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I am trying to develop a morphophysiological dormancy breaking protocol for some forest tree species. Which treatment is better to break dormancy viz. Stratification of seeds for a long duration (months/ Years) or Move along experiment?
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“Women are in back seated in their family in south Asian countries due to extreme gender stratification and men take the opportunity to control them using their male dominant rural culture. Rural men enjoy their muscle power over their women to prove their supremacy. Violence against women (VAW) starts from the family and women are in silence in most of the cases to avoid further familial disharmony as they have no place to go without any earning opportunity. Empowerment can inspire them more to find their own identity to protect themselves by raising their voices against the violence”.
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Empowerment of women can rid them of spousal violence, but not all empowered women can stop domestic violence even by showing resistance against abusive husbands. In the Indian sub-continent, patriarchy excludes any protesting women socially. Thus it silences abused women.
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I am performing a systematic review of the literature and the data is stored as a table including the fields:
DISEASE, VIRUS, TISSUE, ASSAY.
I made a random effect model for each of the first three fields (that is: test the OR for disease x upon infection with virus y on z tissue). But further stratification by assay would be (a) cumbersome (too many groups) and (b) diluting (too few articles into each group).
Is there a statistical way to account for possible bias due to the assay?
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Is confounding factors meaning contributory factors? I am doing a systematic review on occupational health issues. Have you completed your draft to submit?
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Systematic reviews and meta-analyses of diagnostic test accuracy usually pool sensitivity and specificity estimates. However, for clinical/patient-care purposes, positive and negative predictive values (PPV and NPV) are arguably more useful.
Is including PPV and NPV as meta-analytic pooling outcomes sensible? One potential argument against this that I can think of is that these measures are influenced by disease prevalence in the studies that report them (unlike sensitivity and specificity). However, a potential counter-argument to that is some sort of stratification by pre-specified prevalence ranges can be performed.
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You are right that the prevalence of a condition in the tested population will have an important influence on the +PPV and –PPV. However, you can calculate another informative statistic – the clinical likelihood ratio (positive and negative). This is the effect of the test on the likelihood of the person having the condition. It simply compares the odds of the condition pre and post test. A positive test with a clinical likelihood ratio of 10, for example, means that the condition is ten times more likely to be present if the test is positive. And a negative likelihood ratio of 0·1 means that the test is only a tenth as likely to be present if the test is negative.
Likelihood ratios are based on odds, so they generalise across prevalences in a way that predictive values don't. This might help you deal with the prevalence effects.
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Five environmental variables were used as predictors in MaxEnt: sst, sss, thermocline depth, stratification index, and distance to shelf edge. Where we can download these from satellite data freely?
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Interesting question and i am also interested to know about those data Yaoyao Zhang
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What are the measures used in stratifying tree canopies into dominant, co-dominant, intermediate and suppressed in a natural Forest.
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I'm currently working with event history data studying how long after implementation countries abolish certain policies. Regarding the policies I also have an index on how far the countries went with their policies ranging from 0 to 100.
I wanted to control for this, in order be able to control for their point of departure. However the coefficient violates the proportionality assumption.
Can I stratify for the continuous variable of that index? I understand it so, that this would allow every country to have a different baseline hazard with respect to their point of departure. Playing around with the data this didn't produce an error.
Could anyone tell me if I can trust these results or if I have to categorize the variable first?
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The PH assumption relates to the entire model, including all predictors and covariables deemd interesting or relevant. "Restoring" PH by irgnoring or removing a covariable is not ok, as it likely demonstates that the inclusion of the covariable is relevant because it explains so much of the variance in the data that deviation from the PH assumption becomes clear.
If you have non-PH, you might start investigating if the effects of the predictors/covariables in the model are not linear. If this is not successful, an appropriate partition of the time axis might be the key (early effects are different from late effects, but the hazards are proportional within the early as well as within the late phases). If this also does not help, you might really think of stratification (what, by definition, is possible only for categorical variables). I don't consider it a good idea to categorize a continuous variable just to be able to use it for stratification. But if nothing else works, this might be a last rescue. But I would then check if the violation of the PH assumption really does more harm than the categorization of the continuous variable.
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To analyze the thermal stratification of solar hot water storage tanks using numerical simulations, is it possible to apply the turbulence model? What are the parameters of using the model?
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In my opinion, it depends on the model that you are going to develop. Turbulence is a 3D phenomenon caused by inlet jet mixing, plume entrainment, heat losses, etc. Using CFD, of course, you can model the turbulence. However, it is not the case for one-dimensional models since temperature gradient is only considered in axial direction, but turbulence should also be considered in radial and angular directions. Followings are papers that give some hints to solve this issue:
I hope this reply helps!
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There exists an inter-individual response to dietary intervention due to which a sub population may benefit more than others. This underlying variability can be attributed to genetics, age, gender, lifestyle, environmental exposure, gut microbiome, epigenetics, metabolism nutrition derived from diet, and foods. The inter-individual variability to treatments and nutritional recommendations is largely reflected in biomarker values.
How can we screen approproately to stratify patients prior to the study?
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Hi Laura,
Conducting a clinical microbiome experiment warrants careful attention to numerous factors, therefore first and foremost considerations should be given to standardising technical factors and sample processing (e.g., reagents, primers, sample storage, etc.) to reduce associated variation.
Following that, you may use stratification tool by potential confounders to resolve differences in microbiota between groups of interest that might otherwise be masked by a confounder effect (e.g., age, sex, diet, lifestyle factors, alcohol consumption and medications, etc.).
Here is an article published in Nature that you may find useful:
Disentangling type 2 diabetes and metformin treatment signatures in the human gut microbiota (Forslund et al. 2015)
However, using only the stratify tool may not be adequate to screen your patient population. Possible results may include the proportion of patients identified as matching specified requirements at high-level among patients who really match (true positive rate) and the proportion of patients identified as low-level matching that actually matched howsoever (false negative rate).
A good read on stratify tools:
Confounding in epidemiological studies
Therefore, you may use longitudinal studies to control confounding factors and allow for the assessment of community stability.
Here is an article published in Nature that you may find useful:
Dynamics of the human gut microbiome in inflammatory bowel disease (Halfvarson et al. 2017)
I'm not sure what type of study you want to design and stay within the budget, but I know that the progression of the research helps determine which design is most appropriate. Hopefully, you will find this information useful to make meaningful choices.
Warm regards,
Chris
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Hi. I am trying to help provide some rough advice for selecting amongst alternative sampling designs to measure bird density or abundance. The surveys are short-term in duration such as for impact assessments and habitat association studies. In this instance, I am looking at rough guidelines for how to select where to sample (survey design) and not how to sample (survey method). Attached is a rough first draft of a decision tree (see attachment) to select between various forms of study design ranging from conducting a census to spatially balanced sampling & stratified random designs. Do you have thoughts and suggestions? Is neglecting to include simple random sampling a fatal flaw for example? If so, where would you place it? Of course, the main advice will be to consult with a biostatistician, but hopefully this (with come accompanying text and references) can provide some rough guideance and be a starting point for that conversation. Literature, debate and suggestions welcome and appreciated.
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Steven L. Van Wilgenburg I agree with your last post. Have you tried searching the relevant literature?. If I were doing it I would do it as I advised in a recent post. Divide you total area up into strata and take a simple random sample from each stratum. My post here should help:
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We collected data on the natural regeneration of Balanites aegyptiaca by using stratified sampling design with three levels of stratification, so which model can be better for data analysis?
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GLM is more flexible, so use that
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It is a well- known result of population genetics that admixture, heterogeneity, or stratification in a population can make it impossible to draw valid conclusions from a conventional case-control study, since these conditions (”population structure”) can give rise to substantial association even for unlinked loci.
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Thank you
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Hello,
I have a dataset with several independent variables (IV) (possible predictors: AFADR, FAI, ALT, BMI) and an outcome variable (OV: INS). In a hierarchical regression model BMI results as a confounder of AFADR. Therefore I stratified for BMI and then interpreted the real odds ratio of AFADR for the two different stratified groups (BMI < 25; BMI > 25). However, the BMI is also a predictor for INS. But how can I interpret the real odds ratio of the BMI? Because when analyzing it together with AFADR in one model, both IVs influence each other.
Thanks for any answers.
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hierarchical regression uses a liner model I am not sure if this is the right model to address your problems. Moreover from your question they rather appears to be covariates who are influencing each other. I suggest you use multinomial logistic regression using AFADR as covariate of BMI or vise versa, alternatively you can define interaction between two as additive, multiplicative, inhibitive whatever it is while building your model.
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Sample size calculations for my survey yield n = 385. If I proceed to geographical stratification (5 regions), do I need to mutiply 385 by 5 strata? I was told so where I study but could not find a line / reference supporting this, on the contrary (like James R Knaub wrote 1 year ago « If you stratify you will likely be more efficient - i.e., need a smaller overall sample size - but remember that inference for individual strata will not be as good as the overall level» https://www.researchgate.net/post/My_total_sample_size_is_1068_Do_I_need_to_distribute_more_than_1068_questionnaire_or_distribute_exactly_1068
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Hello ,
If you've already determined that a simple random sample of N = 385 would be satisfactory for your research goals, and you've decided to stratify by region, then you do not need 1925 (385 x 5) cases; the 385 will suffice. To the extent that geographic region helps explain variance in responses, you could actually reduce the total N and still have the same precision for estimating the overall population parameter of interest as with the simple random sample.
Here's a pretty standard reference that you could use to support this argument:
Cochran, W. S. (1977). Sampling techniques (3rd ed.). New York, NY: Wiley.
Good luck with your work.
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remote sensing for water layers temperature evaluation, thermal stratification
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Best direct measurements for the temperature is by using PLT (production logging tool) that gives fluids velocity and temperature in multiple layers.
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I would like to find out the answer for the above question urgently
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Hi
I am working on thermal stratification of dam reservoir. Could you please help me about choosing the right turbulence model?
K-epsilon
k-omega
LES
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K-epsilon model
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Our paper published in the Journal of Clinical Epidemiology clearly outlines why doing this is not just inaccurate but actually wrong because it introduces bias. This is regularly done and advocated by Cochrane [1]. I think this erroneous practice should now stop - see link to the paper [2]
[1] Higgins JPT, Altman DG, Gøtzsche PC, J€uni P, Moher D, Oxman AD, et al. The Cochrane collaboration’s tool for assessing risk of bias in randomised trials. BMJ 2011;343:d5928.
[2] Stone J, Gurunathan U, Glass K, Munn Z, Tugwell P, Doi SAR. Stratification by quality induced selection bias in a meta-analysis of clinical trials. J Clin Epidemiol. 2018 Nov 17. pii: S0895-4356(18)30744-3.
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Thanks Godfrey. Even a sensitivity analysis by quality seems questionable based on our results in the paper. So the Cochrane recommendations do not seem to be valid and we should attempt to bias adjust using methods that include all studies.
Thanks for reading my book :-)
Regards
Suhail
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Researchers in sociolinguistic variation sressed on the importance of original regional dialect ORD as the a sentimental social factor when considering sampling and data collection. This importance stems from the fact that samples in any given study should reflect the real stratification of the speech community under study. In other words, samples should be stratified and hence be pure when things come to dialects spoken in that community. And that purification will ONLY be attained through taking this factor into consideration. I am in the process of conducting a study where I will argue that though ORD is very important, it doesn't guarantee the purification required. Instead, another yet more important factor is what researchers MUST take care of besides the ORD factor. That factor is the amount of contact. To sum up, ORD alone is not enough. It should be twined and/or followed by determining the amount of contact for the sample.
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By amount of contact, I mean the degree of cross-linguistic and cross-dialectal exposure.
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I am studying climate change impact on thermal stratification of Sabalan dam reservoir, Ardabil, Iran. I'm not sure which model or scenario to use. As you know there are a wide variety of models to employ for this purpose. Is there like any way that I can figure out which model is more accurate to predict climate change in this region.
38°32'32.3"N 47°57'58.0"E
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Dear Saber
Usually, two scenarios RCP4.5 (low emission) and RCP8.5 (high emission) are used to predict climate change impacts.
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I have a landuse classification and want to do an external validation of it (which is not based on the training data).
Because 1 of my 3 classes is really rare, I cannot safely implement a random sample for the validation.
How do I pick a number for the sample of a stratified validation? Does a stratified validation need to be proportional (between the strata), or can I use the same sample size for all stratas?
As my rare class is also my most important class, I do not want to under-represent it, but I am also afraid to create some bias without being conscious of it.
And I cannot find literature that gives a clear hint or maybe I just got confused about that topic. Is there any fixed that should be used? Or is there a proportion between all classified pixels and the amount of pixels that have to be validated per class.
I am thankful for all hints or literature advice!
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Thanks also to you Ajit kumar Roy
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I am studying thermal stratification effects on a pipeline using CFX (ANSYS) and then compute the thermal stresses using transient structural analysis. This is what I plan to do:
1) Apply an arbitrary force on the pipeline (IN STATIC STRUCTURAL)to compute stresses and continue reducing the element size till my solution becomes grid independent.
2) Compute results using CFX
3) Compute thermal stresses with structural analysis.
As I am involved with two different domains of ANSYS, do I need to carry out mesh independence for these two domains separately or just doing it in STATIC STRUCTURAL(point No. 1) will do the job for CFX as well?
Thanks.
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Indeed you do. Generally speaking, the mesh required to obtain independence for a FEA model may not coincide with the mesh required to obtain independence for a CFD model. This is due to the different scales of behaviour. For example, if you apply a static pressure load to a basic 3-D rectangular body, the FEA mesh independence will occur relatively quickly and easily. If you then wish to use this pressure load to develop a fluid-flow through this body, and investigate the development of the boundary layer and transition from laminar to turbulent (for example), the FEA mesh (even though achieving FEA independence), will be very inadequate for the CFD simulation and you will need to achieve CFD mesh verification separately. Hope this helps!
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My current research compares the detailed performance of two widely used hydrodynamic models. Our study include more than one thousand simulations by each model to see how the stratification dynamics is influenced by the future climate warming and reservoir management. Could anyone recommend me some journals for submission?
The impact factor should be around 3 to 4. Because my research mainly focused on the water temperature and didn't include other ecological indicators (e.g. nutrients, oxygen and algae), I supposed it may not be appropriate to submit to the enviromental journals (Science of the Total Environment, Journal of Environmental Sciences and so on).
Any suggestions will be highly appreciated! Many thanks!!
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Hi Chenxi,
depending on your focus, you could try some of the climate journals (such as climatic change), or limnology journals such as Limnology and Oceanography. If your paper is quite quantitative, you might consider Water Resources Research.
it would also be a good idea to look at where the papers you cite in your introduction and discussion were published and consider submitting there.
finally, publishing is getting more difficult, if you have the bad luck to have your submission rejected from the first place you send it, try to address some of the reviewer comments and submit it somewhere else.
Martyn
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I am looking for some insights on this. I am doing an analysis that considering a binary dependent variable (metabolic syndrome) and a continuous independent variable (muscle mass) according to marital status (married/unmarried). My raw data has around 2 thousand observations, however after the marital status stratification married people were around 1700 observations and just 300 belonged to the unmarried group. My statistical analysis showed significant differences. However, can I rely on this results, or the low number of the unmarried group could affect somehow in the statistical outcomes? Thanks in advance.
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How did you analyze the martial status differences? If you used a regression analysis with an interaction effect (i.e., muscle mass X marital status), then there is no problem with the difference in the group sizes.
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I am trying to determine the best way to randomize my patients for a study I am conducting. There are 2 experimental groups and a control group. I work in a mental health setting so being aware of their diagnoses is critical as I dont want too many of 1 type of diagnosis in 1 group and another in another giving skewed results. I am trying to determine if the best way to do this is through stratifing my patients or doing a cluster randomization or strictly doing a single randomization and doing an anova on each group to make sure that they are equally balanced. Something else to consider is that I work in a 17-bed unit so my n for each group on a weekly basis will always be small. I plan on conducting my study over the course of 6mos weekly to increase my overall N but want to make sure that I am able to divide up my patients as evenly as possible. Thank you in advance for your thoughts!
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Thank you for your response!
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I'm thinking that stratification is important. Even if treatment A has the same effect as treatment B, there may be a diffierence in outcome from the time effect. Could those who are given say the intervention in the first part of the study respond differently to those in the second part (accounting for washout)? This being due to a psychological effect of when the intervention was taken.
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Psychological effects can occur at any time point in a trial.
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Hi everywone!
I'm trying to solve a kind of mystery in the lab... Every time I do a comassie-blue staining of polyacrylamide gels they have two different brackground color intensities separated by a perfect line (attached picture). When I destain the gel, the differences dissapear and the bands in the less stained part seem to have been stained correctly.
I think it's a kind of stratification of the gel that affects the staining process but I don't know why this is happening.
Do you have any idea?
Thank you in advance!
Best wishes,
Paloma.
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I also think Cyrille is right. The pH of the stacking and resolving gels are usually 6.8 and 8.8, and those are shifted by the electrophoretic front. So just out of interest, you could stain a gel without running it to see what happens.
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I want to understand how the meteorological phenomenon is affected by the factors used in the composite stratification.
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A simple example with cdo.
Let's assume you have a monthly netcdf data of OLR from 1970 - 2017 named "olr.mon.mean.nc". And your task is to isolate wet years (1980, 1995, 2002) and dry years (1977, 1982, 1989, 2015) for only June - September (JJAS) months and perform a year mean (i.e. mean of JJAS for each year).
##code
cdo -yearmean -selyear,1980, 1995, 2002 -selmon,6/9 olr.mon.mean.nc OLR_wet_yearmean_JJAS.nc
cdo -yearmean -selyear,1977, 1982, 1989, 2015 -selmon,6/9 olr.mon.mean.nc OLR_dry_yearmean_JJAS.nc
OLR_wet_yearmean_JJAS.nc and OLR_dry_yearmean_JJAS.nc are the composite for wet and dry years respectively.
For more, read the cdo manual
cheers
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I am trying to get uniform growth of tomato seeds with more than 90% or 100%germination rate within 4-6 d.a.g for in vitro growth. The germinated tomato seeds should have similar growth rate with the same radical or root length. Currently I am using 20 mins sterilization in 4% bleach and 10 mins in 20mM HCl, rinse with sterile water several times. However, some genotype gave 100% germination rate and some with less than 50% germination rate after 4- 6 days. With more than 100 genotypes what is the best way to get uniform growth with 100% germination rate for every genotype?
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I have mentioned earlier that different genotypes may need different temperature regimes for germination. You can make grouping of genotypes with respect to behaviour on germination to varying temperatures. But if you want to synchronize germination, seed priming may help.
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I have recorded N, Mean, SD of a variable (X) from N studies. The size of ni varies from 4 to 784. The mean ranges from 22 to 175 and SD ranges from 0.7 to 134.9. With stratification over ni. I see that X follows normal distribution. But the distribution of SD and CV are not following Normal distribution. Both, SD and CV are positively skewed.
Now I want to have a good estimate the mean of that variable under above circumstances. Also I wish to estimate the SD of new estimate.
A variable can be characterised by Mean and SD when it is normally distributed.
In my case, the mean of means from several studies follows Normal distribution but the SD from those studies do not follow normal distribution.
How to handle this situation when my interest is to have combined estimate of mean and SD of variable? If weighted mean is required then How?
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It is required to destroy the stratification and create turbulence inside water mixing tank. This is done by inserting water jet inside the tank. How can the axial velocity at the nozzle exit be measured experimentally?
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We employ microjets to disturb the vortex zones in nozzle flow. There are many articles, You can go through these papers;
  • High-Fidelity Numerical Simulation of a Chevron Nozzle Jet Flow
  • Active volume of mean circulation for stirred tanks agitated with axial impellers
  • 3C PIV and PLIF measurement in turbulent mixing
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stratification and minimization are two randomization options to achieve balance in terms of covariate baselines in small RCTs. in recent years, researchers seem to have favoured minimization, particularly for sequential allocation designs with a high number of covariates. in short, the method involves the choice of some imbalance criterion and then sequentially allocates each new individual to the study arm leading to the smallest new criterion value. this allocation can be done purely deterministically or involving some element of chance.
our question is if the approach could be simplified when the assignment to study arms takes place only after inclusion of all participants is completed. our idea is to use simple randomization without any constraints to generate a large number, say N = 1000, of complete and fully random allocation schemes. in the next step we would identify the, say, n = 100 schemes with the smallest imbalances (using a similar criterion as for minimization) or, alternatively, all schemes with a criterion value below some prespecified cut-off value. finally, we would choose one of these remaining schemes at random.
the whole process would be carried out by a third person not involved in the study intervention or the collection of study outcomes. the investigators would only receive the last resulting allocation scheme from the person responsible for allocation.
the rationale behind our idea is simplicity and that we would like not to sacrifice too much randomness for balance.
has anyone heard of such an allocation strategy before? what do you think of it? are there any considerations concerning bias? (in some way, we would just be rejecting allocation schemes as long as we don't like them because of intolerably low balance. on the other hand, minimization or even stratification contain similar aspects...) and what about the implications for the statistical analysis? would you still adjust for the covariates using covariance analysis? any other thoughts?
thank you very much for any feedback!
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thank you very much vor your answer, aran!
you're definitely right that one has to consider imbalance in unmeasured covariates, but on the other hand: if two covariates are independent then balancing the first one should not lead to imbalancing the second, right? and if both variables are highly correlated then wouldn't balancing one variable - in most cases imaginable - kind of "automatically" co-balance the other?
and even if i'm wrong about the latter, isn't the problem inherent in any balancing algorithm or rather in the concept of balancing itself? in fact, i somehow hoped that my suggestion would do better in this respect than deterministic or "half-determinsitic" minimizing since it preserves "full randomization" at least among the sufficiently balanced allocation schemes...
but maybe my intuition is wrong here... ;-)
thanks again for your comment!
thomas
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Dear Fellows
I have got the survey data “World Bank’s Enterprise Survey 2013” in SPSS form. My research objective is to find out the obstacles faced by the firms while doing business in Pakistan. There are 15 obstacles listed below:
1. Electricity to Operations of This Establishment
2. Transport
3. Customs and Trade Regulations
4. Practices of competitors in informal sector
5. Access to Land
6. Crime, Theft and Disorder
7. Access to Finance
8. Tax Rates
9. Tax Administrations
10. Business Licensing and Permits
11. Political Instability
12. Corruption
13. Courts
14. Labor Regulations
15. Inadequately Educated Workforce
They are measured on 5-point likert scale (
No Obstacle ,Minor Obstacle , Moderate Obstacle, Major Obstacle , Very Server Obstacle).
Sampling Technique: Disproportionate Stratified Random Sampling
Three level of stratification have been used in the Survey: firm size, business sector, and geographic region within a country. Firm size levels are 5-19 (small), 20-99 (medium), and 100+ employees (large-sized firms). The business sector has been breakdown into manufacturing (Food, Textiles, Garments, Chemicals, Non‐metallic Minerals, Motor Vehicles, Other Manufacturing) and services (Retail and other services). Five regional stratification.
However, I am not interested in particular strata (groups) within the population. What kind of statistical tools can be applied here?
Thank you
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Does your research account for the home location of the firm e.g. domestic or foreign?
While frequency is interesting, the actual factum of "what exactly" is where it gets interesting. Focussing on a limited number of difficulties might also help to get more in depth knowledge.
Kind Regards
Roland
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Dear all,
A researcher has developed a new treatment for some medical condition. A clinical trial is being planned, in which 60 subjects are to be enrolled, 30 to each treatment group (treatment and control), therefore, a randomization is needed to minimize bias from various sources.
The trial is multi-center trial, with 4 different sites in which the treatment will be given. A block randomization with stratification by center, yields the same amount of blocks (each block is randomized for treatment and control) for each center, i.e. the same amount of subjects in each center (default of the software). However, some sites are bigger than others, and the sponsor wish to enroll more subjects in sites A and B, and less in C and D.
Randomization need to make sure that baseline characteristics are more or less equal between the two treatment groups, and to ensure that the investigator remains blinded. I wanted to ask you, how to solve the problem of wanting to stratify by center on one hand, but wishing to have more subjects in specific centers due to the fact that they are bigger, enroll faster, etc...Is it legal to give more blocks to some centers? I couldn't find such an example in the FDA guidelines.
For the sake of the example, let's say that I use blocks of 4 subjects, I need 60 overall (30*2), and got 4 centers. How should I do a stratified block randomization without forcing the investigator to enroll an equal number of subject in each site? Can I maintain balance within center and not between centers?
Thank you !
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According to the attached comments, it would be OK with FDA to have unequal numbers in different centres.Why not just do RCTs in each centre. and treat the centre as the block.
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By adding to the title and its anisotropy of this project the non-local or (singular) integral operators = my response to an ask of feedback to this paper, see below (paper put in reference to my own project)= (+ -via google translation, French text below) it is quite interesting = the anisotropy is here xi-cartesian constant (and the study comes out of the 1d to speak of the true multidimensional) and one can imagine more without difficulties The localized varying declinations of this anisotropy with Cartesian bases and ellipsoids/paraboloids and weights and functions, and your localized exponents ai, varying in x all of them in their own way, in centers, angles and Rotations, values etc, for your operators and various weights and functions on which your operators apply, variabilities more or less slow, fast, (ir /) regular, adapted, local, nice or not etc. It is quite speaking when the function is the derivative or the gradient of another or with studies in spaces of besov, sobolev or all functional spaces Es,p,q, with s not zero, s being the index (Integral) of derivation (instead of the spaces with s = 0, Lp, Lq etc) with s, p and p variables in x = we approach geometric anisotropy, foliations and associated irregularities which can eg to account for very natural situations in mathematical physics such as vortex patches and many others. (+-via google traduction, texte francais plus bas) c'est tout a fait interessant = l'anisotropie est ici xi-cartesienne constante (et l'etude sort du 1d pour parler du vrai multidimensionnel) et on peut imaginer de plus sans trop de difficultés, les declinaisons variables localisées de cette anisotropie avec des bases cartesiennes et des ellipsoïdes/paraboloides et des poids et fonctions et vos exposents 'ai', tous localisés, variant en x tous chacun d'eux a sa facon, en centres, angles et en rotations, valeurs etc, pour vos operateurs et poids et fonctions diverses sur lesquels s'appliquent vos operateurs, variabilités plus ou moins lentes, rapides, (ir/)regulieres, adaptées, locales, gentilles ou pas etc. c'est assez parlant quand la fonction est la derivée ou le gradient d'une autre ou avec des etudes dans des espaces de besov, de sobolev ou tous espaces fonctionnels Es,p,q, avec s pas nul, s etant l'indice (integral) de derivation (au lieu des espaces a s=0, Lp, Lq etc) avec donc s, p et p variables en x = on s'approche de l'anisotropie geometrique, les feuilletages et foliations et des irregularités associées qui peuvent eg bien rendre compte de situations tres naturelles en physique mathematique comme les vortex patches et beaucoup d'autres.
(paper and project "Weighted Anisotropic Morrey Spaces Estimates for Anisotropic Maximal Operators" and "weighted anisotropic Morrey spaces...." by Ferit Gürbüz= I pronounce my self on its/their subject and not on the novelty that its author brings to it). the rg-profile of the author has 2 (slightly different) papers with same title, but one of them has a "full text" with the title ending with: "...AND 0 -ORDER ANISOTROPIC PSEUDO-DIFFERENTIAL OPERATORS WITH SMOOTH SYMBOLS" with an additional math paragraph.
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Dear Prof. Serfatti,
                                 You have raised a very importanrt issue which affects our newly discovered Dbranes String FUNCTOR ALGEBRA CALCULUS using Mathematical Physics and Quantitative Finance experiments and is based on the Analysis provided in proving the P vs. NP problem of Millenium Maths problems (Mallick, Hamburger, Mallick (2016)).  However, so far we have been able to formulate only the Fundamental Theorem in plain language which is stated on our www.econometricsociety.org/Soumitra K. Mallick website. The point is that we have not studied convergence properties of the FAC Integrals so I cannot tell you FAC has particular group homology properties over FAC algebras. This is a long drawn process of development of the Mathematical Fields which if you are interested in developing some feel free to communicate. My son who is in this with me will be specialising in Pharmaceutical Engineering Science (now undergraduate) where he studies Analysis as part of his course. So he may take more part in expanding this Maths also. Thanks for your question.
Prof. Dr. S.K.Mallick ForMemEPS, ForMemReS, MES, MAICTE, QC
for S.K.Mallick, N. Hamburger, S.Mallick
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What are the ecological interpretations one can work out when herringbone stratification and hummocky cross stratification are observed in carbonate facies?
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Dear Dr. Sarkar:
Both types of bedding are indicative of near-shore marine depositional environments. Hummocky cross stratification abbreviated to HCS is typical of shoreface deposits and resultant of stroms.  They are common to the seaward part of the shoreface and come into being below everyday or fair-weather wave base. Similar to HCS bedding type are swaley cross bedsets.
Heringbone cross bedding resulted from tidal currents. The back- and from of ebb and flood tidal currents is mirrored by these bedding types.
Carbonate facies sedimentary rocks respond in the same way to the afore-mentioned coastal marine processes as siliciclastic rocks do.
Best regards
H.G.Dill
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I was sowing some seeds of bitter almond after stratification for 45 days, Now the seedlings colored with brown , and leaves are small, bent , also the they grow slowly .
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i saw such sign in salinity and cold stress in my seedlings during germination test
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Our kidney transplant centre is trying to make a DCD(including DBCD) kidney evaluation formula from the data in a multi-centre retrospective study.Since the retrospective feature, some of the variables is not complete. So some univariate analysis is not seeing statistical differences. I'm afraid this may probably effect the multi-variate analysis in the next step. Should i do stratification to solve the data incomplete problem?or do you have any better method?
Could any expert give suggestions on the formula or the statistical methods?
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1. try creating dummy variables for the fields with multiple responses.
2. estimate the multicolinarity and auto correlation
3. then try the factor analysis and short list the variables
4. use the loaded items as dependent variables in the causal analysis.
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One MSc student face this phenomenon in field and in embryo culture, I advice him to treat seeds with previous cool stratification, Is it correct advice and why?  
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Yes, I think stratification is advisable. Other explanations for the lack of germination are dehydration of seeds and/or a possible naturally low percentage of germination in this species.
Andrew :-)
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I want to study ramicolous liverworts (specifically Lejeuneaceae family) in Peruvian rainforests, considering morphological and anatomical aspects, however, I only have information about reports made by other researchers in vertical stratification on trees in South America. I hope anyone can help me with information and suggestions about this topic.
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It seems all conditions in definition of a stratifiable space hold. But the product of 2 copy of Sorgenfrey lines is not normal, countably many products of stratifiable spaces is stratifiable. One has always Stratifiable =>Normal 
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In terms of separation axioms, {\displaystyle \mathbb {R} _{l}} is a perfectly normal Hausdorff space.
In terms of countability axioms, {\displaystyle \mathbb {R} _{l}} is first-countable and separable, but not second-countable.
In terms of compactness properties, {\displaystyle \mathbb {R} _{l}} is Lindelöf and paracompact, but not σ-compact nor locally compact.
{\displaystyle \mathbb {R} _{l}} is not metrizable, since separable metric spaces are second-countable. However, the topology of a Sorgenfrey line is generated by a premetric.
I think it is related to 2nd countability
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It's common for marketers insist on a stratified sample design to ensure adequate representation of the relevant segments for analysis, even when it would lead to a rift with random methods. Some insist on resorting to procedures as closely as possible attached to a probabilistic method and, in any case, carry out post-stratification processes if it is requiee. What is your regular survey roll, if any, and what your view about it?
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For getting representative and random sample, stratification is better prior to the survey.
It is a scientific part of research and survey plan.
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I have a most at risk population (MARP) of about 8,013 with sampling frames as follows. 
Strata 1. MSM – 1674
Strata 2: FSW – 1977
Strata 3: BB- 737
Strata 4: DU-3625
Total = 8,013
If I calculate total sample size with 95% CI, 50% assumed proportion, and acceptable difference as 5% and total population size as 8,013. The sample size would come as 367. With 10% refusal It will be 404.
My question is after stratified random sampling in this scenario, Is it possible me to analyse the strata data independently (MSM, FSW, BB, or DU separately) and generalize the values to the strata?
What would you recommend If I want to analyse the groups independently.
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Karawita -
First, are your data all yes/no data because I have not checked but it looks like you used one of those online 'calculators' that assumes yes/no data?  They also assume simple random sampling, and usually are for the worst case where p=q=0.5, and ignore the finite population correction factor.
As for stratification, it looks like you are really trying to publish for different categories, not use stratification to improve an overall answer, so you have to think of each as its own independent simple random sample, if i read your question correctly. 
The key to sample size is the standard deviation for each population.  Cochran (below) has some suggestions for guessing this, including a pilot study. 
For your purposes, I suggest you check a textbook or two, such as one of these: 
Cochran, W.G(1977), Sampling Techniques, 3rd ed., John Wiley & Sons. 
Blair, E. and Blair, J(2015), Applied Survey Sampling, Sage Publications.
Lohr, S.L(2010), Sampling: Design and Analysis, 2nd ed., Brooks/Cole.
Cheers - Jim
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are 7 days alot?
1 day is too short?
when should i start to worry that stratification might affect my results?
what are best conditions of cold stratification: distilled water/agar/plates/soil/dry seeds? 
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An answer above suggested that the seed should be wet .  A point of clearification , seed should be imbibed with water but then allowed to dry off a bit so that they are not wet but moist ,  too much moisture as in being saturated wet will lead to problems , soak seeds for 24 hrs , the drain immediately and allow to displace excess moisture in paper towels .  After a 24 hr drying period it will be safe to put into a stratification situation ,making sure that they stay moist .  Too much moisture will decrease the amount of time that they can stay refridgerated and might lead to rotting instead of germinating .  Since it takes so few days to stratify I am a bit confused as to why enter into a stratification process until necessary , seems like pushing the length of time in stratification will lead to problems .  Moist cold is an ideal environment for certain cold tolerant fungi that can get into the process , the longer the term , the more likely the chance of fungal problems.
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Dear colleagues
The attached file consists of an image which taken from paleogene phosphatic limestones of Pabdeh Formation in Lar mountains (south west of Iran). Nominated layer belongs to middle part of this Formation and based on planktonic foraminiferal studies (Daneshian et al., 2015) estimated Lutetian-Bartonian stage. Field and petrographic studies denote that there are some sedimentary structures such as: Hummocky cross stratification, cross lamination, ripple marks and amalgamation which can be categorized as tempestites. Please, if you find any mistakes in my opinion, could you please correct them?
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HI,
Please, read this article :
Pomar L., Morsilli, M, Hallock, P. et Bádenas, B. 2012. Internal waves, an underexplored source of turbulence events in the sedimentary record. Earth-Science Reviews, 111, pp. 56-81.
It can gives you more ideas.
Good luck
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 stratification is given by cv=cvpartition(group,'kfold',k))
for my problem i want to do 5-kfold therefore k will be 5, now what about group in the equation above  when i have 78 samples with 4 inputs and 1 output?
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Papers within 3 years are results by 100-fold cross validation.
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I'll conduct a study among university students . First I'll stratified them according to knowledge  are "theoretical, practical and medical" then randomly chose one or two college from each area. The point is that i need to know the difference between  first and fourth year students. So after stratification can i further stratify each group to 1st and 4th year student and to take a group"cluster" from each year???
And in this stuation can i generalize the result among all university  students or should i mention that for 1st and 4th year only as they my target group??
Finally i need the help in calculation of such sample , how to calculate design effect and how to determine the size of each cluster??
Thanks in advance, 
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Mariam -
I'm not certain that you have the correct concept of a cluster. A cluster sample is one where the primary sampling unit is a group, like a city block, or a classroom, from which you select a random sample, or even census, at the next step (called multistage sampling when you use some randomized selection at each stage).  A cluster sample generally requires even more observations than simple random sampling, but is often more logistically feasible and cost effective.
A stratified random sample generally requires a smaller sample size than simple random sampling, so it's design effect is more favorable, because the idea is to group your sample and population such that the variance within each stratum is reduced, and the difference between strata is greater, to obtain a smaller overall variance.  But this is just to improve the aggregate level results. If you really want to get results for each stratum, then your goal is not the same. You are then not looking for stratified random sampling, but really breaking the population into smaller ones for which you have goals, so anything you read about optimized allocation overall would not apply.
As for sample size, for a complex survey, that can be challenging. For any stratum or group where you might do simple random sampling, you might find good, straightforward information, such as the chapter on sample size for continuous and for yes/no data in Cochran, W.G(1977), Sampling Techniques, 3rd ed., John Wiley & Sons. 
I worked mostly with continous data in establishment surveys, and model-based sampling and estimation, which is a different concept, but for both that and the continuous data in Cochran with randomized selection, you need information on the standard deviation for each of those subpopulations or strata, here from your data, in my case something similar for residuals. (Yes/no data are similar, but there is an easier way to get a worst case estimate that is commonly used in online calculators.)
Also, regarding sample size needs, you may need to familiarize yourself with the finite population correction  (fpc) factor.  (I have a definition on my RG page that I did for a Sage Publications encyclopedia.) 
At any rate, to obtain needed information, one thing Cochran suggested is a pilot study. In your case, especially if you do not have a good full time statistician and good software she/he can use, a pilot study would be very useful to get an idea of what you need. It might also help test your questionnaire, etc.  But big changes in your questionnaire may make changes to your sample size needs. And beware that different questions may have very different sample size needs.  Also, if you need a sample size that is too large for your resources, you might substantially increase nonsampling error - an area that is often too much neglected - which can badly distort everything.
So, in summary, I suggest that you review the difference between cluster and stratified random sampling; note where you might mean strata versus separate subpopulations of interest; review multistage sampling  (which increases the complexity of variance estimation); and beware of nonsampling errors.  A good reference(s) such as Cochran is important.  Standard errors are important. A pilot study may be essential.
Beware of both bias and standard errors for both sampling and nonsampling errors.
Note that I am not familiar with count data or likert scales, and information on those are likely found elsewhere, but the concepts of stratification and cluster sampling, bias and perhaps nonsampling error, and of possibly using a pilot study, should, I think, still apply in an analogous manner.
Cheers - Jim
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I am running an opposed jet case, where a stream of fresh reactants is opposed to a stream of burnt products. I am looking at the effects of stratification on the flammability limits of methane. 
In some cases, in the reaction zone, the heat release is about 10^3-10^4 lower than compared to my reference case, which is far from the lean or rich flammability limits. Since I am sitting on or close to those limits, it is important for me to define one (or multiple) parameter for which I can say that the fuel is indeed burning.
Here is my reasoning right now, but it might be incomplete or even erroneous. To check if the fuel is indeed burning, I have been looking at the distribution of key radicals. If the mass fraction of say H2, does not have peak in the reaction zone and only diffuses from one stream to another, then I can definitely say there is no flame. But a contrario, if there is a peak, can I definitely say there is a flame? And how big does this peak needs to be compared to its corresponding value in the reactant and products stream? (I am guessing at least one full order of magnitude). 
If there is a standard definition of a flame in numerical combustion, please share it, preferably with an attached reference. 
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Is this a pure chemical kinetics simulation or a CFD study of opposed jets? What we in my organization usually do in the CFD simulation of furnaces is to use local CO concentrations as an indicator for the flame shape within the combustion chamber. A common threshold for methane-air combustion is 2000 ppm CO (dry). If the local value of CO is higher, we consider it to be within the flame,  if it's below, we consider it to be outside of the flame. This is more of a rule-of-thumb, but it works reasonably well for us.
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Recently, I have been working on a GWAS experiment design. The samples come from the same population, but have extreme phenotypes (classified as 20 cases and 20 controls). When I used Plink (--assoc --adjust) to analyze the data, it reported the genomic inflation factor is about 1.7. I wonder how can there exists population stratification, since the samples come from the same population? How can I solve this "large genomic inflation factor" popular?
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The problem is likely to be your sample size. If I understood correctly, you did genome-wide genotyping in 20 cases and 20 controls. If this is so, the confidence interval of your genomic inflation factor is very large and makes strange numbers possible. Also, stratification can exist for many reasons other than self-declared ethnic background or place of residence,  including technical stratification, if DNA from cases and controls was purified and/or genotyped separately.
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Actually the study area has a total population of about 1 million, consisting of seven blocks (community development blocks) and I want to stratify the universe. After stratification, the population remains six lakhs.
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Hi
Please give me feather data for your question.
After that, I’ll answer your question.
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This is eqn.(17) in the paper
Zilitinkevich (1972) Bound.-Layer Meteorology 3, 141-145 --see eqn. (12) link attached--
and it is used to estimate the height h_u of the turbulent Ekman boundary layer in unstable stratification from the condition that the main variation of the horizontal mean wind speed (U,V) remains within the height range z0 < z < h_u.
The notation: (U,V) are the wind components, (Ug,Vg) are the geostrophic wind components, c is a constant, k is the von Karman constant, u* is the friction velocity, b is the buoyancy parameter, Q is the kinetic turbulent vertical heat flux, z is the height.
Thank you.
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Hi Dan, you should possibly ask Sergej Z. directly. He is very friendly and happy if young people ask questions. He's a good old friend. However, a "proof" in the classsic sense is clearly impossible because many elements of his approach are of semi-empirical nature. You may alternatively start from a more rigorous theoretical approach based on pure elementary physics. Not difficult, but filling the evening ...
Building blocks for a renovated approach you may find in "Marine Turbulence" from Cambridge U. Press, 2005; available as paper back for about 30 euro. If you plan to start such an endeavor, let me know. I might support you if you are ready to work with Mathematica or at least with LaTeX.
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its significance in stratigraphy and types of correlation in Stratigraphy
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All the above are good recommendations.  I would also recommend Grabau's Principles of Stratigraphy (https://archive.org/details/principlesofstra00grab), Sloss's classic papers on cycles (highlighted here by KGS - http://www.kgs.ku.edu/Publications/Bulletins/169/Sloss/), and the AAPG Memoir 26 entitled "Seismic Stratigraphy: Applications to Hydrocarbon Exploration". Two papers in this volume have been influential (1) Vail, P.R. and Mitchum, R.M., 1977, Seismic stratigraphy and global changes of sea level, Part 1—Overview:  AAPG Memoir 26, p.51-52 and (2) Vail, P.R., Mitchum, R.M., and Thompson, S., 1977, Seismic stratigraphy and global changes of sea level, Part 3—Relative changes of sea level from coastal onlap:  AAPG Memoir 26, p.63-81.  I realize this is a broad mix, but the point is that perspective on stratigraphy and methods (that is, what is the intent of your work or question) temper the way one correlates packages of rock.  This final link, a presentation, provides a good historical perspective on sequence stratigraphy, too --> http://www.searchanddiscovery.com/pdfz/documents/2010/50262martinsen/ndx_martinsen.pdf.html
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In finite population survey statistics, for survey methodology and data analysis, data are stratified to reduce overall variance. But sometimes publishing the individual categories becomes important, and this may negate the role of reducing overall variance for a given overall sample size. Further, the categories chosen may not be best for stratification purposes. In the case of regression model-based methods, the goal is the same. In that case, scatterplots and estimated regression coefficients with their standard errors can be used to sort out which data should go into which strata. Thus, regression analysis is important for model-based sampling and/or estimation by prediction.
For design-based sampling and estimation, there is Neymann allocation, but my question is not so much about allocating to strata already defined, but more how to define the strata in the first place. There must be some categorical-type heading, but one might do better by being imaginative as to what such data groupings could be tried.
Sometimes better ways to stratify become apparent after-the-fact, and poststratification is used.
What tips/methods do you propose, and/or examples do you have for stratifying either for design-based sampling and estimation methods, or model-based methodology, or model-assisted design-based methods? 
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Guillermo -
You said that "Sampling is a Science and an Art...." Nicely said. I very much agree.
At the end of your response, with regard to allocation, you have "...but it may be different with each of the variables, then you have to order the variables by their importance and select the allocation generally more suitable." Yes, that would be unavoidable with regard to stratum selection. Good point, appropriate to this question. It also reminds me that at the estimation stage, if a PPS sample had been drawn, then the same kind of compromise or attention to the most important items/target variables would need to have been done at the data selection stage, that would impact the estimation. Here I refer to the measure of 'size' used, which would be attached to each respondent for every response item. However, if model-based estimation ('prediction' from regression) were used, then each item could have its own size measure in the regression weights. But it does get more complex when design weights and regression weights are combined in 'calibration' weights.
So, I had thought of prediction/model-based estimation as avoiding having to compromise or prioritize your survey questions/items, but you have a good point that for stratification, the very question at hand, this kind of compromise or prioritization still occurs.
It is interesting to consider how your sampling method and your estimation interrelate.
Thank you - Jim 
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I have some data for a travel cost application and I would like to use the variant of the negative binomial model that accounts for endogenous stratification. I know that for STATA there is the gnbstrat package... but I don´t have STATA!
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Maybe you can use R, with the COUNT package (its free)
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The data analysis of 1H- and 13C-NMR spectra of the tumor extracts demonstrated a significant increase in the concentration of the 2HG in IDH mutated tumors. On 13C-NMR spectra, 2HG signals were detected in the IDH1 mutated but not IDH wild type tumors. It is expected that 2HG may be actively being produced during the period of 13C-substrate infusion (e.g., [U-13C]-glucose). 
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According to Saka HK et al of Harvard Medical School, intrahepatic cholangiocarcinoma and subsets of neural, hematopoietic and bone tumors are characterized by frequent gain-of-function mutations in the isocitrate dehydrogenase 1 and 2 (IDH1 and IDH2) genes which acts through a novel mechanism of oncogenesis, producing high levels of the metabolite 2-HG, which interferes with the function of α-ketoglutarate-dependent enzymes that regulate diverse cellular processes including histone demethylation and DNA modification. Thus, a form of differentiation therapy is possible in clinical application to inhibit the mutant enzymes. And I think probably you are right in saying that clinically we can use the metabolite 2-HG to classify whether the tumors are IDH-mutant or wild-type which may have different tumor behaviors and tumor biology.
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Hi everyone, I want to ask about proportionate stratified sampling.
This is my sampling frame: strata into 4 (manager,supervisor, engineer, QA&QC executive ) population is 188, manager =63,supervisor=65, engineer 27 and QA&QC=33, 45% proportionate for each strata, then sample should be 85, but due to high non-respond rate, I manage to get only 79 sample , should I change 45% for 85 to 40% for 79(successful respond) ? Or just follow 85, but justify on my writing?
pPease, I need advice,
Thank you in advance;
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If you are planning to use hypothesis/"significance" tests, I encourage you to instead use confidence intervals, as they are far more interpretable than isolated p-values.  A p-value is a function of sample size.  At a given 'level,' a small sample size will tend to 'fail to reject' even an hypothesis that is very far from the truth, whereas a very large sample size will reject an hypothesis that is extremely close to true.  (See the attached link.)  Even if you have to use Chebyshev's Inequality, estimating a confidence interval is better, when you can.  
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I have found both to be high suspect it only drops after differentiation is stimulated by media that encourages this (increasing CaCl2 conc.). Any shared experience will be appreciated. Thanks
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Sorry, I have no idea; this is not in my area of expertise
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We are trying to find a source that can easily explain how to calculate and apply post stratification weights for survey data in SAS. Does anyone know of a source with clear explanations and example code? All we could find on the SAS website was conceptual (no examples), and we have not had much luck with any other sources we have found.
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I do not use any automatic tool in post-stratfication since it requires to understand the whole process from the sampling design to this stage. And post-strata need to be tested in various ways if seriously used. Technically it is easy to do by any software, especially by SAS..
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Hypertension is the most common medical problem encountered in pregnancy and remains an important cause of maternal and fetal morbidity and mortality. It complicates up to 15% of pregnancies. assessment of arterial stiffness, PWV and some biomarkers may help in prediction and stratification of pregnancy induced hypertension/Pre-eclampsia.
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hi:
yes, we can partially  predict PIH or preeclampsia whit some biomarkers and Roll over test in 26 -28 week of pregnancy. 
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Hello everyone,
I am testing for statistical interaction between two variables in a logistic regression model and I am finding that from a biologically plausible level the interaction changes. However, I want to back up this finding statistically so I have an additional argument for stratification. Therefore I added a three way interaction as continuous1*continuous2*cut-off continuous2, with p=0.01, so fitting with my observation.
Can anybody tell me whether this is valid and perhaps provide me with some evidence (I am so far unable to find any papers)?
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Thanks for your answer Peter. Considering that there is a specific threshold within my data I do feel that the interaction representss my data, however, I have further explored Pat's advice and now I have added the quadratic terms, and their product to the model and I now see that the lines diverge from approximately the breakpoint that I used as a cut-off for the continuous variables. It seems to fit very well.
Thanks again for your responses.
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Hi,
I have some Arabidopsis line with less than a 10 % germination rate. I have tried to increase the germination extending the stratification period (until 2 weeks) and treating with GA. The ratio didn´t increase. I´m now wondering if my seeds have normal embryos or not but I cannot find an easy way to see the embryos (I have mature seeds already). Could anybody help me with this? Maybe an staining?
Thank you very much!
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Dear Ana, If your non germinating seeds are alive (tetrazolium test will give the answer) they could have a strong dormancy. In this case there is other ways than GA treatments which have been described to stimulate the germination of Arabidopsis dormant seeds . You will find them easily in detail in literature, for instance longer stratification, or scarification or afterripening, or NO3, or fluridone treatments.
Regards
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This term is used in the Global Environmental Stratification.
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Stratification is the layering of habitats within an ecosystem with the presence of distinctive physical and biological boundaries between the strata (layers). For example, in a temperate deciduous forest, you typically have 5 vertical layers: the canopy layer, the sapling layer, the shrub layer, the herbaceous layer, and the moss layer. Similarly, the stratification of a lake typically has three distinct layers: the Epilimnion (top layer), the Metalimnion (middle layer; may change depth during the day), and the Hypolimnion (the bottom layer). As such, ecosystem stratification is dependent on the ecosystem (e.g., the stratification of a forest is different than the stratification of a lake). Furthermore, ecosystem stratification does not only occur vertically, but can occur horizontally within an ecosystem as well.