Student's T (What It Is, Basic Concepts, And Features)

  • Jul 26, 2021
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Statistics is one of the many branches of mathematics that is responsible for collecting, organizing, projecting, analyzing, interpreting and presenting data following laws of probability, this allows us to predict certain types of behaviors applying them to the scientific, industrial or Social.

Within statistics we can use several hypothesis tests, one of the most complete is the test Student's t, was developed by the English mathematician and chemist William Sealy Goset better known by his pseudonym "Student".

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This statistical test consists of the probability distribution, due to the need to estimate what is the mean of a population with a small, normally distributed sample. That is, less than 30, which is why this test is widely used in the field of medicine.

To perform this test you need a normal distribution of data, since this statistical test is a parametric test and is used when the population standard deviation is unknown due to that if this statistical data were known, instead of using this test, the normal distribution would be used for hypothesis tests.

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In this article you will find:

Basic concepts of Student's T

To correctly apply the test of Student's t we must take into account several basic concepts of decision theory theory for large samples.

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The percentile

It is the result of dividing a set of data into one hundred equal parts, each of those parts represents 1% in the representation of the graph of the Gaussian bell is made from the left part to the part right.

Gauss's bell

It is a graph that represents the normal distribution of a set of statistical data. The normal distribution is used for large samples, this means a statistical data greater than 30 while the Student's t is used for small samples, less than 30.

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Characteristics of the Student's T

  • It belongs to a family of bell distributions.
  • It is symmetric around a mean of zero.
  • It is more flattened than the standard normal distribution.
  • It has more area at the ends and less area in the center.
  • As the sample size increases, it approaches a standard normal distribution.

Scenarios where to apply the Student's t

There are several scenarios in which we can apply this statistical test and it will always depend on the type of sample that has been collected.

A related sample

This means that there are two measurements which have been obtained at two different times and which are also related, an example of this is when an intervention is carried out, Under this context, we can have data and information before the intervention and after the intervention, then we can observe if the result before and after the outcome varied in each subject. later.

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Two samples with homogeneous variances

It refers to the fact that the samples taken for our statistical test are similar in the two samples.

Two samples with heterogeneous variances

This means that our statistical test has totally different samples, data and information.

How to determine the stage to know?

To determine which of the two-sample scenarios is being used, it is necessary to know homoscedasticity, if the data from the two samples have this characteristic then it is necessary to use the scenario of two samples with homogeneous variances, in the case that the samples do not have homoscedasticity, the scenario of two samples with variances should be used heterogeneous.

The statistical test Student's thas several assumptions, in this case, for the scenarios that have two samples, it is assumed that the data have a normal distribution, and it should be presented in each one of the two samples and also these samples are totally independent, the values ​​that we have in one sample do not depend at all on the other show.

When we use the scenario of a related sample, we have only one assumption and the assumption is that the difference between the two variables related has a normal distribution and the perfect example is when an intervention is carried out, since we have data from before and after it, From this we can find the difference between each subject since the values ​​of before and after are subtracted thus finding the values ​​of the difference.

This difference must have a normal distribution, in this scenario it is not indicating that the data in each of the samples or groups have a normal distribution, indicates that the difference is the one that has a normal distribution and not the data for each of the groups, which is what the assumption with two or two variables indicated. samples.

Degrees of freedom

The statistical test Student's t depends on the degrees of freedom. It is the determined number that allows us to know the variability of events in a sample, in more words simple, we can say that they are the number of values ​​that we can choose freely, existing a total permanent.

Two exists degrees of freedom formulas, one formula when we have a sample that is related, and the other formula that is when we are working either of the two scenarios with two samples.

To visualize this in a more comfortable way, we can imagine a family in which there is a mother and 4 children, the mother prepares 10 loaves with ham, the fixed total is the 10 loaves with ham, the first son tells his mother that she wants to eat 3 loaves, the second son asks for 2 loaves, the third son asks for 3 loaves and the fourth son for having Arriving late, he will not be able to choose how many ham loaves he wants, because he was conditioned by what his other 3 siblings asked for, so the fourth child only had 2 left breads.

The important thing is that of the 4 brothers only 3 were able to choose how many loaves they wanted, in this case the grade freedom is 3 who were the ones who could choose and last was conditioned to complete the 10 breads.

We hope you enjoyed reading. If you have any questions, leave us your comment!

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