Group 1
T-DISTRIBUTION
definition
It is used when the data are approximately normally distributed but the
population variance is unknown, making it a more conservative estimate
than the standard normal distribution. As the sample size increases, the
t-distribution approaches the normal distribution. It is particularly
useful for hypothesis testing, constructing confidence intervals, and
regression analysis when dealing with small sample sizes or when the
population standard deviation is not known.
COMPuTATIONS/FORMULA
The t-distribution has a specific formula used for calculating the t-
score, which is essential in hypothesis testing when the population
standard deviation is unknown and the sample size is small. The t-
score is calculated as follows: t = (x̄ – μ) / (s/ n) √
WHERE:
x̄ = sample mean
μ= population mean
s= sample standard deviation
n= sample size
This formula allows you to standardize the difference between the
sample mean and the population mean, taking into account the
variability of the sample. It’s particularly useful when you’re working
with small sample sizes and don’t have access to the population
standard deviation, making it a staple in statistical analysis and
research.
Use/Function in OTHER RELEVANT PROVIDE TWO WORKS OF
Practical Research: INFORMATION LITERATURE
Hypothesis Testing: Degrees of Freedom: The shape of 1. " A simple proof of the
the t-distribution is determined by characteristic function of
The t-distribution is the degrees of freedom, which are
Student’s t-distribution”:
essential for related to the sample size. As the
Research Methodology: This
degrees of freedom increase, the t-
conducting t-tests, distribution becomes more similar to study likely involved a
which compare sample the normal distribution. mathematical proof approach,
where the researchers
means to assess History: The t-distribution was provided a straightforward
whether they are developed by William Sealy
proof of the characteristic
Gosset under the pseudonym
significantly different “Student”. It was originally
function of the t-distribution.
from the population The methodology would have
created for analyzing small
sample sizes in brewing science.
included rigorous mathematical
mean or from each derivations and validations to
other. Variance: The variance of establish the proof.
Confidence Intervals: the t-distribution is always 2. “Visualizing High-Dimensional
greater than 1, reflecting the Data Using t-Distributed
It is used to determine Stochastic Neighbor Embedding
increased variability
the critical values for (t-SNE)”
expected with smaller sample
confidence intervals sizes. The t-distribution’s
Research Methodology: The
research on t-SNE, a machine
around sample means ability to accommodate the
learning algorithm for
when the population uncertainty inherent in small dimensionality reduction based
variance is unknown. sample sizes makes it a on the t-distribution, would
powerful tool in statistical have employed computational
Regression Analysis:
analysis, ensuring that experiments. The methodology
In regression analysis, researchers can make probably included the
the t-distribution informed decisions even when application of t-SNE to high-
helps in estimating the dealing with limited data. Its dimensional datasets and the
robustness in such scenarios evaluation of its performance
coefficients and in visualizing data in a lower-
is why it remains a
assessing their dimensional space. It would also
cornerstone of statistical
significance. involve statistical analysis to
methods in research.
compare t-SNE with other
dimensionality reduction
techniques.
REFERENCES
Bevans, R. ( 2020, August 28) T-Distribution | What It Is and How To Use It (With Examples.
Frost, J. (2024) T Distribution: Definition & Uses.
Hayes, A. (2022, October 24) What Is T-Distribution in Probability? How Do You Use It?
Katara, H. (2024, March 15) T Distribution Formula
Levine, D. (2014). Even You Can Learn Statistics and Analytics: An Easy to Understand Guide to Statistics and Analytics 3rd Edition.
