Yes.

Thanks Mehmet for your answer, but my doubt still persists.

Recently I have come across an article where PCA is considered as an inferential statistics (it states ..."Inferential statistics range from simple t-tests (PROC MEANS),

anova (PROC GLM), regression (PROC REG) to multivariate analysis (factor analysis, principal component analysis,

multivariate anova, discriminate analysis, structural equation modeling, etc".; REFERENCE: Suhr, D. (2011). Answering your research questions with inferential statistics.)). Kindly clarify the same.

There are some techniques like PCA that are not descriptive nor inferential. Im my opinion, PCA is more a preparatory analysis.

It is used to reduce a larger number of variables by a smaller number of artificial variables (principal components) constructed to keep the maximum of the initial variance.

The basics principle is the supression of the redundancy between the original variables.

If you use the two or three principal components, instead 10 original variables, to do an anova,by example, then you are trying to say about the population through a sample, PCA participates in a inferential process.

But if you construct a graphic, only to show the characteristics of the sample, then it is participating in a descriptive process.

Thank you,Marcelo...Now I have a clear picture....PCA can be considered as more of a  pre- inferential statistics..

I like Wikipedia's definition of inferiential statistics :

Quote (https://en.wikipedia.org/wiki/Statistical_inference on 2016-05-21) :

Inferential statistical analysis infers properties about a population: this includes testing hypotheses and deriving estimates. The population is assumed to be larger than the observed data set; in other words, the observed data is assumed to be sampled from a larger population.

Inferential statistics can be contrasted with descriptive statistics. Descriptive statistics is solely concerned with properties of the observed data, and does not assume that the data came from a larger population.

With that definition, as soon as confidence intervals or p values are given, the statistic is inferential. PCA may be descriptive if the statistician is solely interested in the sample, and may be weakly inferential if the statistician interprets results as a clue of the population-wide PCA.

Most statistician misunderstand discriminant analysis is inferential statistical method as same as regression analysis. But, Fisher never formulated the equation of standard error of error rate and discriminant coefficients.

However, I developed the 100-fold cross validation for small sample method.

This method gives us the 95% CI of error rate and discriminant coefficients. Howevere, I think this computer-intensive approach is different the traditional inferential statistics.

Genuine statistician introduce SE based on the theoretical distribution by his brain.

This is traditional inferential statistical approach.

See my several recent papers about your questons from RG upload papers.

Thank you, Sir for your valuable feedback.

Sayoni, good day. Give me 3 positive univariate values from a sample made of  N=20 to 50 values: maximum value, minimum value and media (without mentioning units used neither kind of research). I will return a proxy distribution graph and equation of K(P) where K is variable and P is cummulative distribution fraction for Ki bigger than K. This is a kind of inductive inference that starts with a descriptive statistics model of Lorenz curve of your sample (or fraction of total  distributed variable K, versus fraction of total cummulative population for top to low ordering). Thanks. Emilio

PCA is an exploratory data analysis. It gives you suggestions on how to read your data by showing the aspects that differentiate in the best way the elements studied.

• Read the following books below and see if it would be of benefit to you

Thank you  so much for your responses...

OK, John Tumaku and others, question is about causality and their correlations with other variables. That requires other kind of previous research, methods and intuitions. My point is that if we can find a model of distribution for each main variable, then we may link pairs of them if they were measured in a controlled context. But the link or correlation does not always imply causation neither linear correlations among variables. Thanks for your corrections and suggested book.

it is descriptive statistics as you are exploring the phenomenon of underlying structure of items that make up each variable scale.

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=rja&uact=8&ved=2ahUKEwiFsu255_XuAhWh3OAKHSZDC50QFjAMegQIIBAD&url=https%3A%2F%2Fstatisticsbyjim.com%2Fbasics%2Fdescriptive-inferential-statistics%2F&usg=AOvVaw0tSKvOZrIfN7YzN5QkzBGD