# How T-Distributions Are Used in Statistics

2021-05-27
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T distribution also known as student's t-distribution is used in the estimation of population parameters. The sample size to be estimated can either be small or unknown. The values of t-distribution are obtained using the formula t = [x - m] / [s / sqrt (n)] whereby x represents the sample mean, m represent the population mean and s the standard deviation (Michener, 2002). According to William (2006), t-distribution makes it possible to carry out analysis for data sets that have cannot be analyzed appropriately using the normal distribution.

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Characteristics of t-distribution

The mean for every particular distribution is always zero.

The variance is evaluated using the formula v/ (v-2) whereby the v represent the degrees of freedom, and it is a requirement that the v should be equal or more than 2.

The variance should always be more than 1, but in some cases, it is close to one in situations where there are many degrees of freedom.

When is t-distribution used?

The t-distribution is used in biostatistics for any statistic that contains a bell-shaped distribution (Michener, 2002). There are conditions that need to be satisfied to use the t-distribution, that are:

The distribution of population should be normal

There should not be outliers in the distributions that is the population distribution needs to be symmetric, and its minimum sample size needs to be 30 on the lower end.

There should be a moderated skewed distribution.

The sample size under study needs to be more than 40 with no outliers at every particular time.

Summary of Article

Zika virus is a disease that is spread through mosquito bite thus it can be controlled the elimination of mosquitoes and their larva. The sample population for the research was obtained from Miami where there was an outbreak of the viral disease. Pregnant women and adult males were the target sample population since they were the ones who were infected by the infectious virus. Blood samples were derived from the sample population, and 22 samples analyzed per run time.

The main software used in analyzing sample was the real-time PCR software Sentosa SX 10. The software detects the virus RNAbecause it has the Sentosa SX Virus Total Nucleic Acid v2.0. The run time for sampled blood is three hours and can only analyze 22 sample blood serum. The data obtain will prove if one is affected or not (January News, 2017). The information of the infected and not infected individuals is then tabled and t-distribution method used to calculate the infection rate in Miami.

Real-time PCR software like Sentosa SX 10 is revolutionized software that enables detection of viruses, bacteria and other organism DNA in a blood sample (January News, 2017). The software is a device that is very useful in medical research since it enables collection of data needed when researching on disease caused by viruses. Zika Virus is an example of such disease, its presence in the human body can only be detected through used of PCR that detects its RNA. Since the virus is in blood, even blood must screen through PCR before transfusion. Real-time PCR software is thus a revolutionized research tool that medical researchers should embrace when dealing more refined research that needs analysis of DNA.

References

William, M.K. (2006). The t-test. Retrieved December 30, 2016, from http://www.socialresearchmethods.net/kb/stat_t.phMichener, R. (2002). Retrieved December 30, 2016, from http://people.virginia.edu/~rwm3n/pdf/When%20do%20you%20use%20the%20t%20distributionpdf.January News. (2017). Retrieved 1 January 2017,from https://cid.oxfordjournals.org/content/64/1/i.full#sec-4

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