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Related Concept Videos

Types of Hypothesis Testing01:11

Types of Hypothesis Testing

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There are three types of hypothesis tests: right-tailed, left-tailed, and two-tailed.
When the null and alternative hypotheses are stated, it is observed that the null hypothesis is a neutral statement against which the alternative hypothesis is tested. The alternative hypothesis is a claim that instead has a certain direction. If the null hypothesis claims that p = 0.5, the alternative hypothesis would be an opposing statement to this and can be put either p > 0.5, p < 0.5, or p...
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Statistical Hypothesis Testing01:16

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Hypothesis testing is a critical statistical procedure facilitating informed, evidence-based decisions. It begins with a hypothesis, which is a tentative explanation, or a prediction about a population parameter. This hypothesis can be either a null hypothesis (H0), indicating no effect or difference, or an alternative hypothesis (Ha), suggesting an effect or difference.
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The actual hypothesis testing begins by considering two hypotheses. They are termed  the null hypothesis and the alternative hypothesis. These hypotheses contain opposing viewpoints.
The null hypothesis, denoted by H0 is a statement of no difference between the variables—they are not related. This can often be considered the status quo. As  a result if you cannot accept the null, it requires some action.
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Statistical inference techniques, paramount in hypothesis testing, differentiate into two broad categories: parametric and nonparametric statistics.
Parametric statistics, as the name suggests, assumes that data follow a specific distribution, often a normal distribution. This assumption enables robust hypothesis testing and estimation. Parametric methods, like the Student's t-test or Goodness-of-fit test, are frequently employed in biostatistics due to their robustness. For instance,...
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The test of independence is a chi-square-based test used to determine whether two variables or factors are independent or dependent. This hypothesis test is used to examine the independence of the variables. One can construct two qualitative survey questions or experiments based on the variables in a contingency table. The goal is to see if the two variables are unrelated (independent) or related (dependent). The null and alternative hypotheses for this test are:
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When performing a hypothesis test, there are four possible outcomes depending on the actual truth (or falseness) of the null hypothesis and the decision to reject or not.
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Detecting nonlinear stochastic systems using two independent hypothesis tests.

Yoshito Hirata1,2,3,4, Masanori Shiro5

  • 1Mathematics and Informatics Center, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.

Physical Review. E
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Summary

This study introduces novel hypothesis tests to identify nonlinear stochasticity in systems. These methods can distinguish complex behaviors in real-world data, such as financial markets.

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Area of Science:

  • Complex Systems Analysis
  • Nonlinear Dynamics
  • Time Series Analysis

Background:

  • Real-world systems often exhibit complex nonlinear and stochastic behaviors.
  • Existing nonlinear time series analysis methods struggle to differentiate between nonlinear stochastic and nonlinear deterministic systems.
  • There is a need for robust methods to test for nonlinear stochasticity.

Purpose of the Study:

  • To propose a novel set of independent hypothesis tests for nonlinearity and stochasticity.
  • To provide a method for identifying nonlinear stochastic systems.
  • To analyze the behavior of real-world time series data.

Main Methods:

  • Development of two independent hypothesis tests: one for nonlinearity and one for stochasticity.
  • The nonlinearity test utilizes Fourier-transform-based surrogate data with a nonlinear test statistic.
  • The stochasticity test is based on the theory of ordinal patterns (permutations).

Main Results:

  • The proposed hypothesis tests successfully distinguish between different types of system dynamics in toy models.
  • Analysis of a foreign exchange market time series revealed nonlinear and stochastic characteristics.
  • A temperature series from Tokyo was also found to exhibit nonlinear and stochastic properties, with occasional determinism.

Conclusions:

  • The developed hypothesis tests offer a reliable approach to identifying nonlinear stochasticity in time series data.
  • These methods can be applied to diverse real-world systems, including financial markets and environmental data.
  • The findings highlight the complex, often nonlinear and stochastic, nature of many natural and economic phenomena.