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T test as a parametric statistic.

Tae Kyun Kim1

  • 1Department of Anesthesia and Pain Medicine, Pusan National University School of Medicine, Busan, Korea.

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|December 4, 2015
PubMed
Summary
This summary is machine-generated.

Statistical tests rely on probability distributions. The sample mean follows a normal distribution, but when population variance is unknown, the t distribution is used for hypothesis testing, particularly in t tests.

Keywords:
BiostatisticsMatched-pair analysisNormal distributionProbability

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Area of Science:

  • Statistics
  • Statistical inference

Background:

  • The probability distribution of statistics is crucial for valid statistical testing.
  • Understanding the distribution of sample means is fundamental in statistical analysis.

Purpose of the Study:

  • To explain the distribution of sample means under different conditions.
  • To introduce the t distribution and its application when population variance is unknown.
  • To outline the conditions for conducting t tests.

Main Methods:

  • Describing the normal distribution of sample means (X̄) from a population N (µ, σ(2)) with sample size n.
  • Explaining the standardization of statistics under a null hypothesis (µ = µ0).
  • Introducing the t distribution for statistics when population variance is unknown and sample variance (s(2)) is used.

Main Results:

  • The sample mean (X̄) follows a normal distribution N (µ, σ(2)/n) when population variance is known.
  • When population variance is unknown, the statistic follows a t distribution with (n-1) degrees of freedom.
  • The t test (independent-group or paired) is applicable for comparing means.

Conclusions:

  • The t distribution is essential for hypothesis testing when population variance is not known.
  • Parametric tests like the t test require specific assumptions, including normality, equal variances, and independence of samples.