instrument geometries maybe also different instrument generation so correlation addresses the relationship between
Different tests the performance of materials the property change of materials in different test scenarios yeah but correlation as statistics and yeah with Statistics is always a little bit difficult I would say um for statistics is important that the data you use for the evaluation for the statistics are relevant data so
Relevant data means that the data has the same cause the same influencing Factor um so all um the data are cause and effect and just to give you an example from The Real World the real non ring world I would say um we have the correlation between the outside temperature and the
Ice cream V and actually in Germany and in Germany we like ice cream but only in summertime so the higher the temperature so more ice cream is sold so cause and effect and it’s obviously a good correlation how however correlation is statistics and um you can yeah do a
Correlation with any type of data either relevant or not relevant and here we have the comparison over several years between the points of the lowest scoring team in the German Football League which is hopefully not in Frankfurt which is my um Team um and this shows actually a
Relatively similar pattern to the annual Harvest of red cabbage in Germany so hm a good correlation statistically um between the uh lowest scoring points of the lowest scoring team and the annual harvested red cabbage is this real correlation yes it is it’s real correlation or pseudo correlation but the data are not
Relevant again correlation typically is a completely statistical evaluation of data and it’s not asking for the relevance of the data so it’s and you typically if you search long enough for fitting data sets you find something which fits and so you can do a correlation between but the reason for
For the correlation is completely out of context so correlation is just the quantitative the statistic evaluation of data the mathematical uh relationship between different test results in weing however it’s always important to also look at the relevance of the data in weing for example very often many materials have different Pathways for yellowing
Different mechanisms for yellowing and you always have to check if the same root cause is causing the same effect and um therefore it’s very important on the one side you can do the correlation study simple statistics but the best um way to approach correlation is you do an additional plausibility
Check to check if the data are relevant this can be done with some an analytical methods like FTR carbon Nile index and so on um but typically that’s not done typically ining correlation is simply done on appearance changes like yeah color change yellowing gloss loss and so
On and the relevance is very often yeah taking for granted I would say but if you want to do it 100% correct you also have to always look at the relevance of the data which leads me to a f first short poll I want to do today and actually I
Want to ask you which factors may have a negative effect on correlation what do you think which factors have a negative effect on correlation and actually I’m launching it right now and um you can choose now between um different answers first of all a short wavelength exposure below
The natural UV cuton can have a negative effect on correlation or a spectral distribution with high deviation from solar radiation high intensity High irance testing can have a negative effect or continuous exposure to light so neglection of dark phases relaxation phases or unrealistic specimen temperature so high temperatures um are
Likely to have a negative effect on correlation so what do you think I see questions coming in okay so actually it’s relatively evenly distributed that’s coming in let me maybe 10 more seconds um to collect the responses I see a answer in the chat coming in
Okay okay I close the poll and actually I’m not very good in showing the results of the poll actually can I share it yeah yeah I can share so most of you voted for short wavelength exposure or unrealistic High specimen temperatures and I must say yes you are right but you are all
Right all of these factors are actually known to decrees correlation to have a negative effect on correlation and I got a question comment coming in um which actually mentioned that um it’s all of them and it’s true it’s all of them so all of these factors all of these unrealistic um
Yeah um factors we using stress factors we’re using um are likely or can increased correlation and even more um I did not list it all of them and those factors are commonly known and already um stated even in standards like basic standards like iso48 92- one for Plastics or ISD mg1
151 um basic ring um these standard they mentions those factors which are known to decrease correlation to have a negative effect on correlation which are known to be unrealistic in testing however if you attended last uh week’s seminar on acceleration you might remember that these especially the first five of these
Um um factors or influencing factors are the factors which are actually used for acceleration to speed up aging to speed speed up up testing so and this shows um in Principle as soon as you accelerate you decrease the you’re likely to decrease you may decrease the correlation so you always have to find
The balance between acceleration and correlation um to get realistic results but basically the closer to Nature the more likely is that the results will correlate but you lose of course acceleration so it’s always again a balance yeah how to describe correlation and vering and there are yeah
Some different approaches I would say in weing to address correlation to quantify correlation and um a very simple way to describe correlation and we see this relative frequently in ring also in ring publication is just do a correlation statement based on pass fake criteria and you probably also saw this
Example before where Florida out of a ring for brown Poli the coings um is compared to UVA weing and UVB weing and for this test set up The Path F criteria was a color change of Delta e of three or great or greater and actually Florida weing and UVA weing they have the
Same um or in those two scenarios the same material pass tests so quoting number one two and so on the ones on the left side and quoting number nine and8 they fail in Uva in out of Florida so the same pass fake criteria um causes the same materials to
Fail and the same materials to pass the test conditions so there is a correlation between UVA and Florida ring if you compare Florida revering to U exposure um remember in last slide short wavelength exposure typically very unrealistic and yeah that’s shown by the data here actually it’s um the reverse
Order the material which Pass Florida pass UVA they fail in UVB and the materials which fail in Florida and fail in Uva um they pass actually UVB testing so a reversed correlation I would say but in general there is no correlation between UVB and um outo Florida ring in general
That’s a simple correlation based on pass fake criteria where some materials pass and some materials fail but sometimes you even find um Publications um claiming um sometimes correlation where all materials actually pass the tests and no materials fail the test there is one material shown here in
The middle which actually is below the path F criteria in this study but actually here the um outdoor varing counterpart was lost or not considered in the study so this could not be considered in the study in this example Ultra durable Powder Coatings in a brownish red oxide color have been
Exposed so different formulation have been exposed to Florida for three years and even longer and um to U be ring for 600 hours so it’s a very comprehensive study uh where this is taken from and this was one of the few examples where a correlation was found a good correlation
Was found between U testing and Florida testing because all of the specimen passed the test there was no failure however um this is another example for correlation based on a simple past F criteria but here we don’t have any differentiation between the different codings and in principle there’s no statement on causality and
Test sensitivity because the tests could not differentiate between the codings and as you might see by the residual Closs here the ranking is completely different between the two test scenarios but we come back to that later but pass F criteria is very simple to um do a statement on correlation based on past
Criteria but you actually need materials which pass and need materials which fail to do a statement here otherwise it becomes a little bit dubious I would say so it’s better in general to do also statistics and there are common two commonly used um statistics used in ring
Um one is the Pearson correlation one is a Spearman rank correlation and we will go through both methods the next slides and to look at examples of both meth methods in the next yeah 40 minutes yeah first of all the pieron correlation um assigns a a correlation coefficient with which describes um how
Good the correlation is uh the the piercing correlation coefficient typically lies between minus one and plus one while plus one would be a perfect correlation to identical data and minus one would be a perfect negative correlation zero would be completely statistical data and the pon uh formula which is
Used to calculate actually the pon um correlation coefficient is shown here and I’ve never calculated with this formula because this formula is actually embedded in msxl and we will look at that also later how to use msxl to calculate the Pearson correlation coefficient but first of all you need
Data to do a correlation and as mentioned in the beginning for a simple correlation study you need data from at least two data sets so from two test setups and you need um um also different criteria for the data for the evaluation methods so in Ving
You look at a set of materials typically in a test uh scenario and a test method and in this example we have um three different materials material one materials X and material n in a typical bevering test where we look at the gloss loss during the
Exposure and you either can test to a spec uh specified degree of property change this can be the pass fake criteria for example 50% of residual gloss that would Mark the end of your test setup and this would be your um evaluation uh or your um test
Criteria and the next step is what differs the different specimen to reach this gloss loss and that’s either the radiant exposure that’s better or sometimes also the test duration can be used to reach that time and that would be your evaluate evaluation criteria so aging criteria the time it takes or the
Radient Expos exposure to get to a specific property change and evaluation criteria is the time or the radiant exposure at this stage or you can do it another way and that’s what we most commonly see in weing you test until you get to a specific radi in exposure of a a
Specific time and you do a correlation at the end of uh the test duration the time it takes to reach the um specific radiant exposure and then you do can do a um correlation with the gloss at that time for as evaluation criteria and actually the best way to
Approach correlation to select data for correlation is you do a continuous exposure have a continuous recording of the gloss over the full exposure time and then you pick the time where you have the biggest differentiation between the different data you can do a simple standard deviation and where you have
The maximum standard deviation between the different data points that’s the best time to to actually do a correlation study this shows the biggest difference between the different test materials it’s the highest efforts method see see but it’s probably the best way to approach correlation however again typically it’s
Done more simple you test until until you get to a specific gloss and then do you do an evaluation of the time it takes to get to the gloss or the radiant exposure do you take to the specific loss change or you typically um also Expos to a specific radient exposure and
Then you just do a correlation study at the end point of that exposure that’s commonly done but again um to see the biggest differences however Al in our example here we use method a so we expose in two test scenarios test one and test two PR different materials the same materials
Of course in both test setups and we um do the exposure until we get to a residual gloss of 50% and then we do an evaluation with a evaluation criteria the r and exposure it takes to get to that specific um Closs loss for the different materials
And then we can simply do a correlation between the three materials and we can calculate actually um the pieron correlation coefficient again we come back to that later in more detail and it shows an almost perfect correlation however here we have three data points on only and yeah it would be
Even easier with two data points to just draw a line between the data and you get yeah a good correlation so and that leads me to the next poll how many different materials you think you actually um do you need for a correlation study let me launch the Paul yeah so what do
You think do you need at least three materials like in in the example or do you need at least five materials at least seven materials or some more the better or at least five but no more than 20 because when it’s getting too much sets of materials it becomes too
Complicated and it’s more likely that there are outliers too complicated maybe better um to stay with lesser okay I see answers coming in maybe 10 more seconds oh I actually see how many percent voted so I maybe allow 10 more seconds to okay let me close the poll and let me share the
Results yeah so we have some more the better uh leading and second at least threee and next come at least five so yeah I think um here in this case not all answers are correct I would say but all answers have some motivation in principle um let me hide
This and go to the next slide what’s important is the data uncertainty and in statistics to Pearson you can calculate the uncertainty based on the path you can have you can vary and with only three test specimen which you compare in two test scenarios the uncertainty is relatively high so if
You calculate for example a piercing correlation coefficient of 0.7 the uncertainty is plus minus 3 so the variability it’s actually between 04 and one so three is definitely not enough um to do a correlation study the uncertainty is just too high if you have more specimen the uncertainty decreases
So if you have at least five specimen um the uncertainty is plus minus 04 and that’s I would say an acceptable uncertainty it’s not perfect but it’s an acceptable uncertainty and the higher the number the lower the uncertainty and so in principle the answer the more the better is correct however with
Limitations and the more the better the more data uh you have the more reliable St statistics however it’s also more likely that the correlation coefficient is maybe not close to one maybe close to 7 and if you have a high amount of data this can still be a very good
Correlation so it depends also it’s not a um the pon correlation coefficient it’s not a um just a number you also have to look at the data and consider how many data actually the basis for this pearon corre correlation coefficient we saw the example with the fre data points and a good correlation
And here we have um different distributions um on um data with yeah one pieron correlation coefficient of one where all data are identical perfect correlation and correlation coefficients of9 9.8 actually you see it’s actually atively spread it out already but still I would cons consider a excellent almost perfect correlation
9 spread it out even wider um but still very good and so on to completely statistical a lot of data means very often that the correlation coefficient of 7 or so still means a relatively good correlation so a high number of data um um typically is better but you have can
Or you need to accept a lower correlation coefficient with a very high number of data and now coming back how to really calculate the peon correlation coefficient what you need actually so you need data sets data sets from two exposures and here we have a set of yeah some
Automotive um textiles interior Tex stes which have been evaluated according to the color change Delta e and there was a Florida exposure behind window glass for 12 different materials and after one year the color change um was evaluated and the same was done in a Zenon AR test
Instrument after 100 hours after 500 hours and after thousand hours and so you have the names of the test specimen the names of the textiles and the according the recorded color change in both test setups that’s all you need for a piercing correlation and in Excel it’s relatively
Easy you just have to type in is that uh in a uh cell that it’s equal to Pearson then you have to um include the first data set so here from Florida 16.8 to 3.8 so cell C11 to c22 followed by the second set of data and that’s in this example here the
Lab ring results after 100 hours from d11 to d22 and then you just have to close the um equation press enter and the um program is automatically calculating the um piercon correlation coefficient and yeah it’s 0.45 so not a really good correlation I would say some tendency maybe but not a good
Correlation but you can actually do the same calculation after 500 hours it gets a a little bit better and you can do the same calculation after thousand hours in the instrument and it’s actually 085 I would consider a really it’s a good correlation for this for 12 material so
There is correlation between one year Florida and lab weing um after thousand hours however as mentioned this is just a simple value it’s always recommended to also always look look at the distribution of the data do a plot of the data and compare how the data actually
Align and in this example we see yeah it’s relatively spread it out yeah but overall there is a clear linear tendency between the data so this can be considered a realistic um piering correlation coefficient why I’m this mentioning this because with pearon you have to be very careful because pearon Works only with
Normally distributed data as soon if you as you have some order in the data you can calculate but the meaning of a p and correlation coefficient is not it’s not really meaningful so it’s um here we have four different examples in a similar to the example we just
Calculated um I think it’s 11 data points um yeah relatively normally distributed that would be a typical Pon um suitable data set in B we have some order I have no idea what’s the background behind this scenario but um um in Z we have perfect correlated data and one outlier and inde
That’s very interesting that’s Sometimes some something we sometimes Z in ring we have one test which can actually different differentiate between different set up materials and another test where all materials are actually behaving exactly the same and one outlier and the critical part here if you just do statistics and do a pieron
Correlation coefficient calculations all of these data sets I’m showing here have the exactly the same Pearson correlation coefficient and actually it would only work for the normally distributed data so it’s be careful with piercon correlation and piercing correlation works best when you have similar materials which react similar to the
Test conditions in both tests to get a normally distributed h test set and also it’s also very important that you have similar sensitivity so do not include extremely sensitive or unsensitive materials because that would definitely spread out the data distribution and cause some line linearity which might not be realistic so similar material
With similar sensitivities and normally distributed data typically gives the most meaningful correlation results yeah let’s go into some examples um some are relatively historic but again statistics do not change do not need to be updated it’s just to V visualization to give you some examples
On how to use and yeah how to manipulate also a little bit um Pearson and later Spearman correlation yeah here we have a um um example where Automotive Fabrics in different colors different dyes have been tested um and actually two different types of Automotive Fabrics have been
Dyed in 31 different colors in um with different dispersed D in four different colors actually and also um an additional material was considered in the study um which was identical to matal B but with a foam backing so three types of fabrics a b and c and each in
31 different disperse dce and those have been exposed um to artificial and natural revering and the the evaluation criteria was the color change after a specific radiant exposure so here we have the exposure conditions um just more more for your reference so in Black Box underglass outo exposure was done with control
Temperature so where the temperature was prevented from from overheating um and set to 95 degrees during the daytime during the exposure time and also a artificial setup a c Arc test setup was chosen which uses a high IR Radiance about three times higher IR Radiance and the typical um IR Radiance
Level we use in artificial weing and also at relatively high temperatures so one exposure conditions using the natural sun and one exposure conditions using artificial solar r ation and the test has been done up to a specific radiant exposure with intermediate evaluations of course and here we have the results
From the outdoor exposure we still we see color change for in here for two dice two Fabrics uh two dice in for all of the fabrics and we see a relatively linear fading in the outdoor exposure and yeah also in the Zen Arc exposure we see a similar actually Behavior after
The different exposure periods and the next is to do a plot of all the test specimen of all the um yeah 93 formulations different specim which are considered in the study and we do a um Pearson correlation coefficient calculation of all of those data and overall the p and correlation
Co I is 0. 52 which is yeah not necessarily a good correlation however if you look at the data sets for the different materials um colored in different colors you see that the different materials are actually yeah behaving a little bit more linear than the um overall
Setup and um so material A and B yeah different chemistry maybe so it might make sense to do a separate correlation between the two of those and material B and C again the same fabric but C with a foam backing and a foam backing causes higher temperatures and there might be a
Slight differ between the two test setups typically Z Arc exposures are continuously at the maximum temperature so very hot obvious the same amount of Rance so and while in a realistic more realistic outdoor exposure um you have maybe the continuous 95 degrees but you have less Radiance in the daytime in the
Morning and the evening so there might be a systematic difference between B and C so it makes sense to separate the two sets also and if you do actually a um evaluation of all the independent Fabrics you get much better Cor corelation coefficients so because the test specimen behaved differently to the
Stress factors so it’s yeah appropriate to to several correlations and to avoid a general correlation in that sense so there is a very good correlation for all of those now not perfect in all cases but only for the individual Fabrics but not for all Fabrics together so and
That’s a general guidance if you compare huge set of data different materials different polymers different Fabrics different fibers different type of Coatings sometimes you find the overall correlation um maybe a little bit yeah not nonperfect but if you do it either by polymer type or maybe by color you
Might get a better correlation for the individual um yeah groups you can for and that’s always also very helpful ful if you have huge amount of data yeah a very comprehensive correlation study was done yeah also several years ago by Dr Scott Crump and at that time uh Dr Scott Crump was
Director of a company called Co Composites and they actually acquired a lot of different shil coding companies and all of those sh code companies had their specific individual test method and they once and for all wanted to find out which test method gives actually the best correlation to Florida Outdoor ring
And we did a very comprehensive study on J codes in 10 different formulations and each formulation in three colors so red white and blue probably an American study and so 30 different specimen and the looked at several different um um exposure me methods and they were looking um
Continuously um after specific steps at the color change and the gloss loss of those specimen they looked at Florida auto ring that’s the rence they looked at UVB ring UVA carbon Arc revering and different type of Zenon instruments um a larger cenon instrument CI verom meter in this example and a small cenon
Instrument uh Sun test CPS was used so with a relatively limit control and they included also um natural accelerated um testing in the comparison so the amaka devices the solar concentrator devices with nighttime spring have also been used in the study and overall they did did a
Evaluation on the gloss on the um color change of all of the specimen and the question was which of those um test scenarios gives the best correlation to Florida weing and overall um looking at the gloss and the color change UVB did not show good correlation UVA a
Little bit better Carbon Arc also not a very good correlation especially when it comes to gloss maybe a little better when it comes to color change um SE on Arc devices the the smaller the AR device with limited yeah temperature control limited humidity control um really in
The middle range for the um larger um yeah Zenon verom meter in that example um showed the best results actually of the artificial methods and overall the best results actually could be we achiev achieved with the m Aqua with the solar concentrators not for white um the right
Color change um shows a little bit discoloration which was a little bit off but the other colors showed the best color change yeah they did also a cross correlation between the different methods but I don’t want to go into detail here so overall and you probably saw the slide also in the
Acceleration um presentation um based on these statistical methods they found out that the they can get a balance between acceleration and correlation by mostly realistically simulating the revering appearance the revering effects so realistic sunlight realistic temperatures control temperatures and artificial artificial ring give the best correlation and also
An acceptable acceleration so some more realistic the more likely it will correlate yeah however not all materials behave the same not all materials behave linearly so typically what’s happening and that’s actually happen very often is that the ranking is changing during the exposure here we have A um2 would be the corresponding standard today and we saw that um in this set of codings the Delta e is actually changing the ranking during the exposure of 3,000 hours so in the beginning the green material C it was not really a green material it’s just shown here as green
Material C shows the fastest aging but then it’s the color change is decreasing material a is almost linearly decreasing D is linearly decreasing B is the best in the beginning but then suddenly the um the fading the color change is actually in increasing so the ranking is changing continuously in the
Exposure and the best time for comparison actually to Florida in this example would be for the instrument exposure after 2,320 hours where we have the same more almost the same ranking as in the Florida exposure so it’s important to know when you have the best ranking between different exposures that
Where Spearman correlation comes into play and Spearman correlation it’s actually relatively similar like Pearson correlation it assigns a correlation Factor correlation coefficient and again this would be one when it’s perfect correlation and zero when the data are completely statistical and Spearman is mostly useful to find the best time to compare different data
Sets and the formula which is used to calculate the Spearman rank correlation is unfortunately not embedded in msxl so you have to actually calculate the Spearman rank correlation coefficient yourselfself however you only have two variables you have n as the number of pairs and you have D the different
Ranking and the sum of all the different rankings squared and that’s all you need to cut calculate the Spearman rank correlation coefficient but we will go through that with an example and also a data calculation based um on six codings where the clo was evaluated and here we see the Aging in a
The Arc exposure for 1,400 hours with intermediate evaluation each 200 hours and the question is when do we get the best correlation to Florida weing to one year Florida and we start with the evaluation for um 400 hours in the instrument and for both scenarios like for Pearson we need the um evaluation
Criteria which is the Closs after the exposure we have the Clause here for material a b to F uh after one year Florida and after 400 hours in the instrument and then you simply have to assign a ranking from the best which would be material D in Florida second
Best material e third material a and so on and you do the same ranking for the device exposure here you see it’s it’s a different ranking and the next step according to the Spearman correlation formula is you have to calculate the difference in D it doesn’t matter which way you make
It which way you calculate the differ because then you have to calculate the square out of it and sum up all of the uh squared differences and that’s this part of the Pearson uh Spearman correlation um formula then you have n n is the number of specimen the number of
Materials you have in the study which is six and actually it’s a bad example because this six shown here in the formula is part of the formula is not related to the number of pairs it’s always a six no matter if you have 10 or 20 um specimen under
Consideration and that’s all then you can simply calculate the Pearson cor Spearman correlation coefficient and it’s actually after 400 hours the Spearman correlation is minus 4 4.43 so it’s actually a yeah more or less bad negative correlation so definitely not the best time to compare it to Florida Ving however you have
Other data sets you have 600 hour 800 hours and you see the ranking is changing so you can do the same calculation for each of those exposures just assign the ranking and do the calculation of the Spearman correlation coefficient and then you see after thousand hours in the instrument you get
A Spearman rank correlation coefficient of yeah8 you don’t see it but it’s 08 around 08 then it’s dropping again so and that would be the best time to compare Florida Outdoor weing to the artificial weing to the Zen Arc exposure thousand hours in the instrument and one year Florida shows the best comparable
Ranking of the materials yeah we have another example I will not go into detail here it’s very similar specimens are exposed to a specific until they achieve a specific color change in Arizona and in artificial wearing and then um the evaluation criteria was the time it takes to get to the specific color
Change and then the ranking was assigned you get this in your materials yeah another correlation study on ranking of different materials is done here a very yeah small set up only four materials two printing inks in two uh in two colors so four materials overall I just showing this to you um because
Spearman has another benefit over Pearson because it can use different evaluation criteria for the statistics and here in the in an outdoor exposure those for printing in have been exposed until a color change of 30 was achieved in the device the color change was measured after 48 Hours of exposure so
Completely different approach in both test scenarios but if you assign just a ranking um from the exposures and a floresent UV B exposure was done here a Cen Arc exposure was done here a UVA exposure was done here and a Arizona and a Florida exposure you can simply assign
Rankings and from based on the rankings you can actually calculate the span rank correlation go even though you um have different evaluation criteria but um briefly coming back to the example I showed you in the beginning the example showing good correlation between UVB weing and Florida weing yeah um done regularly
Based on pass fa criteria however with pi Spearman you can easily assign a ranking from the best performing in the one exposure to the worse performing in the other exposure you can just yeah number it by the residual gloss and then you can calculate the difference in the ranking
The square and the different and you can easily even without knowing the Absolute Data you can do a Spearman rank correlation and actually um Spearman says based on the ranking it’s a very poor correlation which is um shown here so no correlation between Florida ring and UVB ring just
Based on the way to approach correlation so it’s very important if you talk about about correlation you know which statistic was used to um determine the correlation coefficient because this also has an influence on the evaluation what’s better to use Spearman or Pearson or both as mentioned in the
Beginning Pearson works for normally distributed data as soon you have outliers um it’s completely screwing up everything while Spearman is not so sensitive to outliers and typically Spearman correlation coefficient is bigger compared to pearon correlation coefficient if that’s not the case um then you don’t have a monotonic
Correlation anymore it does not preserve the given Order anymore and then typically something’s wrong or something’s off and something has to be considered if the piercing correlation coefficient is bigger compared to the Spearman correlation coefficient and in this example we have here on the right side a perfect correlation on the left
Side statistical data and actually on the right side is the same data and one outlier which makes it to a yeah linear correlation but it’s not a real linear it’s only lar linear because of the outlier yeah so you have to sometimes select the data by the sensitivities of
The materials especially if you consider color change color change is different for each polymer it’s is different for each color so and here yeah just an um yeah theoretic example for Po polycarbonates and polypropylenes both can show yellowing but the root cause for yellowing is can be different the sensitivities in
Different tests can be different however if you do a correlation overall you get a perfect correlation because the data sets are far away from each other and if you even consider a completely different material PVC different causes leading to yellowing you get a completely off correlation um by the different groups
So if you do a correlation by material you might not get the best correlation coefficient but you get a realistic correlation coefficient for the individ individual group and here’s also an example for what plastic Composites um from a federal funded research um project in Germany from the frown frover Institute
For wood research and they looked at different formulations of wood plastic Composites with different amount of stabilizers and it was relatively interesting that they found overall a good correlation between an Zen Arc test according to ISO for 892 dish uh two and outdoor ring in brown trike in Germany
And however the correlation is only uh good because if you consider all of the materials behave completely different polyethylene is much more um stable in this study shows less color change compared to PVC compared to polypropylene and so just because you have completely different materials it shows good correlation if you look at
The individual materials yeah I would say the correlation is actually relatively limited to yeah completely statistical and if you look at the numbers of the stabilizer content um in the different formulations um it’s surprisingly that it’s not um actually um yeah um depending on the amount of stabilizers used so it’s relatively
Sensitive here so it’s yeah not um the best to do a correlation study for all of those materials and it’s yeah no real statement can be make made here on um the overall correlation in this study yeah correlation is on data selection correlation is statistics and wincon Churchill once said the only
Statistic you can trust are the ones you have falsified yourself and the same is true for correlation you need to somehow look at the data and in the first uh worst case manipulate the data if we have reasons for this so reasons for manipulation for selection of data can
Be you have different type of materials maybe different colors so you do correlation only for the specific type of materials or you have uh materials which behave differently to different specific stress factors so thicker specimen for example um show higher temperatures because of the insulation and that’s a general um tendency of
Thicker specimen you might separate fix specimen from fin specimen and do the separ correlation separately and you can remove outliers if they really screw up and you can yeah either explain or not completely explain it but if we screw up everything you have to include them in the report report but for the
Correlation it’s sometimes advisable ible to remove the outliers yeah have one final example um so far we have correlated different exposures materials in different exposures however it might not necessarily um be appropriate typically a correlation factor is similar like an acceleration factor it’s related to a specific
Property change so there can be for example good correlation related to color change but B correlation related to gloss loss so a correlation Factor corresponds to the set of materials into the specific property change of the set of materials however there can be cases where different uh property changes have
This can have a realistic correlation with each other and that’s the case when you have the cause of a property change and the results of the property change correlated to each other for example the residual strength of a typical polymer film is decreasing with continuous exposure um and simultaneously the
Oxidation rate the carbony index is increased increasing with the exposure oxidation means change so the oxidation is actually the root cause for the uh reduction of the Tensai strength so therefore here there can be really correlation a real correlation with the with relevant data between the different
Properties um carbon index by ftrr and um teni strengths between the polymers so and that’s a principally a realistic correlation which can be done here and over a wide range of different polymers in a study there was found that there’s a good correlation a good negative correlation because the higher um the
Spearman rank correl uh the higher the carbonal index the less the residual strength the less the elongation at at break and this was evaluated by Spearman and showed again uh almost perfect negative piercing correlation Coe spe correlation coefficient for a huge amount of different types of polypropylene formulations so causality
Is given and the good thing is here a destruct destructive criteria like elongation at break can be replaced by a nondestructive method the Caron index yeah again to summarize a compromise must be made between correlation and acceleration the more the closest to Nature typically so more likely it will correlate you have to
Consider the test conditions um related to the specific sensitivities of the materials generally the more you know about the Aging of the materials the better you find the the easier you find the balance between correlation and acceleration um correlation factors um are best done um using the statistical
Methods and in principle you always need sensitive materials which show some sensitivity that you really know that the um test conditions cause effects on the materials in general test recommendations for correlation studies and for many ring results now at the end of ring testing now at the end of the
Serious in principle for vering testing and especially for correlation studies it’s always advisable to include materials you know control our reference material and always also it is recommended to include materials which will will fail which will show the test actually causes effect to the materials and for correlation studies
Use at least five different material sets in different exposures the more the better use similar materials or groups of similar materials for the study so same polymer similar formulations maybe similar amount of stabilizers similar color so that it’s not linearly spreading out by the setup of the study
Already PL generous in the amount of specimen you’re preparing it’s always good to have some as back up backup if you want to do additional correlation studies in the future and have you still have test resmen it’s much better than have new formulation then you in principle have to restart everything
Again do intermediate evaluations so this G gives you the development of the Aging maybe a change in ranking from time to time and um you can be sure that you do not miss a point of time where we have some Maximum difference variation between the different type of
Materials and yeah use at least two different test methods for correlation studies but you can easily use more and um in a more General correlation studies and from each comparison you learn something about the um performance of your materials and the Rel reliability of your study and yeah in the end
Correlation study is takes a lot of time but it in the end gives you confidence in your test method if you know how it’s correlate to your material to your product and the the real world performance and if you start with a new formulation and you develop a new
Product and you already know on your test conditions on your test method how the correlation is this gives you much more confidence in the performance of your product than it would be without a appropriate correlation study yeah that’s it from my side um you probably saw that slide
Already where you find find us our or find our information on our home page and um yeah with that that’s it I don’t see any questions coming in right now I will stay maybe for five more minutes if there are some questions but if there are no more questions thank you for
Attending our seminar today um I hope yeah you learned something through the series and currently we are also um having basic seminars for Asia for Europe in the morning hours in the European morning hours so however starting I think in December or in January the latest in January we will
Have also again seminars um in yeah the American time zone and also basic seminars again and also an additional topics yeah a lot of Statistics here it’s in the evening so everybody is probably exhausted by now so I don’t see any questions coming in yeah thank you
Again have a great day have a great evening and hope to see you somewhere maybe in person thank you and goodbye