Thursday, January 7, 2016

Averaging can produce misleading standardized effect sizes

Recently, there have been many calls for a focus on effect sizes in psychological research. In this post, I discuss how naively using standardized effect sizes with averaged data can be misleading. This is particularly problematic for meta-analysis, where differences in number of trials across studies could lead to very misleading results.




There are two main types of effect sizes in typical use: raw effect sizes and standardized effect sizes. Raw effect sizes are what you typically see in a plot: for instance, the effect of a priming manipulation might be 30ms. The advantage of raw effect sizes are that they are closer to the process of interest and more interpretable. We all know what it means for something to take 30ms to happen.

Another kind of effect size is the standardized effect size. With a standardized effect size, the raw effect is compared to the some measure of variability in the population. For instance, if the standard deviation of childrens’ heights at age 10 were 3 inches, and a “good” diet had an effect of 1.5 inches on average, we could say that the effect of the diet was .5 standard deviations. This is the logic of Cohen’s \(d\), for instance. The disadvantage of this is that it is more difficult to understand what an effect of “half a standard deviation” means (and the variance-accounted-for statistics such as \(\eta^2\) and \(\omega^2\) are even more difficult to interpret); but standardized effect sizes have many good properties, including a close relationship to the concept of statistical power, comparability across paradigms, and the fact that they can often be computed from reported statistics such as \(t\) and \(F\).

For these reasons, standardized effect sizes are very common in meta-analysis. However, the common practice of averaging over trials in cognitive psychology makes them difficult to compare or even interpret.

Consider a typical cognitive experiment in with 30 participants, each performing 10 response time trials in two conditions. Typically each participant’s data will be averaged to form a single, average response time in each condition; these average RTs are then submitted to a repeated measures ANOVA (in fact, some R packages, such as afex do this automatically).

Hypothetical data is shown in the plot below. These data represent two hypothetical experiments, one with 10 samples per participant and one with 50.


Error bars represent Morey (2008) adjusted within-subject error bars, computed using this code.

I have generated the data so that everything is the same across the two experiments except the scale of the “error”: the scale of the error in experiment 2 is \(1/\sqrt{5}\) times that of experiment 1, because each averaged “observation” represents five times more data. The raw effect size is precisely the same, but our certainty about the effect size is greater in experiment 2. This is exactly as it should be.

We can now perform the typical repeated measures ANOVAs on these two data sets, using the afex. The package will, if requested, compute the common partial \(\eta^2\) standardized effect size statistic.

The results of the ANOVA for the “condition” in experiment 1 are:

Effect df MSE F pes p.value
condition 1, 29 0.08 7.72 .21 .009

And the results of the ANOVA for the “condition” in experiment 2 are:
Effect df MSE F pes p.value
condition 1, 29 0.02 38.58 .57 <.0001

This is would not be unexpected by anyone who routinely uses repeated measures ANOVA. Typically, the whole point of running more trials is to get more power. We perform more trials, and we obtained a higher \(F\) value for the comparison of interest.

Notice that the sum of squares for the effect is precisely the same for both experiments. That’s because the raw effect is precisely the same. What is driving the higher \(F\) value is the lower residual mean square (MSE) for the comparison, which is about 5 times smaller in Experiment 2. Again, this is what we expect. More trials, less “noise”.

But notice what happens to partial \(\eta^2\). Because the MSE is smaller, the proportion of variance accounted for by the condition effect is larger. This drives the partial \(\eta^2\) from .21 in experiment 1 to .57 in experiment 2. Researchers have previously warned about using partial \(\eta^2\) for comparisons across designs (see for instance, Olejnik & Algina, 2003), but these two experiments appear to have the same design; at least, from the perspective of someone used to only analysing averaged data, they do.

This has the potential to wreak havoc on meta-analyses. Suppose someone combs the literature looking for \(F\) values and computing partial \(\eta^2\) values from the \(F\) values (or, alternatively, Cohen’s \(d\) from \(t\) values). Assume experiment 1 represents a patient group; due to time constraints, the patients only had time for 10 trials per condition. Suppose experiment 2, on the other hand, represents a group of college students, who had time for more trials. The figure below shows the standardized effects in the two experiments.



Although the raw effect size is precisely the same across the two experiments, the standardized effect size is radically different, possibly leading to erroneous conclusions. Even if there are no systematic differences in number of trials across experiments experiments with different kinds of groups, this introduces a new source of variability into estimates, as well as making it nearly impossible to interpret the effect size. What is the “true” standardized effect size? It seems difficult to say. How can we solve this problem?

Solution 1: Generalized \(\omega^2\)


One option is generalized \(\omega^2\) (see for instance, Olejnik & Algina, 2003) Instead of using the residual variance to standardize against, generalized \(\omega^2\) standardizes against all measured (as opposed to manipulated) factors. For instance, the variability in participants is a measured source of variability. These sources of variability are assumed to be stable properties of populations and not effected by mere design choices. We can compute generalized \(\omega^2\) again using the afex, which yields \(\omega^2_g=0.011\) for the experiment 1 and \(\omega^2_g=0.012\) for experiment 2; notice that these very similar. The effect “looks” smaller, because participants vary quite a bit relative to the size of the effect.

One problem with this approach is that the statistics necessary to compute generalized \(\omega^2\) are not typically reported, meaning that this solution is useless for meta-analysis of existing literature. Ideally, we’d like a way to use reported statistics to at least compare across studies, when designs are similar enough.

Solution 2: Adjust the MSE


If we know the relative numbers of trials across two studies that have the same basic design, we should be able to “adjust” the MSE in the formula for the effect size (whichever effect size it happens to be) for the number of trials. In our example, experiment 2 has five times as many trials as experiment 1; we therefore would expect the MSE of experiment 2 to be one-fifth as large as that for experiment 1. To make the effect size computed from experiment 2 comparable to that from experiment 1, we can multiply its MSE by 5 before applying the formula for the effect size of interest. For partial \(\eta^2\), this leads to an easy adjustment:
\[ \eta^2_2 = \frac{1}{c/\eta^2_1 - c + 1} \] where \(c\) is the adjustment factor, \(\eta^2_1\) is the original partial \(\eta^2\), and \(\eta^2_2\) is the adjusted partial \(\eta^2\).

As an example, take our experiment 2, which had a partial \(\eta^2\) of 0.571 and a sample size 5 times larger than experiment 1. Applying the formula above yields
\[ \begin{eqnarray*} \eta^2_2 &=& \frac{1}{5/0.571 - 5 + 1}\\ &\approx&0.21 \end{eqnarray*} \] which matches the partial \(\eta^2\) from experiment 1 very well.

The problem with this approach is that it uses experiment 1 as a “reference” experiment. It is therefore not clear what the standardized effect size means in this case, except as a way to compare across experiments with similar designs. This may be enough to someone performing a meta-analysis — particularly if they can’t obtain the statistics to compute generalized \(\omega^2\) — but as a general reporting solution, it is unsatisfactory.

Wrap up


Although standardized effect sizes have been advocated as a general tool for science and are increasingly reported, they are difficult to interpret because they are affected by trivial, common design decisions. The issues I raise here should be of interest to anyone working with standardized effect sizes, particularly those performing meta-analysis. They affect repeated measures designs with averaged data most acutely; however, between-subjects designs are also affected if each participant contributes an “average” score to the analysis. In the between-subjects case the adjustment would have to be different, but for large number of trials per participant might be acceptably ignored, if the error each participants’ score is small enough.

Added postscript


After a re-read, I want to ensure that I make clear that I'm not implying that the only problem here is with meta-analyses; that's just what drove me to write this post, and how I decided to frame it. But consider this: if an arbitrary decision (driven merely by the resources at hand, such as time or money, or even whim) such as "how many trials will we perform per cell in this experiment?" can cause the standardized effect size to increase almost 200%, that standardized effect size should not be taken to reveal any psychological "truth" and is useless for drawing substantive conclusions.

78 comments:

  1. Great post. You might also be interested in:

    http://janhove.github.io/reporting/2015/02/05/standardised-vs-unstandardised-es/

    http://janhove.github.io/design/2015/03/16/standardised-es-revisited/

    ReplyDelete
    Replies
    1. Good news this is to everyone out there with different health challenges, as I know there are still a lot of people suffering from different health issues and are therefore looking for solutions. I bring you Good news. There is a man called Dr ehiaguna a herbal practitioner who helped cure me from HSV (2), i had suffered from this diseases for the past 5 years and i have spent so much money trying to survive from it. I got my healing by taking the herbal medicine Dr ehiaguna sent to me to drink for about 14 days . 3 days after completion of the dosage, I went for a medical checkup and I was tested free from HSV. all thanks to God for leading me to Dr ehiaguna who was able to cure me completely from this deadly diseases, I’m sharing this so that other people can know of this great healer called Dr ehiaguna because I got to know him through elizabeth who he cured from HIV. I was made to understand that he can cure several other deadly diseases and infections. Don’t die in ignorance or silent and don’t let that illness take your life. Contact Dr ehiaguna through his email  drehiaguna@gmail.com You can also whatsapp/call him on:+2348073908953 . Visit his website  https://effectiveherbalcurehome.blogspot.com/   He cure all forms of disease {1}HIV/AIDS {2}DIABETES {3}EPILEPSY {4} BLOOD CANCER {5} HPV {6} BRAIN TUMOR {7} HEPATITIS {8}COPD{9} SICKLE AND ANAEMIA.etc Be kind enough to share as you received.  

      Delete
  2. Thanks! You make some nice observations there, which are particularly relevant in this comment: here. I didn't expand on it too much above, but I think you're right about the difficulties inherent in standardised effect sizes. Although standardised effect sizes do allow for comparison across paradigms, given the difficulties, I wonder if the meaningfulness of such comparisons is merely illusory. It would definitely be profitable to at least consider what meta-analysis would look like based solely on raw effect sizes.

    ReplyDelete
    Replies
    1. Actually, those are not my blog posts, and so not my interesting observations (though I agree with them). So sadly, I cannot take credit.

      Delete
    2. With a mere 14-month delay: Thanks to jwdink for linking to my blog, and thanks to Richard for his comments!

      Delete
  3. Interesting post!
    I had recently come across this issue myself, and observed that including random intercepts and slopes in the simulations attenuates the overestimation of the effect sizes (depending on the ratio between the within- and between subjects variability).

    I have presented this at our labmeeting only (and do not have a blog to summarize this), but I thought it might be useful to share these slides here, in case you would be interested: https://www.dropbox.com/s/o2ss3iehjnl808f/Labmeeting_12112015.pptx?dl=0

    As you highlight in the post-script, I agree one of the most important implications of this is that standardized effect sizes behave in unanticipated ways when researchers first average across trials for each participant before analyzing the data, but this has implications for power analysis, and meta-analysis indeed.

    ReplyDelete
    Replies
    1. Very nice. It looks like we're thinking along the same lines.

      Delete
  4. This comment has been removed by a blog administrator.

    ReplyDelete
  5. Richard, can you provide intuition/explanation for why the standardize effect sizes are so much lower In Expt 1 vs. Expt 2? I could see it if it were Cohen's d because Expt 1 would have higher same mean difference but higher standard deviation, thus Expt 1's d would be lower than Expt 2's. How does this work for eta-squared though, which according to Wikipedia is SS_treatment / SS_total? https://en.wikipedia.org/wiki/Effect_size#Eta-squared.2C_.CE.B72

    There, you have SS in both numerator and denominator, so why aren't the ratios in both experiments roughly the same? Is it because the SS_total is similar/same in both experiments, and Expt 1 has higher SS_treatment than does Expt 2?

    Also, would be interested in seeing code that underlies this running example.

    ReplyDelete
    Replies
    1. edit: "Expt 1 would have higher same mean difference" should be "... have same mean difference"

      Delete
    2. Still wondering about the specifics behind why the standardized effect size is lower in Expt 1, if anyone has an idea...

      Delete
  6. This comment has been removed by a blog administrator.

    ReplyDelete
  7. Can Solution 2 be applied also when for adjusting reliability coefficients?
    e.g. If I measure reliability using the split-half method, I am really only measuring the reliability of a measure with half as many trials as the actual measure used in analysis.

    ReplyDelete
  8. Quantitative data depicts the quality and can be scrutinized, but measuring it precisely is daunting enough; in contrast quantitative data can be easily measured and is depicted in number or amount. See more qualitative analysis with nvivo

    ReplyDelete


  9. It was very useful for me. This was actually what I was looking for, and I am glad to came here! Thanks for sharing the such information with us.

    Server 2016
    Microsoft Server 2016 Migration

    ReplyDelete
  10. COEPD LLC- Center of Excellence for Professional Development is the most trusted online training platform to global participants. We are primarily a community of Business Analysts who have taken the initiative to facilitate professionals of IT or Non IT background with the finest quality training. Our trainings are delivered through interactive mode with illustrative scenarios, activities and case studies to help learners start a successful career. We impart knowledge keeping in view of the challenging situations individuals will face in the real time, so that they can handle their job deliverables with at most confidence.

    http://coepd.us/

    ReplyDelete
  11. Irrespective of receiving daily oral or future injectable depot therapies, these require health care visits for medication and monitoring of safety and response. If patients are treated early enough, before a lot of immune system damage has occurred, life expectancy is close to normal, as long as they remain on successful treatment. However, when patients stop therapy, virus rebounds to high levels in most patients, sometimes associated with severe illness because i have gone through this and even an increased risk of death. The aim of “cure”is ongoing but i still do believe my government made millions of ARV drugs instead of finding a cure. for ongoing therapy and monitoring. ARV alone cannot cure HIV as among the cells that are infected are very long-living CD4 memory cells and possibly other cells that act as long-term reservoirs. HIV can hide in these cells without being detected by the body’s immune system. Therefore even when ART completely blocks subsequent rounds of infection of cells, reservoirs that have been infected before therapy initiation persist and from these reservoirs HIV rebounds if therapy is stopped. “Cure” could either mean an eradication cure, which means to completely rid the body of reservoir virus or a functional HIV cure, where HIV may remain in reservoir cells but rebound to high levels is prevented after therapy interruption.Dr Itua Herbal Medicine makes me believes there is a hope for people suffering from,Parkinson's disease,Schizophrenia,Cancer,Scoliosis,Fibromyalgia,Fluoroquinolone Toxicity
    Syndrome Fibrodysplasia Ossificans Progressiva.Fatal Familial Insomnia Factor V Leiden Mutation ,Epilepsy Dupuytren's disease,Desmoplastic small-round-cell tumor Diabetes ,Coeliac disease,Creutzfeldt–Jakob disease,Cerebral Amyloid Angiopathy, Ataxia,Arthritis,Amyotrophic Lateral Sclerosis,Alzheimer's disease,Adrenocortical carcinoma.Asthma,Allergic diseases.Hiv_ Aids,Herpes,Inflammatory bowel disease ,Copd,Diabetes,Hepatitis,I read about him online how he cure Tasha and Tara so i contacted him on drituaherbalcenter@gmail.com even talked on whatsapps +2348149277967 believe me it was easy i drank his herbal medicine for two weeks and i was cured just like that isn't Dr Itua a wonder man? Yes he is! I thank him so much so i will advise if you are suffering from one of those diseases Pls do contact him he's a nice man.

    ReplyDelete
  12. My life is beautiful thanks to you, Mein Helfer. Lord Jesus in my life as a candle light in the darkness. You showed me the meaning of faith with your words. I know that even when I cried all day thinking about how to recover, you were not sleeping, you were dear to me. I contacted the herbal center Dr Itua, who lived in West Africa. A friend of mine here in Hamburg is also from Africa. She told me about African herbs but I was nervous. I am very afraid when it comes to Africa because I heard many terrible things about them because of my Christianity. god for direction, take a bold step and get in touch with him in the email and then move to WhatsApp, he asked me if I can come for treatment or I want a delivery, I told him I wanted to know him I buy ticket in 2 ways to Africa To meet Dr. Itua, I went there and I was speechless from the people I saw there. Patent, sick people. Itua is a god sent to the world, I told my pastor about what I am doing, Pastor Bill Scheer. We have a real battle beautifully with Spirit and Flesh. Adoration that same night. He prayed for me and asked me to lead. I spent 2 weeks and 2 days in Africa at Dr Itua Herbal Home. After the treatment, he asked me to meet his nurse for the HIV test when I did it. It was negative, I asked my friend to take me to another nearby hospital when I arrived, it was negative. I was overwhite with the result, but happy inside of me. We went with Dr. Itua, I thank him but I explain that I do not have enough to show him my appreciation, that he understands my situation, but I promise that he will testify about his good work. Thank God for my dear friend, Emma, I know I could be reading this now, I want to thank you. And many thanks to Dr. Itua Herbal Center. He gave me his calendar that I put on my wall in my house. Dr. Itua can also cure the following diseases ... Cancer, HIV, Herpes, Hepatitis B, Inflammatory Liver, Diabetis, Fribroid,Parkinson's disease,Inflammatory bowel disease ,Fibromyalgia, recover your ex. You can contact him by email or whatsapp, @ .. drituaherbalcenter@gmail.com, phone number .. + 2348149277967 .. He is a good doctor, talk to him kindly. I'm sure he will also listen to you.

    ReplyDelete
  13. I am bold enough among many others to state that there is now a potent cure to this sickness but many are unaware of it. I discovered that I was infected with the virus 3 months ago, after a medical check-up. My doctor told me and I was shocked, confused and felt like my world has crumbled. I was dying slowly due to the announcement of my medical practitioner but he assured me that I could leave a normal life if I took my medications (as there was no medically known cure to Herpes). I went from churches to churches but soon found that my case needed urgent attention as I was growing lean due to fear of dying anytime soon. In a bid to look for a lasting solution to my predicament, I sought for solutions from the herbal world. I went online and searched for every powerful trado-medical practitioner that I could severe, cos I heard that the African Herbs had a cure to the Herpes syndrome. It was after a little time searching the web that I came across one Dr Itua(A powerful African Herbal Doctor), who offered to help me at a monetary fee. I had to comply as this was my final bus-stop to receiving a perfect healing. My last resolve was to take my life by myself, should this plan fail. At last it worked out well. He gave me some steps to follow and I meticulously carried out all his instructions. Last month, to be precise, I went back to the hospital to conduct another test and to my amazement, the results showed that negative,Dr Itua Can As Well Cure The Following Desease…Cancer,Hiv,Herpes, Hepatitis B,Liver Inflammatory,Diabetis,Fribroid,,Non Hodgkin Lymphoma,Skin Cancer,Uterine Cancer,Prostate Cancer Dercum,Infertility,fibromyalgia,Get Your Ex Back,Als,SYPHILLIS,Genetic disease,Epilepsy, Parkinson's disease..You can free yourself of this Herpes virus by consulting this great African Herbal Doctor via this e-mail: drituaherbalcenter@gmail.com or call and whatsapp him on +2348149277967 He will help you and his herb medication is sure. he has the cure on all disease .You can talk to me on INSTAGRAM..tashamoore219....

    ReplyDelete
  14. I have long felt a special connection with Herbal Medicine. For one thing is natural, Charlie we went to the same small college in Southern California — Claremont Men’s College — though he dropped out and ultimately enrolled at the Julliard School of the Performing Arts in New York. Had he stayed at Claremont, he would have been a senior the year I started there; I have often kidded that I was the reason he left when he finds out I had herpes. So my life have been lonely like hell all day I couldn't bear the outbreak pain, Tasha then introduce me to Dr Itua who use his herbal medicine to cure her two weeks of drinking it. I place an order form him and he delivers to my post office then I picked it up and used for two weeks all my sore was healed completely no more outbreak I'm honestly telling you this man is a great man, I trust him and his herbal medicine so much I'm sharing this to show my appreciation also to let sick people know there is hope with Dr Itua Herbal Made Medicine.Dr Itua Contact Email.drituaherbalcenter@gmail.com,Whatsapp.+2348149277967
    He cures.
    Herpes,
    STROKE.
    Hepatitis
    H.P.V TYPE 1 TYPE 2 TYPE 3 AND TYPE 4. TYPE 5.
    HIV
    SYPHILIS.
    Liver/Kidney Inflammatory
    Epilepsy

    ReplyDelete
  15. You have come at the right place! Why not relax, while our professional hands do it at affordable rates? With a diverse range of services like Nursing Assignment Help, Finance Assignment Help, Law Assignment Help, Online Assignment Help, report writing, and many more in a plethora of subjects, working round the clock with dedication and striving to deliver 100% satisfaction to clients.

    ReplyDelete
  16. Thanks for sharing, nice post! Post really provice useful information!

    Hương Lâm chuyên cung cấp bán máy photocopy và dịch vụ cho thuê máy photocopy giá rẻ, uy tín TP.HCM với dòng máy photocopy toshiba và dòng máy photocopy ricoh uy tín, giá rẻ.

    ReplyDelete
  17. COEPD LLC- Center of Excellence for Professional Development is the most trusted online training platform to global participants. We are primarily a community of Business Analysts who have taken the initiative to facilitate professionals of IT or Non IT background with the finest quality training. Our trainings are delivered through interactive mode with illustrative scenarios, activities and case studies to help learners start a successful career. We impart knowledge keeping in view of the challenging situations individuals will face in the real time, so that they can handle their job deliverables with at most confidence.

    https://www.coepd.us/

    ReplyDelete
  18. I was haven herpes 2 on my private part. I have had them for about 2 and a bit years. I am so scared what my mates are going to says if there should fined out i have herpes on my private part and due to the virus my girlfriend broke up with me. I have been to the Doctors 9 times to get it treated. They all come back. I have been using Tee Tree Oil and Wartner (You freeze them at home) and they seem to be keeping the smaller herpes small but they can't seem to treat the larger ones. They don't get any bigger, but then they can't shrink as much. They get smaller a little part at a time. At least they are getting smaller! As soon as I see a new herpes appearing, then I treat it. At the moment I have been using Tee Tree twice a week and then using Wartner every 2 weeks. I was wondering if there was any other information about how to get rid of it. I am only a teenager and I hate it most when it get pi-chins me to scratch it, it get sweets when scratching it most times! I want to get rid of it so bad! DR.ONOKUN website has been a huge help and has helped me realize a lot more about me and my family of genital herpes! so that was when i switch for natural remedy to see if there could be any help by herbal remedy, i search and i saw a great posts by Sarah devise adebayo ehijactor and shanttel Merritt on about the great herbal doctor that get them rid of there disease infection. and this great herbal doctor was called DR.ONOKUN so that was when i contacted him for my own treatment and he prepared me some herbs which i takes for some couples of days, and i take it as he says before i am to no me and my family was perfectly cure for it and never experience it again. please friends if you have herpes virus and you really wants to get rid of it, please contact this great DR.ONOKUN for herbal treatment and you will get rid of it. EMAIL. dronokunherbalcure@gmail.com 

    ReplyDelete
  19. COEPD LLC- Center of Excellence for Professional Development is the most trusted online training platform to global participants. We are primarily a community of Business Analysts who have taken the initiative to facilitate professionals of IT or Non IT background with the finest quality training. Our trainings are delivered through interactive mode with illustrative scenarios, activities and case studies to help learners start a successful career. We impart knowledge keeping in view of the challenging situations individuals will face in the real time, so that they can handle their job deliverables with at most confidence.

    https://www.coepd.us/

    ReplyDelete
  20. We at Coepd declared Data Science Internship Programs (Self sponsored) for professionals who want to have hands on experience. We are providing this program in alliance with IT Companies in COEPD Hyderabad premises. This program is dedicated to our unwavering participants predominantly acknowledging and appreciating the fact that they are on the path of making a career in Data Science discipline. This internship is designed to ensure that in addition to gaining the requisite theoretical knowledge, the readers gain sufficient hands-on practice and practical know-how to master the nitty-gritty of the Data Science profession. More than a training institute, COEPD today stands differentiated as a mission to help you "Build your dream career" - COEPD way.
    https://www.coepd.com/AnalyticsInternship.aspx

    ReplyDelete
  21. OMG i am here to tell you all how i was cured from Hepatitis B by dr Adigba with his herbal medicine i once had the problem of Hepatitis B which affected my work for years i have been using different medication but there was no solution,i search the net and i found the contact of Dr Adigba who help me with his product on curing Hepatitis B problem and other deadly diseases, he also assured me that it is a permanent cure,so i work with him as he ask and i took the medication for just 1 weeks and i was back to normal. for two weeks now i have been doing fine.I give all thanks to Dr Adigba for helping me out of such problem now am the happiest person on earth for seeing myself doing better again.you can also contact him on email dradigba@gmail. com whatsapp him on +2348077875210..dr adigba cure the flowing virus
    1 cancer cure
    2 diabetes cureringing ear
    3 ringing earwarts cure
    4 herpes cure
    5 warts cure
    6 HPV cure
    7 Jaundice
    8 pregnancy herbal medicine
    9 prostate enlargement
    10 Hepatitis B and many more  

    ReplyDelete
  22. If you are stuck with your Management assignment then in this case you can opt for our Management Assignment. we provide the bestOnline marketing expert.We also provideHelp with Presentations help for students across the globe. for more information contact us +16692714848.

    ReplyDelete
  23. Looking for Academic Assignment service? Get Quality Assignment Help Online by Best Assignment Writing Experts at an affordable price. My Assignment Help is the best assignment service provider offered online by a team of experts tutors of Australia , UK and USA. Our support team is available round the clock to help you.

    ReplyDelete
  24. Get the best Accounting Homework Help from our accounting experts. Our professionals aim to provide best possible Online Homework Help for school level, College level and university level students. Urgenthomework is one of the best online assignment service portal that provides quality Accounting Homework Help and Accounting Assignment Help. Also, do check our marketing homework help. you're at the right place if you need Marketing Homework Help, Marketing Assignment Help and this is where you will find the answers to all your queries related to marketing.

    ReplyDelete
  25. We are glad to announce that in COEPD we have introduced Digital Marketing Internship Programs (Self sponsored) for professionals who want to have hands on experience. In affiliation with IT companies we are providing this program. Presently, this program is available in COEPD Hyderabad premises. We deem in real time practical Internship program. We guide participants through real-time project examples and assignments, giving credits for Real-Time Internship. Our digital marketing certified mentors tutor our learning people through modules of Digital Marketing in an exhaustive manner. This internship is intelligently dedicated to our avid and passionate participants predominantly acknowledging and appreciating the fact that they are on the path of making a career in Digital Marketing discipline. We upskill and master the nitty-gritty of the Digital Marketing profession. More than a training institute, COEPD today stands differentiated as a mission to help you "Build your dream career" - COEPD way.
    http://www.coepd.com/DMInternship.html

    ReplyDelete
  26. the common practice of averaging over trials in cognitive psychology makes them difficult to compare or even interpret. Online Homework Service the best online assignment service portal that provides quality Homework Help and Assignment Help.

    ReplyDelete
  27. The poem Cinderella is a part of Anne Sexton’s book of poems called “Transformations”, which is entirely dedicated to the re-interpreted children’s stories and fairy tales Read some details about it here https://primeessays.com/samples/world-literature/cinderella-poem-story-comparison.html

    ReplyDelete
  28. Happiness is all I see now. I never thought that I would be cured from the HERPES virus again. I have been suffering from a deadly disease (HERPES) for the past 3 years now, I have spent a lot of money going from one place to another, from church to church, hospitals have been my home every day. Constant checks up have been my hobby not until this faithful day, I was searching through the internet, I saw a testimony on how DR OLUTA helped someone in curing his HERPES disease, quickly I copied his email which is dr.olutaspellcaster@gmail.com just to give him a test I spoke to him, he asked me to do some certain things which I did, he told me that he is going to provide the herbal cure to me, which he did, then he asked me to go for medical checkup after some days after using the herbal cure, behold I was free from the deadly disease, he only asked me to post the testimony through the whole world, faithfully am doing it now, please brothers and sisters, he is great, I owe him in return. if you are having a similar problem just email him on ( dr.olutaspellcaster@gmail.com ) or you can whatsApp his mobile number on +2349065326267
    You can also contact him if are diagnosed with any the virus below
    {a1}HIV and AIDS
    {2}Diabetes
    {3}Epilepsy
    {4} Blood Cancer
    {5} He Can Make you get Pregnancy
    {6.} HPV
    {7} ALS
    {8} Hepatitis B
    {9} Diabetes
    {10}Love Spell
    (11) Fibroid  
      https://m.facebook.com/pages/category/Product-Service/Drolutaherbalhome-100710878112591/  

    ReplyDelete
  29. Good news this is to everyone out there with different health challenges, as I know there are still a lot of people suffering from different health issues and are therefore looking for solutions. I bring you Good news. There is a man called Dr ehiaguna a herbal practitioner who helped cure me from HSV (2), i had suffered from this diseases for the past 5 years and i have spent so much money trying to survive from it. I got my healing by taking the herbal medicine Dr ehiaguna sent to me to drink for about 14 days . 3 days after completion of the dosage, I went for a medical checkup and I was tested free from HSV. all thanks to God for leading me to Dr ehiaguna who was able to cure me completely from this deadly diseases, I’m sharing this so that other people can know of this great healer called Dr ehiaguna because I got to know him through elizabeth who he cured from HIV. I was made to understand that he can cure several other deadly diseases and infections. Don’t die in ignorance or silent and don’t let that illness take your life. Contact Dr ehiaguna through his email  drehiaguna@gmail.com You can also whatsapp/call him on:+2348073908953 . Visit his website  https://effectiveherbalcurehome.blogspot.com/   He cure all forms of disease {1}HIV/AIDS {2}DIABETES {3}EPILEPSY {4} BLOOD CANCER {5} HPV {6} BRAIN TUMOR {7} HEPATITIS {8}COPD{9} SICKLE AND ANAEMIA.etc Be kind enough to share as you received.  

    ReplyDelete
  30. I will love to inform you about a great herbal medicine man in Africa now as (Dr Odiagbe) and his herbal product he is capable of curing disease infection mostly Common in the U.S.A. and all over the world. I will love to share with others who are suffering from the same symptoms.  Herpes, Cancer. Chronic lower respiratory disease, Alzheimer's disease. Diabetes,Influenza and pneumonia. Kidney disease. hepatitis A&B and he can also bring back your ex . You can contact him via whatsapp (+2349011108005  ) or email him via (Drodiagbeherbalhome82@gmail.com)
     @dr odiagbe
      
    His Website: https://drodiagbeherbalhom.wixsite.com/drodiagbeherbalhome

    ReplyDelete
  31. Do you want to get rid of the tedious Database assignments and still score A Grade? Get Database Assignment Help from our professional PhD Programmers experts. Assignment Hippo is the best assignment help and writing service provider offered online by a team of experts . Avail Economics Assignment Help From Economics Experts.order now to get quality assignment help or visit our Database Assignment Help Blog to get more detailed information.
    https://edu-assignmentservices.blogspot.com/2020/11/the-best-online-database-assignment-help.html

    ReplyDelete
  32. Our corrections ensure guarantees that you'll get totally reliable assignment help in Melbourne. We won't quit dealing with your assignment until you get what you requested. It's in our bit of leeway to convey splendid work from the main endeavor, and we center around doing that. more- assignment help melbourne, assignment help australia

    ReplyDelete
  33. While getting complication in assignment writing, always prefer to have assignment help from ABC assignment help that provides online essay help, paper help, study help, dissertation help and many more from the top writers in Australia.

    ReplyDelete
  34. Contact My Assignment Help online website to get our assignment help service for all your academic tasks. Through a team of over 3000 subject experts we offer individual attention to every student making the assignment help experience completely unique and stress-free for students aiming to score high in every assignment.

    ReplyDelete
  35. Nice Blog !
    Our team at QuickBooks Customer Service Number 1-877-751-0742 plays a significant role in troubleshooting all the problems of QuickBooks in less time so that you can peacefully work on your software.

    ReplyDelete
  36. Searching for quality Finanace Assignment Help? Get instant Assignment Help at an affordable price that too plagiarism free work from genuine experts online. Get in touch with My Assignment Help to get quick Finance Assignment Help within the deadline. Our team is active 24x7, and you can talk directly to our Finance Assignment Help experts any time you want. Visit our website for more detailed information.

    ReplyDelete
  37. Nice & Informative Blog !
    QuickBooks Error 15222 mainly occurs while upgrading QuickBooks Desktop or Payroll. If you find so, fix it by dialling our Qb experts.

    ReplyDelete
  38. Nice Blog !
    Our team at QuickBooks Customer Service takes pride in delivering quick services in the face of current circumstances.

    ReplyDelete
  39. Your blog is filled with unique good articles! I was impressed how well you express your thoughts.


    Regards,
    Online Dissertation Help

    ReplyDelete
  40. Our research paper thesis help covers everything. From thesis statement to all the complete all necessary research tasks.

    ReplyDelete
  41. Are You Looking Perfect contract law case study assignment Assistance? Assignment Studio Have Top Phd Expert at Best Price .on-time Delivery,order Now,24/7 Help.chat Now.

    ReplyDelete
  42. Do you need marketing homework help? Assignment Studio Provides Professional Assignment Writing Services With Top-quality Assignment With 100% Plagiarism Free Content.

    ReplyDelete
  43. At Assignment Studio, we have professional labor economics assignment help expert to assist and provide you with affordable writing services.

    ReplyDelete
  44. Hire experts for scientific report writing help in australia. At Assignment Studio we offer high quality services at affordable rates.

    ReplyDelete
  45. This comment has been removed by the author.

    ReplyDelete
  46. Our aim is to provide the best quality services at the best price. If you are seeking for, then you are at the right place. Rado first copy watches in india. We have more than 10+ years of experience in this business. Our customer care services are available 24/7 to assist all your needs. You can get the best quality Replica watches in India at the best price. Just visit and choose according to your need and budget. 100% secured online payment gateway.

    ReplyDelete

  47. I was diagnosed as HEPATITIS B carrier in 2013 with fibrosis of the
    liver already present. I started on antiviral medications which
    reduced the viral load initially. After a couple of years the virus
    became resistant. I started on HEPATITIS B Herbal treatment from
    ULTIMATE LIFE CLINIC (www.ultimatelifeclinic.com) in March, 2020. Their
    treatment totally reversed the virus. I did another blood test after
    the 6 months long treatment and tested negative to the virus. Amazing
    treatment! This treatment is a breakthrough for all HBV carriers.

    ReplyDelete
  48. HPV HAS CURE....I finally got cured out of this mess that has been in my body for 2 years. I also recommend you if you’re living with (Human papillomavirus) you can contact him on his Email....oyaguherbalhome@gmail.com or call and whatsapp him +2348101755322 contact him for solutions Like 1) HSV Cure 2) Diabetes Cure 3) Cancer Cure 4) HIV/AIDs Cure and Any kind of Sickness, Disease and Infection

    ReplyDelete
  49. Assignment writing administrations are extremely normal nowadays. There are such countless organizations offering quality paper help however not every one of them are solid and trust commendable. We never think twice about the nature of our substance since we realize that it will influence your grade and disappoint our customer that is the reason we focus on giving top quality article help regardless of the way that we keep our costs low. essay writing help , assignmenthelp

    ReplyDelete
  50. I'm 40 years old female I tested genital herpes (HSV1-2) positive in 2016. I was having bad outbreaks. EXTREMELY PAINFUL. I have try different kinds of drugs and treatment by the medical doctors all to know was avail. Six months ago I was desperately online searching for a helpful remedies for genital herpes (HSV1-2) cure, which I come across some helpful remedies on how Dr OYAGU have help so many people in curing genital herpes (HSV1-2) with the help of herbal treatment because I too believe there is someone somewhere in the world who can cure herpes completely. At of the past 2 months, however, I've been following his herpes protocol Via oyaguherbalhome@gmail.com or +2348101755322 and it stopped all outbreaks completely! To my greatest surprise I was cured completely by following the protocol of his herbal medicine . Don't be discouraged by the medical doctors. There is a cure for HSV with the help of herbs and roots by a herbalist Dr call Dr OYAGU he is so kind and truthful with his herbal treatment, kindly contact him for more information Via oyaguherbalhome@gmail.com or WhatsApp DR on +2348101755322 or visit his website https://oyaguspellcaster.wixsite.com/oyaguherbalhome you will be lucky as I am today

    ReplyDelete
  51. helpful post for "Averaging can produce misleading standardized effect sizes". we read this blog.
    App Development Company

    ReplyDelete
  52. I used to suffer from HERPES GENITAL for about 3 years so I can relate to people who have the cure. No medications or treatments ever really did anything for me (i tried them all no one worked. but I was actually able to completely cure HERPES naturally after countless hours of online research. What worked for me is as follows: I saw  Dr Oje Abacha Information online that he normally cure and treat disease and infirmities with his Herbal Medicine, I never really believed the people who were recommending him thou i saw on blog about 6 people where also testifying on how they were cured by Dr Oje Abacha and stillEllen recommend Dr Oje Abacha who uses herbal medication to cure HERPES GENITAL VIRUS and gave me his email, so i mail him He told me all the things I need to do and also give me instructions to take, which Followed properly. Before I  didn"t know what was happening after two weeks the Herpes GENITAL VIRUS that were in my body got vanished . so if you are also heart broken and also need a help, you can also email him: oje.herbalsolutioncentre@gmail.com . or WhatsApp   him on +2349050957732 if you are infected with any disease like HIV,AIDS,CANCER,LOVE SPELL, HERPES.PVC, or any other disease you can also be happy like me by contacting.....Name: Dr Oje Abacha His website  https://ojeherbalsolutioncentre.wordpress.com     

    ReplyDelete
  53. Am freaking out, I had oral sex with my partner, in the morning he said his lip felt swollen and within a couple of hours it developed into a blister/ cold sore! I’ve never had one before and am freaking that I may have contracted herpes!!! 2 days later my bottom lip is tingling but I’m really worried about it developing down below, we did not know he had one as there were no symptoms one was coming, So i decided to search for possible cure on how to eradicate this virus after the doctor confirmed that me and my partner we diagnose with this virus then miraculously i came across a woman on a blog how she testify about this great herbal Dr. Kham that she was cured after taking the dosage of his herbal medication for two weeks, Then i decided to contact him also for a help, He explain everything to me concerning this virus an he told me to worry no more that he is going to get me cure, Then he prepared the herbal medication and shipped it to me and my partner and we start taking the dosage for two weeks as he prescribed an we found our results total Negative after completing the dosage, Please if you have any Relatives, Friends who is having this health issues kindly contact herbal Dr. Kham on Email: dr.khamcaregiver@gmail.com and here is his Whatsapp contact number +2348159922297, You can also check his Website on https://herbal-dr-kham.jimdosite.com/ or visit his Blog at https://drkhamcaregiver.blogspot.com/ Here is his FB PAGE: https://web.facebook.com/Dr-kham-herbal-remedies-101928302031061

    ReplyDelete
  54. Now a days students cannot figure out how to write an assignment thus they plan to take the assignment help from the academic writing service provider. For taking the best assignment writing help you must check the assignment samples provided by the assignment writing service provider. Reviews are also important so read the reviews of the customers that have taken the help for writing the assignments from them.

    ReplyDelete
  55. I'm recommending Dr babaiba to everyone who have herpes simplex virus to get the cure from him. I was diagnose of genital herpes in 2019 and i have been searching and asking questions to see if i could get something to cure the disease because i did not believe what the doctors say that no cure is found yet. I came across a comment on Youtube and the person testify how she was cured from herpes and hpv after using Dr babaiba herbal medicine. I quickly contact Dr babaiba and explain my problem to him and he prepare the herbs and send it to me through UPS and gave me instructions on how to use it and tell me to go for checkup after usage which i did after two weeks of taken the herbal medicine and my result was NEGATIVE. I waited another month and retested the result was still NEGATIVE and my doctor told me that am completely free from herpes. Am so happy and grateful to Dr babaiba for what he has done for me and i will continue to share this for people out there to know that there is cure for herpes. You can contact Dr babaiba on email and WhatsApp to get the cure from him. Email:drbabaibaherbalsolutiontemple@gmail.com and WhatsApp +2348140046509

    ReplyDelete
  56. Dear friends online My name is Destiny Hudson And I live in the USA, Dominica I am here today to appreciate the good work of Dr Oyagu, for helping me curing my HSV 1&2 Disease, I contacted the virus from my Partner, i found out he was cheating on me, so i broke up with him, 2 month later i went to test myself in the hospital when i was seeing sore on my mouth and Private areas, i was diagnosed of HSV 1&2. i tried using the acyclovir medicine but it didn't help in curing it, i went on a search and found out Dr Oyagu curing people illness, and so i got his email and i was told how i can get his herbal cure, 3 days later i received his medicine after using it for 2 weeks i was tested again and was confirm negative, today i am totally free. If you are over there looking for solution email: oyaguherbalhome@gmail.com or contact him on whatsapp +2348101755322 or visit his website https://oyaguspellcaster.wixsite.com/oyaguherbalhometoday and share your own testimony. And He also has herbal cure for the Following DISEASES, eczema, urethra wart, chronic problems. Herpes, Cancer, Als, Hepatitis, Diabetes, HPV ,Infections, ulcer ETC

    ReplyDelete
  57. Psychology is a relatively recent field in the realm of science, and indeed is not considered a firm science by some people due to its newness and theoretical basis. This is both a good and bad thing. Psychology gives students a lot of freedom when it comes to interpreting theories and behavior, but its relative lack of concrete concepts can be bewildering for some individuals. We are at assignment help . Assignment helps under our psychology assignment help so that students can complete their assignment on time and score good marks.

    ReplyDelete
  58. Am here to testify about the miraculous work of a great traditional doctor called Dr. Kham.....I have been suffering from Herpes Virus since the last 2 years but today I am happy that I am cured from it with the herbal medicine made by Dr. Kham the great healer, I was browsing the internet searching for the possible cure when I came across a testimony shared by someone on how Dr. Kham cured her from Herpes Disease. I quickly contacted him to get the cure and today i am now free from the Virus, I am so much happy today that we have someone like this great healer out there, so people out there kindly contact this great doctor on his email address please sir keep your good work cause there are people out there who is in need of your healing medicine .please in contact with him with this information,
    .
    .
    *EMAIL*..... dr.khamcaregiver@gmail.com

    *WHATSAPP/CALL*...... +2348159922297

    *WEBSITE*......https://drkhamcaregiver.wixsite.com/drkhamcaregiverherba

    *FB PAGE*.........https://web.facebook.com/Dr-Kham-Herbal-Remedies-101547721440460/

    I assure you that Dr. Kham can prepare Herbal medicine for all kinds of diseases like,, HIV, CANCER, HEPATITIS B, DIABETES, COLD SORES, SYPHILIS. HBV, HPV, AND ANY OTHER STDs, Contact Dr. Kham to get your healing Today.

    ReplyDelete
  59. Hey! Fabulous post. It is the best thing that I have read on the internet today. Moreover, if you need instant support for QuickBooks Error, visit at QuickBooks Customer Service Phone Number Our team is always ready to help and support their clients.

    ReplyDelete

  60. myassignmenthelp is the service which is provided by My Assignment Help. It helps to complete the assignments of the students within a given deadline. It provides proper guidance related to the assignment and facility among the students.

    ReplyDelete
  61. Expertise in major locations of India - Chennai, Delhi, Mumbai, Bangalore, Ahmedabad, Hyderabad, Kolkata and Cochin. Our digital marketing agency service assures 100% best results never seen before.

    Digital Marketing Agency in Chennai

    ReplyDelete
  62. Biostatistics is an integral skillset for the advancement of knowledge and I not restricted to public health policy assessments. It also plays a crucial role in biology, in the field of health policy, clinical medicine, in data analytics of health economics, in the advanced science of Genomics, Proteomics, and a number of other allied disciplines. Therefore, in response to the worldwide shortage of biostatisticians, Australia has thus established a national consortium of high ranking eight universities to develop skilled biostatisticians for data analysis and interpretation. We are at assignment help . Assignment helps under our Biostatistics assignment help so that students can complete their assignment on time and score good marks.

    ReplyDelete
  63. https://valueassignmenthelp.com is the finest website for assignment help online and homework help services. We have 10years of experience PhD level experts for all subjects. Value-assignment-help highly searched website for paper work and content writers. Check our services and our coverage range.
    Assignment help
    Australia assignment help online
    case study assignment help
    essay writing services

    ReplyDelete
  64. Avail the best quality Assignment Help in Australia by top assignment writing experts. Assignment helps under our Citation machine assignment help so that students can complete their assignment on time and score good marks.

    ReplyDelete
  65. I am really feel glad to read out published post on this blog. Apart from this, I am still waiting other post for escalating my knowledge power. You can get your unical cut off mark for law

    ReplyDelete