Many things have to be said and underlined. The first is that the so-called Fisher's statistics is now considered obsolete (by the way, the famous cutoff p

You are referring to three widely different concepts. Let's say you are interested in whether there is a difference in weight between species A and B. That refers to a biological difference you are interested in. You then sample some of each species, and you might find that the average weight in your sample is higher for A and B. However, since you did not base this average on the populations of A and B, but only a sample, you need to account for sampling variation: should you draw another sample it could very well be that you find other values for the average weight of A and B. That's why you calculate statistical significance. If the observed difference is not statistically significant (e.g., p>.05), this means that you could observe said difference even though in the populations the average weights of A and B are identical.

So, if you do not have statistical significance, you cannot conclude that the observed difference is also present in the population (which you call biological difference).

Dear Nicola Bragazzi, I agree with your view point but my point is a statistically significant difference is not necessarily biologically significant.

Dear Masood Sepehrimanesh, Having powerful computing it is possible to observe that statistical results either reject the null hypothesis or don't reject the null hypothesis. So, to decide we need the exact P value if they want to combine your results with others into another analysis (meta-analysis).

I absolutely agree with Afaq Ahmad. Findings need to be replicated and meta-analysis and systematic reviews are useful to confirm previous results.

Good question and hard to define. p0.05 pretty much means no difference but in some paper people will claim 0.1>p>0.05 means significance if the sample size is small and practically can not be large enough. Now the problem is how you define biologically different? Say I have an overfed fat rat which is bigger than a cat does that mean the rat is really bigger than cat? For that specific fat rat it is true there is a biological difference but we can not apply to rat in general so we have collect enough number of rats and cats for statistical analysis. Now we have a group of minipigs in wild and they are all smaller than regular domestic pigs but when we raise them as pet they can reach the size of domestic pigs. The problem will be what is context to view the difference. I also agree that statistical difference does not guarantee biological difference. This is especially true for clinical study using multiple regression when several independent variables will go into the final model but make completely no biological sense. We need to have a rational model for the statistical analysis to get a p-value small enough to assume there maybe a biological significance. Also, do not forget about the issue of multiple comparisons when you have one dependent variable and multiple independent variables that maybe significantly link to the dependent variable then p

for genomics, other statistics such as the Benjamini-Hochberg and the FDR should be carried out

Thanks a lot all dear colleagues

Dear Nicola and dear Rue-Jeng

Thank you very much for your repleis

Please discuse about this differences: Blood pressure of control group (13±0.8) and test group (15±1.3). These values are not significantly differences but control group have normal BP with no implications and test group have high BP with some other implications. Therefore, there are no statistical differences but there are biological differences.

The issue will be what is the end point? How did you define "biologically significant"? Say the test group (I guess you mean they were hypertensive) had 15±1.3 mm-Hg drop and they SBP were down to 140 and below then yes it is biologically significant whereas your control group has mean SBP of 83 then the treatment is harmful since most of the control become hypotensive. Without the detail in your design and defined end-point any interpretation will be inappropriate. And, another problem with your question will be the control group is normal and treatment group is hypertensive then the baselines were internally different which prohibits appropriate comparison unless you have controlled all the confounding variables. To summary my point as below:

1. Are the two goups comparable?

2. What is your end point?

3. Are the treament same?

Apparently there are more things we need to consider before we can interpret the findings.

Let me to put it this way. Say you have one group of full term infants and another group of premature infants. The first group took 20 cal/oz formula and the second group used 24 cal/oz formula. Daily growth for 1st group was 30 grams whereas the second group was 15 grams. Can we say the 20 cal/oz formula is better than 24 cal/oz formula? No, since the first group weight is about 3 kg and the second group is 1.2 kg. Unless you know the detail of the study otherwise it will be dangerous to draw the conclusion. We may say surprisingly the second formula is better since it provide higher g/kg/d growth. But, you should also know if the premature baby gains too much weight in their early life increases the chance of coronary artery disease, diabetes, and other metabolic syndroms. So, biological significance in one sense may not be appropraite in another sense.

In my opinion biological difference will be confirmed by statistical significance to have an objective value for making a scientific evidence-based conclusion.

The statistical difference gives us the proof that how much difference is available between two things.which can be applied on biological factors.

Thanks dear ramzi for valuable discussion

Thanks Dear Marianne and dear Muqader

my humble appreciation, (being statistician) is that the statistics do not answer all, there are many variables to watch: sample size, sample type, variance, outliers, and others, to make a good decision.

distances according to the works which statistic is sensitive to factors listed above, so the "eye of the researcher" is important. Never ignore.

The importance in the use of these three concepts depends of the specific issues that you referring to. For example is you are talking in general terms without specifying any particular issues or field, then the use of the concept difference is more appropriate than other two. However, if you are talking about quantities in an specific field then the most important concept is statistical difference. On the other hand, if you are talking about human beings, animal or plants then the use of the concept biological difference is in most case the more appropriate of the three concepts mentioned in the debate.

I think that biological data must be quantificated. That's a sure way to eliminate subjectivity in appreciating results. So, statistical tests are mandatory in such appreciations.

In medicine we often use the concept of a clinically significant difference (which is similar to your biological difference). For example, in walking speeds, a difference of 0.03m/s may be statistically significant, but imperceptible to the individual and so not clinically significant.

Dear Dr. Jonathan Norton, In medicine your parameters are very vital and human life is on stake. Difference may be improvement in health condition. Decay requires statistical model and analysis. Whereas, spectrum of biological difference matters. So for you doctors you can not leave any difference.

Dear Masood,

The answer could not be that simple. Among other factors already discussed, it also depends on your research question.

Any statistical difference that is not a consequence of Biological difference is likely to be a result of random sampling variation and as such is not important. Having said that, we would not know a priori whether something is biological or not until much more data is available.

Someone can have small biological differences that have no practical impact, on the issue under study, but yet they are statistically significant because we have made an oversized experiment.

In other experiment, someone can have a major biological difference, which if confirmed would have a good impact, i.e. be of practical importance, but do not become statistically significant because our test is underpowered, because the experiment is not large enough. If then we could repeat or enlarge the original experiment, this apparent biologically important difference may be confirmed, it may disappear or it may reduce most of its previous importance.

It is best to have an experiment able to detect any biological difference of practical importance, with a statistically significant difference.

Dear Masood Sepehrimanesh, Now let us think in context to "Nano Scale" which difference would be better?

In medicine only clinical significance is meaningful. Statistical significance only might be hypothesis generating.

In my field which is malignant diseases, in common advanced solid tumors all so called personalized targeted treatments which are the hype presently, are statistically significant and e.g. in lung cancer at best add a couple of months in overall survival. Very often the situation is tragically ridiculous: In advanced pancreatic cancer the standard therapy is gemcitabine and overall survival is 6 months. The addition of erlotinib, frequently used and very costly, adds 10 (ten) days of survival. Statistically (p< 0.05) very significant, hence marketed and used.

Regarding your question: the setting shoould tell you what to use.

Regards.

The two situations of interest for this discussion are a) biological significance in combination with statistical non-significance and b) vice versa.

Examples

a) Experimental study with two treatment groups and small sample sizes.

b) Epidemiological risk factor study with many thousand participants.

Issues

a) The size of the effect estimate is biologically relevant. However, whether this result is just due to pure chance or a reflection of reality cannot be concluded from the data.

b) The size of the effect is so small that it is biologically irrelevant. A significant P-value doesn't overrule this judgement but rather confirms that a small effect has been estimated with high precision.

Remedies for a) and b)

The sample size should be chosen with regard to the expected and the relevant effect size.

Keywords for further reading

Type I and II errors, power, significance, overpowered and underpowered studies

Additional clarifications:

"Biological", "clinical", "medical", etc. are equivalent for the purpose of this discussion. Although experimental and epidemiological studies are prone to under-powering and over-powering, respectively, the reverse situation may occur as well.

If there is no biological significance (but there is statistical significance), there can be two possibilities either our biological understanding of the situation is low and need improvement to find why there is a statistical significance, or the statistical significance is meaningless. However, biological / scientific understanding should get the priority. If we could not find any biological meaning to the statistical significance then that statistical significance have no meaning.

I agree with Azeez. A statistcal difference without biological meanining gives us nothing in practical world. If you do not have a priori hypothesis please, and please, do not try to use statistics to fish out any difference. I have heard many times that some researchers say that they have a huge data bank and just throw the net you can find something publishable in high IF journals with the help of statistics. This attitude bothers me a lot.

Thanks all dear coleagues

Dear Mario, Azeez, Afagh, Matthias and Ru-Jeng

Thanks for your valuable comments

I agree with all of you but my means from this question is two points:

1. very low differences with no statistical significances are also important

2. statistical analysis is not enough completely for biological sciences

Please discuse agreement/disagreement for these two point

Cheers

While I agree with the first, but not fully; In that case I feel that the investigator should examine why there is no statistical significance - He / she should think seriously about the design of the experiment, and re-look at the hypothesis that he / she is trying to test / validate.

Same is the case with the point ii: I agree with some reservations - an appropriate statistical tests should be thought of to test the biological phenomenon; However, the biology gets priority over the statistical results

I also wish to make the point that it is neither the defect of statistics nor of biology; but of our understanding of both. We need to devise and develop appropriate statistics for certain situations. Similarly we need to develop further understanding about the biological aspects; may be the contradictory statistical results hid some important biological concepts, that need to be revealed after further explorations?

Haim.

Both differences are important. it is based on the researchers interpretation and the presence of no statistical significance help him to ask questions and think.

If you could see a clear biological difference in a well planned experiment, we do not need to statistics to prove your hypothesis. When the differences are marginal and perhaps inconclusive (visually), we have to use some statistical tests to confirm whether the differences are acceptable at a given probability level. General acceptance level is 95% probability. In most of our biological experiments we are testing biological variances with the aids of ststistics. The statistical inference is important to accept or reject our set hypothesis. We are testing biological variations with mathamatically structured statistical designs and well planed experiments. For researchers, both differences are important to make conclusions. At the end, if you are not using the correct model to test the variances, it could easily mislead you and others. In this case biologists and statisticians should work together and understand fully about the concept & hypothesis that you are testing before conducting your experiments.

Biological differences are all that matter. Statistical differences, whether p0.05, are an attempt to quantify reality. Biological differences may be real, but not statistically significant. Statistical differences may be significant, but not real. Statistical differences may look good in figures and tables, but unless they support observable differences, they are not real. Statistics may be used to mine databases and find correlations that the human eye cannot see, but unless they make logical sense (biological differences), it is only a number crunching exercise. One of the most common errors in statistics is sampling error. If one chooses the sample incorrectly, statistical significance is irrelevant.

I am reminded of a joke which makes this point: There are statistics, damned statistics, and then there are lies.

Thanks alot all dear friends

Your comments are very valuable and usefulness

With best regards