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Related Concept Videos

Statistical Hypothesis Testing01:16

Statistical Hypothesis Testing

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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.
Statistical significance measures the probability that an observed result occurred by chance. If this probability, known as...
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Errors In Hypothesis Tests01:14

Errors In Hypothesis Tests

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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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Hypothesis Test for Test of Independence01:16

Hypothesis Test for Test of Independence

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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:
H0: The two variables (factors)...
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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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Decision Making: Traditional Method01:14

Decision Making: Traditional Method

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The process of hypothesis testing based on the traditional method includes calculating the critical value, testing the value of the test statistic using the sample data, and interpreting these values.
First, a specific claim about the population parameter is decided based on the research question and is stated in a simple form. Further, an opposing statement to this claim is also stated. These statements can act as null and alternative hypotheses, out of which a null hypothesis would be a...
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Null and Alternative Hypotheses01:16

Null and Alternative Hypotheses

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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.
The alternative hypothesis, denoted by H1 or Ha, is a claim about the...
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A Note On Specifying Parameter Values For Testing Covariance Matrix Hypotheses.

M E Eiting, G J Mellenbergh

    Multivariate Behavioral Research
    |January 27, 2016
    PubMed
    Summary
    This summary is machine-generated.

    Monte Carlo simulations are crucial for testing covariance matrix hypotheses. This study suggests using empirical estimates for parameter values in future simulations for more realistic results.

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    Area of Science:

    • Psychometrics
    • Statistical Modeling

    Background:

    • Eiting and Mellenbergh (1980) explored statistical power in covariance matrix hypothesis testing using Monte Carlo (MC) simulations.
    • Previous MC studies may have used incorrect assumptions for common variance, potentially affecting results.

    Purpose of the Study:

    • To evaluate the validity of MC simulation results in covariance matrix hypothesis testing.
    • To provide recommendations for improving the methodology of future MC studies in this area.

    Main Methods:

    • The study involved two Monte Carlo simulations to investigate statistical power.
    • Analysis focused on hypothesis testing related to covariance matrices.

    Main Results:

    • While the initial reasoning for parameter specification in the first MC study might be flawed, the outcomes of a subsequent MC study were deemed realistic.
    • The findings highlight the sensitivity of simulation outcomes to parameter value assumptions.

    Conclusions:

    • It is recommended that future Monte Carlo simulations in this field utilize empirically derived estimates for parameter values.
    • Adopting empirical estimates can enhance the realism and applicability of simulation findings in covariance matrix hypothesis testing.