Statistics is the science of learning from data, and of measuring, controlling, and communicating uncertainty; and it thereby provides the navigation essential for controlling the course of scientific and societal advances (Davidian, M. and Louis, T. A., 10.1126/science.1218685).

Many economic, social, political, finance and investment decisions cannot be made without statistical techniques.

As a discipline, statistics is the development and application of methods to collect, analyze and interpret data. Modern statistical methods involve the design and analysis of experiments and surveys, the quantification of biological, social and scientific phenomenon and the application of statistical principles to understand more about the world around us. Since data are used in most areas of human endeavor, the theory and methods of modern statistics have been applied to a wide variety of fields. Areas that use modern statistical methods include astronomy, physics, genetics, education, engineering, manufacturing and management, government, research labs, public health, sport and even the military.

"The best thing about being a statistician is that you get to play in everyone else's backyard." (John Tukey, Bell Labs, Princeton University).

in psychology, for example, you can not establish a link without statistics. The data is too much noisy and you need a threshold (the so-called "p-value"), however controversial its level is, to determine whether a hypothetical link is verital or not.

@Ivilin: Not only psychology and social science, it is sometimes become necessary to use statistics in natural sciences and technology when it is hard to establish link between model and the world. For example statistics or probability theory is applied in Statistical mechanics or statistical thermodynamics when population is large and a ubique exact mathematical solution is not possible.

Wright. Statistics should be used however very carefully, and not only blindly applying certain methods because they were already applied in some other conditions. Analogy is good, but creative analogy is better.

We need to be very carefull about how we interpret statistical results, for statistics can be true but misleading at the same time!! So even when statistics are technically accurate, particular statistical facts can be very misleading. I give below two examples:

1-I once heard a statistic that the rate of teenage pregnancy in a conservative religious group was higher than the national average. This seemed surprising until it became apparent that the reason wasn't a high percentage of unwed mothers - it was a high percentage of women who got married while still in their teens.

2-I recall hearing apparently conflicting claims about employment during a presidential election campaign a number of years ago. The challenger claimed that unemployment was up during the President's term in office. The President's campaigners said that employment was up! It turns out that both were true. The population had increased, and it turned out the number of people who were employed and the number of people who were unemployed had both increased.

one should distinguish between statistically signigicant link and confounds.. Lefthandes cut bread with their left hand because it's bread? Surely not. They cut bread with their left hand because they are more skilfull with their left hand. The same is valid for the examples given by Issam

@Issam: You are right in that governments, firms and others use statistical gimmickry to their advantage. It is why to many statistics is one of the blatant lies. However, Ivilin also has an important point with respect to use/application of statistics. In the toolkit of statistics, there are a number methods which can be applied to solve a problem. A careless use of a method may give erroneous results. Therefore, proper understanding of the problem and the methods which may be applied can only help in exercising right choice of a statistical method/technique.

In science, sometimes a researcher is so sure about his idea that he becomes "blind" to basic confounds explaining the result. Worse, he could hide, mishandle, or consciously not report factors, in order to publish. It's a reviewer's role to verifies the corectness of the declared method and eventually point out confounds. Sure, a new result becomes a real result only when it's independently confirmed.

In politics.. the general pubblic hear only the outcomes and now nothing about the methods. It should be the opposition, informed journalists, and others, to verify the correctness of the published information.

Deborah Hilton Statistics Online

http://sites.google.com/site/deborahhilton/

see this video - tells you why it is important.

http://www.getstats.org.uk/latest-video/

@Deborah

Thank you for the video link. My only comment is I wish it was a bit longer!!

@Deborah: Thank you for your input.

I've just watched the statistics in sport video on the get stats site and this is also very good. I had an error initially but it is working now.

I am curious to watch that video. Deborah Please do attach it.

Hello Mohammad, sorry it is on the other website where the other one was so I cannot attach it at all, you'll have to go to that URL and then find it under videos but it plays OK and is interesting. Good luck, Debbie

I always figured the progression was "Lies, Damned Lies and Statistics" because misused statistics can mean someone may think they are telling the truth but aren't.

As I recall from the days I thought I might like to become a physicist, Einstein's argument vs quantum physics was that he saw the universe as a mostly deterministic system that could understood and interpreted, and he saw the quantum theorists as throwing that way.

Statistics has sort of a middle ground...you don't know for sure, but you can constrain the possibliities. Or as someone once said, all statistical models are wrong but some of them are useful.

"There are lies, damned lies and statistics"------Mark Twain

But, Issam, Mitchell is very right when he says, "Statistics has sort of a middle ground...you don't know for sure, but you can constrain the possibilities." In fact in the absence of hard data, or system that are not linear are easily amenable to mathematics, comes statistics to rescue. However, we should not forget that the discipline of statistics is based on mathematical foundation..To me nature as a whole is nonlinear in very many different aspects. At every level of analysis deterministic models in most cases fail to grasp the reality.

@Mohammad

I was merely trying to give the author name of the quote used by Mitchel. I totally agree with what Mitchel has said.

Dear Prof Khan

Thanks for initiating an interesting and relevant debate on statistics. I have gone through the various answers posted till now. Most of the answers implicitly assume statistics as tool to test some hypothesis. In this sense, I agree with Mitchell's all comments and especially when he says, "Statistics has sort of a middle ground...you don't know for sure, but you can constrain the possibilities."

However, this may be true to any tool or method used to verify or test a hypothesis. As we all know that it is possible with a single contrary evidence to reject any hypothesis but it would never be possible to say that a hypothesis is true despite the infinite evidences in favor of it. As it assumes that in future some contrary evidence may appear and this possibility can not be denied.

Thus, for instance if any mathematical equation or model explains certain phenomenon at a given moment or during a specified period it does not mean that it is the only and the true explanation of the phenomenon at hand. There is implicit assumption that the law of nature (or a given phenomenon) can be better explained by some other mathematical model from among the theoretically existing (but currently unknown) set of alternative explanation.

The falsifiability of any theory or model is the implicit assumption of science and only on this assumption we are making progress in science by rejecting the earlier models (whether mathematical, statistical or otherwise) and presenting the new one.

If one agrees with the doctrine of falsifiability of any theory or model then one has to accept that there is certain degree of uncertainty (that may be expressed in terms of probability).

I do agree with you that mathematical models may be better than the statistical one in some respect and would also add that in many of the statistical analysis the element of subjectivity also enters but such subjectivity is less likely to be associated with mathematical analysis and models. For instance, in factor analysis, there are several steps where subjectivity enters (e.g., in interpreting the factors).

Dr. Pandey

Thank you for your invaluable contribution. I am in full agreement with your observations. But, I would like to add that in cases where mathematics fails statistics is the refuge. Not only in early days, still now, in spite od two decades progress in quantum/wavelet algebra, quantum scientists depend more on statistics than mathematics.

Why statistics matter? Because it is usefull. Say, you are investigating the (hypothetical) influence of carrots on the mass of a rabbit. You can, of course, test your hypothesis on a pair of rabbits feeding one of them with carrots and the other one with anything but carrots. Will you be able to get any meaningfull and unquestionable results from such an experiment? Obviously not. Using two groups of rabbits, and statistics, is much better choice.

Statistics will tell you what is likely and what is unlikely. But unlikely doesn't mean impossible. Statistical mechanics of gases works wonderfully in steam machines, but this need not to be the case at nanoscale, when the number of involved particles (perfectly identical in contrast to rabbits) is much lower, say merely few thousands.

Quantum theory is still another story. One should distinguish between deterministic and indeterministic point of view. Indeterminism doesn't imply probability (or statistics) in an automatic way. Specifically, we have a nice quantum description of a single electron (or atom). There is no place for statistics here, but it makes sense to talk about probabilities to find the said electron here or there, in given time interval.

But be careful: one of the greatest probabilists, de Finetti, once said "probability doesn't exist".

Lots of good thoughts from each of you. I'm still in the process of assimilating the details. Thanks!

Pure unbiased statistics is one thing, but interpretation could be highly subjective and "human error" prone. A perfect example is the clear difference of opinions after years of research regarding "Global Warming". Is it there? Or is it a long term cycle we are experiencing? Is bovine flatulence a critical component of this phenomenon? At this point I must discount the fraud, abuse and miss-leading that can be perpetrated with "statistics" and only focus on the scrupulous use of statistics.

Similar predicament arises in the case of "Radon" gas, a naturally emanating gas from under-ground. Is it detrimental or beneficial? Some studies indicate a possible reduction of stomach and lung cancers. Is the exposure to dilute Radon gas therapeutic or deleterious to human health? At what concentrations/levels?

Another example of statistics! Is the predominance of a certain race or group of people in the jail population indicative of the bias of society for that denomination or does that group need some sociological intervention?

That said, my interest in statistics is from the point of view of XRD (X-ray Diffraction) data analyses. Statistical analysis provides me with a key to experimentation - measurement of PRECISION!

Very interesting discussion.

First of all, statistics is a very powerful mathematical tool for understanding an extremely wide variety of phenomena that arise from the joint action of a big number of individual values. For example, every macroscopic physical magnitude is the result of a huge set of "smaller" numerical values (pressure, temperature, electrical current....).

So the nature of scientific method is esentially statistical.

Another quite different issue is than every tool can be used by expert/non expert hands. Then, the "statistical lies" arise only as a consecuence of wrong or bad intended usage of the method.

all the best

Carlos

Dear Professor Mohammad Firoz Khan, In my opinion probability is essential element and it matters. In many situations we fail to apply any other approach to model a system but probability escapes us from that situations,

Dear Afaq Ahmad,

I agree with you 100%. It is the actual reason of the importance of Statistics.

Dear Professor Mohammad Firoz Khan, Thank you for the comment (agreeing 100%). We frequently use non-deterministic signals (random in nature) and therefore, realize the importance of Statistics.

Dear Ravi,

Your observation is quite valid in that people in power and in business or other people where it is felt necessary, generally statistics is manipulated to serve their ends. We have a term “statistical gimmickry" to describe such situations enumerated by you. It is no fault of statistics. Statistical results do not speak themselves, these are interpreters who speak on the behalf of statistical results. It is, therefore, necessary to use critical thinking when evaluating a statistical interpretation.

Right you are, Firoz! Fortunately, in the field of XRD Microscopy, the only statistics I'm concerned about is "Noise". No pun intended. But this is an inevitable fact about acquiring information, determining actual SIGNAL from NOISE. Pun intended!

Statistics is the key in distinguishing SIGNAL from NOISE (SNR - Signal to Noise Ratio) experimentally. Understanding experimental statistics better will help enhance SNR unequivocally. It is quintessential in real time XRD imaging!

BTW you were also correct about my RG score. It went from 4 to 29 quick. Have no clue how? I wasn't even focusing on it so far and it is inconsequential for me. Interesting though!

[email protected]

http://www.flickr.com/photos/85210325@N04/10221065324/

I think that Statistics without an informed sense of reality, a great mind for synthesis and the ability to recombine previously disconnected disciplines and results falls apart. Statistics is, being it driven by big or small data amounts, a necessary but not sufficient condition to understand complex phenomena.

Francesco,

Yes it is. From selection and application of an appropriate statistical method to the interpretation of the results, one should know what reality is being capture, represented and interpreted. Without reference to the framework of a specific reality, one cannot choose, apply or interpret results. Results should be critically evaluated with reference of the domain of the reality. It is what I refer to as Critical Thinking in the case of applications of statistical methods. .

It is correct

Dear Mohammad,

You formed your question very precisely:

Why does a researcher need to learn statistics?

I agree with all the previous statements, which explicitly shows the crucial importance of knowledge in the field of statistics, for the correct interpretation of the results - and hence - for proper inference.

I just wonder about whether the consequence of so great importance of statistics must be obliging all researchers to perfect mastery of statistics as a science?

Personally, I think that statistic is the key area for almost all scientific research, but it is so complex and does not leave room for "cursory" analyzes, that the most appropriate solution is probably to entrust these important statistical analyzes to those skilled in this field.

At this point we would begin the discussion on various aspects of research and the creation of multidisciplinary teams, but this theme is not the place for such discussion.

At the end I will say in such a way: every scientist should have mastered the basics of statistics, and aware of how important it is and how much damage it can bring its omission or improperly implemented. However, the statistical study of the results - especially in the case of complex issues - I will left to those skilled in this field.

Dear Professor Andrzej Szymanski, Stating about your personal experience and fair enough while concluding giving the complete answer in the theme of the question. Thanks!

Dear Andrzej,

Your observations are fully agreeable. It is true that in most cases simple issues may be addressed by deterministic mathematical methods through analytical solution, approximating a complex function by a simpler one or using numerical analysis. However, as almost all the respected contributors have pointed out, it become indispensable to use statistics when number of variables are large or problem is too complex to be solved by mathematics.

I am highly obliged for your invaluable suggestions.

Dear Mohammad

In your recent post you made a short summary of what up to now most of us in this topic wrote.

I think we are unanimous in finding that the development of complex, multi-threaded, multi-disciplinary research, requires the help of a good-class, professionals from statistics.

Maybe...

So, let's we doing step forward in this topic. Let us make an attempt to answer the question: when you actually need the help of specialists from the statistics, is it effective?

Unfortunately, it seems to me that we are still in a situation that the answer to this question is "NO".

I have a feeling, that this may be related to the lack of habits and beliefs to the effectiveness of interdisciplinary research teams. Although in this case I would be rather inclined to say, that statisticians collaboration with scientists from the natural sciences, requires a lot of experience, skill and ability to present a clear vision of what we expect from each other.

I think, the lack of fulfillment this last condition is the main reason that on one hand, we all see the need for assistance from the statistics (and statisticians), but, on the other hand, the results of this cooperation are rarely satisfactory - to the extent that the indiscriminate jokes like: "There are three kinds of lies: lies, blatant lies, and statistics" or "Statistics do not lie, only statisticians ", still have many supporters.

Dear Professor Mohammad Firoz Khan, There are many instances where statistics is the only way to evaluate the performance and failure predictions, like in Fault-Tolerance Systems the parameter Mean Time Between Failures (MTBF).

At the risk of plagiarizing myself, there is always a "half full cup" story to every "half empty cup" story. Every "heads" has a "tails"! Just staistics!

Statistics is indispensible to science. Statisticians on the other hand apparently need to be carefully monitored and verified. Jesting!

Dear Andrzej,

I would like to differ from your observation, "Unfortunately, it seems to me that we are still in a situation that the answer to this question is "NO"." The fact is that failure of normal science (one of its important function for informed decision making to control future events to the advantage of mankind) for instance in the case of global, regional and local environmental crises, there has developed postnormal science that uses not only hard scientific methods, statistics and finding of social sciences to inform decision maker. It does not amount to that science has failed on all fronts but in some important respects. Therefore, in cases of scientific uncertainty and risk it is statistics that holds ground and attention is turned to statistics for answers.

A very intresting discussion and valid arguments. But statistics is based on the input data and the end results are not going to be any different. Most of the stastistical operations will not result in drastically opposite results. The difference and issues are with interpretation of teh stastistical results. To cite an old example : a person was asked to put half of teh body in freezer and rest in an oven. It was asked to statistician what is his situation like after lost of calculations one came up he is comfortable (that was simple averaging) but current statistical operations will show in either situation he is uncomfortable as they will be using various other operators rather than mere averaging of temperatures.

It is a necessity now looking at the enormous volume of data espically the wide and varied environmental data, thsi data assimilation would have been a nightmare without statistical tools.

Dear Mohammad Firoz Khan,

Silicon Valley as well as in Silcon Hill they adapt all the processes of Quality Testing because one in a Million faulty component creates a high level of most probable risk of damage to the next process where this component is to be used. But this is also a fact that a company can't test each and every component that they ship to us (the consumer). The company test just a few samples using statistics. If the sample passes quality tests, then the company assumes that all the items in the batch are good.

I guess using statistics we can easily handle enormous amount of data that is otherwise impossible to assimilate.

Also using statistics a researcher with very low mathematical understanding can undertake complex analyses.

Dear Saif Uddin,

Your simile of freezer and oven is better formulated in another joke about the average. A person was drowned for crossing a shallow river when told that on average, the depth of water in the channel on a cross-section is not more than knee deep. His last words were “Is ausat ne duba dia” (literally: the average has drowned me).

However, from metrology through modern Climate Science to high energy physics none has claimed that mean (average) describes central tendency incorrectly. Of course, one has to give critical thought where what statistic is to be used. A student noted prices of eggs from a news paper over the years in a city and from a magazine related to work related stress and depression proportion of persons suffering one or another type of mental disorder over the years. He calculated the correlations between the two for the corresponding years, the correlation was as high as -0.974 and its significance was 0.0002, he from the perspective of a long held notion in the subcontinent (dimagh pe garmi chdh gai hai = it is caloric heat (energy) of the highly nutritive food that had reached the brain and resulted in mental disorder) concluded that the calorific energy of eggs had been the culprit of mental disorder of the mental disorder of the people. The question is does modern medical science supports this notion, if yes, then conclusion is correct and if not conclusion is not justified. However, sometimes such futile exercises or such exercises with intention may through surprises which sophisticated mathematical models or formulation.

In the last, let me suggest a few research papers (these can be downloaded from http://arxiv.org/) which use probabilistic models of interpolation from quantum wave, field and spin through astrophysical mass to molecule-surface interactions in physical chemistry. Methods may be highly reliable, robust and mathematised but have probability or statistical solution at their core.

Spin effects and compactification by Alexander J. Silenko and Oleg V. Teryaev

Constraints on RG Flow for Four Dimensional Quantum Field Theories by I. Jack and H. Osborn

Multidomain Spectral Method for the Helically Reduced Wave Equation by Stephen R. Lau & Richard H. Price

Are interpolations in metallicity reliable? By L. Angeretti G. Fiorentino and L. Greggio

Representing molecule-surface interactions with symmetry-adapted neural networks by Jörg Behler, S¨onke Lorenz, and Karsten Reuter

Firoz! I just noticed that you have included only two topics to display this query on. RG will allow up to 5 topics to be included. I submit that you will have better readership and hence input if you expose your question to a variety of professionals who use statistics. I'm not sure as to other topics to include, but you are the best judge in that matter.

Query statistics as of December 16th, 2013: 7 / 0 · 43 Answers · 1348 Views

Ravi,

Thank you for your suggestion. But, I visit this post of mine after quite a while. Sometimes, I find myself obliged to respond.

Dear Professor Mohammad Firoz Khan,

What is your opinion if I say that Statistics is Like Law. Lawyer interprets the law to hammer the defense for the benefit of the clients. Here we researchers interpret statistics to hammer our points of interests.

Dear Professor Mohammad Firoz Khan,

Statistics is the science of collecting, analyzing and making inference from data. Statistics is a particularly useful branch of mathematics that is not only studied theoretically by advanced mathematicians but one that is used by researchers in many fields to organize, analyze, and summarize data. Statistical methods and analyses are often used to communicate research findings and to support hypotheses and give credibility to research methodology and conclusions. It is important for researchers and also consumers of research to understand statistics so that they can be informed, evaluate the credibility and usefulness of information, and make appropriate decisions.

Source:

http://www.bcps.org/offices/lis/researchcourse/statistics_role.html

My impression is that many conclusion we get by means of Statistics are quite similar to those we might get by using common sense and experience. But, human being need numbers and fit measures to be heart's-ease.

@Francesco,

You may be right when data set is small and a guess may provide an answer. Situation is like, in emergency we cannot waste time using scientific method, people need a lucky guess that take them to safety or avert risk or safe them from risk.

But, when we are doing research and are in search of pattern or trend, no argument of a lawyer or commonsense lead to a close answer when data set is quite large. Commonsense is required in selecting a method that can give the best results, but no amount of commonsense may decipher the true pattern or trend in data with conviction.

That is right Feroz! Statistical methods in science improve the confidence of others as well. The certitude of precision is dramatically improved through statistical methods and techniques. It is invaluable when data sets are humongous as in XRD Microscopy & Image Processing.

Feroz! I invoked your discussion in the following RG question with reference to the context of statistics.

It is interesting how statistics can be used in medicine. Help these fellows out. Jump in! I applaud the highly expert RG membership participating in this articulate discussion and ask you to share your knowledge and opinion in statistics. This topic of health care is relevant to all of us at some point in our lives. We'd be a statistic too! Just being punny.

https://www.researchgate.net/post/Clarification_needed_on_Statins_and_associated_adverse_events-can_anyone_please_help?cp=re68_x_p2&ch=reg&loginT=RDwJhAINXTF_eEOgAo8vAtXaS7VBu_pIIfl7zdLSUQI%2C&pli=1#view=52e94bdbd3df3e2f1a8b45c7

Question by Deepak Kumar B of Vaagdevi College:

"Clarification needed on Statins and associated adverse events - can anyone please help?

There is still a confusion- though atorvastatin (lipitor) is the world's largest selling drug it causes major adverse events like myalgia, erectile dysfunction etc. I have gone through literature where few investigators say statins leads to ERD and few says statins cure ERD?"

@Ravi,

Please again go through my response to your answer,

"Dear Ravi,

Your observation is quite valid in that people in power and in business or other people where it is felt necessary, generally statistics is manipulated to serve their ends. We have a term “statistical gimmickry" to describe such situations enumerated by you. It is no fault of statistics. Statistical results do not speak themselves, they are interpreters who speak on the behalf of statistical results. It is, therefore, necessary to use critical thinking when evaluating a statistical interpretation."

Apart from number persons involved as volunteers on which Statins was tested or those who have different complaints associated with Statins may vary quite largely. Since, according to age, diet and lifestyle and genetic makeup influence of drugs may be different. Unless, a representative sample is not involve from various climatic zones, food habits, vitality and lifestyle are involved, to conclude about side-effects of Statins will be premature. Another aspect may be buissiness rivalry, some firm which has developed similar product may get a research highlighting its side effects. I am not advocating Statins, because drugs are release in market after noticing immediate action of the drug on an inadequate number of volunteers.

This is not my area. However, for the common people who aren't mathematicians or scientists I find that statistics are important because they are sometimes the only empirical way of cross-examining statements like "America's poverty is just as bad as most other countries" or "People who study science usually become atheists because science proves there's no evidence for God."

Statistics can enable people to speak beyond their own personal experience to these issues and say "Actually ... that's not true. Studies have shown that ..."

Now I've just given a few examples, but I hope you can see how statistics can get us beyond our own (extremely) limited personal experience to find out what objective evidence exists for claims like that. However, as the thread has already mentioned, statistics is just like any other form of "reasoning" - subject to all sorts of error in the reasoning process. So Instructor's should study it so they can be prepared to evaluate empirical claims based on statistical studies.

Bradley

Statistics is the study of the collection, organization, analysis, interpretation and presentation of data. Research involves a good amount of data particularly in engineering disciplines. We make it as an essential course to be taken by all graduate students. This helps them to present their data in a logical manner and establish the validity for their hypotheses and explanations.

Statistics matter because researchers derive information from statistics which ultimately becomes intelligence and knowledge to be used in identifying, describing, explaining, modeling and predicting phenomenon.

Do you know examples of research activities that do not require statistical methods?

Perhaps researchers can use photos or documentaries/movies to illustrate existence of natural phenomena not requiring statistics (e.g. bird A is attracted to flower A can be illustrated with a film). We only need one picture and we can conclude the phenomenon exists....

Thanks@Marcel M. Lambrechts. When you have to quantify some phenomenon, you don't need photos or documents. You would ask for statistics, I think so.

The roots of the Oxford English Dictionary (The Oxford English etymology dictionary) statistics are defined as follows:

The word has many meanings and is hit by a mass noun, refers to a set of numerical data, such as unemployment, accidents, insured, revenues, expenses and so on. Many people still hit just as confusing set of figures and tables aware that describes various situations, demographic, economic, political and more. Of statistics in one, the last two centuries, it has been a big change as the most important argument is based on the data presented. Achieved advances in science statistics confirm that this is another of many theories, has led to the development of science. The numeric displays only a minor aspect of the science of statistics has been a very limited number of professional experts Tabulated Statistics and drawing diagrams are engaged in normal activities. The statisticians of several statistical methods for inference based on a set of data gathered and extract information from them as tables, charts, technical analysis Khlashsazyha and benefit.

Data in a systematic way and with the specific purpose of these events and Azpyshtyynshdh collected and placed in tables and graphs are linked. "

As before, all the features of statistics in the form of the following characteristics:

1 - Summary of Events

2 - influenced by a number of

3 - described numerically

4 - estimated with an acceptable level of error

5 - gathered in a systematic way

6 - gathered for a specific purpose

7 - Mrtbshdh the connection between the tables and charts

Statistics as a proper noun, as a branch of mathematics that aims to develop methods for inference based on a set of data gathered and extract information from them as tables, charts, and analysis Khlashsazyha specialty. Various methods are used. The knowledge of statistical methods (statistical methods) and who's used this method, called statistician.

The modern definition, the science of statistics is to "collect, describe, analyze and interpret qualitative and quantitative data" is. Rvshhary statistics, especially when the data is observed variability in size (the natural phenomena of human life) are useful and are employed.100, where a number of large and important, but this number is negligibly elsewhere.With this knowledge, it is not equal to four percent of the trust, the four know.

The modern definition, the four steps described in the following statistics:

1 - Data

2 - Description of the data

3 - Analysis

4 - Interpretation of data

Perhaps for the fifth stage of the assessment. This step can be described as organized.

Could you please tell me why many researchers do not apply statistical methods in their research? Nageswara Rao Posinasetti Mohammad Firoz Khan

They think:

https://www.researchgate.net/post/Is_the_inner_meaning_of_lies_damned_lies_and_statistics_still_true

https://www.cracked.com/article_20318_the-5-most-popular-ways-statistics-are-used-to-lie-to-you.html

https://www.york.ac.uk/depts/maths/histstat/lies.htm

https://www.theguardian.com/science/blog/2010/sep/29/statistics-lies-abuse

https://www.nationalheraldindia.com/democracy/lies-half-truths-and-statistics-nine-big-ones-of-2018

https://www.datapine.com/blog/misleading-statistics-and-data/

https://www.nateliason.com/notes/lie-statistics-darrell-huff

Mohammad Firoz Khan Thanku sir