Is a branch of mathematics dealing with the collection analysis presentation interpretation and conclusion of data?

Statistics is the branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data. Stats is all about data and in order to get useful information from these data(s), it is important to apply different techniques to interpret the relation which exists between the data.

Statistics are mainly classified into two sub-branches:

1. Descriptive statistics: These are used to summarize data, such as the mean, standard deviation for continuous data types, whereas frequency and percentage are useful for categorical data.
2. Inferential statistics: Sometimes the data might be pretty large, so it is not always possible to take the entire data to evaluate the relationship and interpret conclusions among the data, hence a subset of the data is collected, also called a sample, and conclusions about the entire population will be drawn, which is known as inferential statistics. Inferences are drawn using hypothesis testing, the estimation of numerical characteristics, the correlation of relationships within data, and so on.

What is Hypothesis testing?

Hypothesis testing is the process of making inferences or interpretations about the overall population by conducting some statistical tests(T- test, Chi- Square test, ANOVA test, etc.). Another term which is associated with hypothesis testing is p-value.

In statistical hypothesis testing, the p-value or probability value is the probability of obtaining test results at least as extreme as the results actually observed, assuming that the null hypothesis is correct.

Steps involved in hypothesis testing are stated below:

(i). Make an initial assumption — Null Hypothesis (a null hypothesis always tries to assume that there is no anomaly pattern and is always homogeneous, and so on).

(ii). Collect data sample or evidence.

(iii). Try to understand & analyze data by using various statistical tests from the sample data to verify that whether the hypothesis is statistically significant or not.

(iv). Decide either to accept or reject the null hypothesis based on the test statistic.

There is one more hypothesis which is known as Alternate Hypothesis. The alternative hypothesis is the hypothesis used in hypothesis testing that is contrary to the null hypothesis.

Type I & Type II error:

Performing inferences about the population from samples comes with its own costs, such as rejecting good results or accepting false results, not mention separately, when increases in sample size lead to minimizing type I and II errors:

Type I error: Rejecting a null hypothesis when it is true.

Type II error: Accepting a null hypothesis when it is false.

Let us consider a small example:

lets say our our null hypothesis (h0) is : The stock market will crash, and our alternate hypothesis (h2) is: The stock market will not crash.

And after analyzing data, we conclude that alternate hypothesis is true due to lack of evidence to support the null hypothesis, but it maybe possible that null hypothesis was our true statement but alternate hypothesis becoming true, we reject null hypothesis.This resulted in type I error. Now, this can result to a great loss. So, Type I & II error play a major role and in hypothesis testing and while solving any machine learning use case, make sure to look type I and type II error. It depends on the use case you are solving, that whether type I error is more harmful or type II error.

Is the branch of mathematics dealing with the collection organization analysis interpretation and presentation of data?

Is a branch of mathematics dealing with collection of data?

Which branch of mathematics is used to summarize analyze and interpret data?

Is the mathematical science involving the collection analysis and interpretation of data?