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Estimating Population Mean with Known Standard Deviation01:16

Estimating Population Mean with Known Standard Deviation

To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
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William S. Gosset (1876–1937) of the Guinness...

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Bootstrapping to test for nonzero population correlation coefficients using univariate sampling.

William Howard Beasley1, Lise DeShea2, Larry E Toothaker1

  • 1Department of Psychology, University of Oklahoma.

Psychological Methods
|January 9, 2008
PubMed
Summary
This summary is machine-generated.

Two new bootstrap methods, hypothesis-imposed (HI) and observed-imposed (OI) univariate sampling, effectively control Type I error rates for testing population correlation (rho). The OI method is recommended for nonnormal populations with moderate rho values.

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Area of Science:

  • Statistics
  • Biostatistics
  • Psychometrics

Background:

  • Accurate statistical testing is crucial for reliable research findings.
  • Traditional methods for testing population correlation (rho) can exhibit inflated Type I error rates, especially with nonnormal data.
  • Existing bootstrap methods may not adequately control error rates under certain conditions.

Purpose of the Study:

  • To introduce and evaluate two novel bootstrap approaches for testing a nonzero population correlation (rho): the hypothesis-imposed univariate sampling bootstrap (HI) and the observed-imposed univariate sampling bootstrap (OI).
  • To compare the performance of these new methods against traditional parametric approaches and conventional bivariate sampling bootstrap in controlling Type I error rates.
  • To provide guidance on selecting appropriate methods for correlation testing based on population distribution and effect size.

Main Methods:

  • Simulation study involving correlated populations with combinations of normal and skewed variates.
  • Implementation of the hypothesis-imposed univariate sampling bootstrap (HI) and observed-imposed univariate sampling bootstrap (OI).
  • Comparison of empirical Type I error rates at alpha = .05 for parametric r, bivariate sampling bootstrap, HI, and OI methods.
  • Analysis conducted with sample sizes (N) greater than or equal to 10 and population correlations (rho) up to 0.4.

Main Results:

  • Parametric r exhibited the highest Type I error rate (.168).
  • The conventional bivariate sampling bootstrap showed a Type I error rate of .081.
  • The novel HI and OI methods demonstrated superior control of Type I error rates, with maximum rates of .079 and .062, respectively.
  • Both HI and OI significantly outperformed parametric methods in controlling Type I error rates under simulated conditions.

Conclusions:

  • The observed-imposed univariate sampling bootstrap (OI) offers superior alpha control compared to parametric methods for testing nonzero population correlations (rho) when nonnormality is suspected.
  • The HI and OI methods provide more reliable results than traditional approaches when dealing with moderate population correlations and nonnormal data.
  • Researchers should consider employing the OI method for robust correlation testing in nonnormal populations.