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Sample Size Calculation in Simple Linear Regression under Two Scenarios

Yang, Li
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1721233071853519

Abstract Details

2024, PhD, University of Cincinnati, Medicine: Biostatistics (Environmental Health).
Sample size determination is key to the success of any statistical investigation prior to exploring a causal relationship between a response variable Y and a single predictor X. A hypothesis about the relationship is presages sample size calculation. Several steps are involved in testing a hypothesis: data collection; building of a test statistic, Type I error control and power specification, are spelled out prior to the start of the investigation, and sample size is needed to meet the power requirement. Besides Type I error probability and power, the population’s variance or conditional variance of the response may be needed. We focus on the sample size calculation in this disquisition from of a simple linear regression perspective. Both independent variable (X) and dependent variable (Y) are introduced in the regression model. The interest of the simple linear regression is whether X impacts Y. A sample size of n will be needed for the detection of the degree of dependence of Y on X. The significant level a (Type I error) and power 1-ß (ß Type II error) are pre-specified, besides effect size. We need data to estimate the regression coefficient from the conditional model by using the least square method. Software like PASS and nQuery take the wrong approach in calculating the required sample size. The error has been pointed out in the literature. This work falls under methodological research. The aim of our research is to contrast sample calculated under different but equivalent environments. The error was fixed in earlier research by deriving the distribution of the likelihood estimator of the regression coefficient when the predictor is taken to be normally distributed. We follow a different approach in this disquisition. We assume the and response has a bivariate normal distribution. Testing null correlation is equivalent to testing null slope. We calculated sample size under the testing environment of null correlation. Sample sizes thus calculated are contrasted with the sample size calculated in the environment of null slope. We showed that the sample sized calculated under the environment of null correlation are lower but not substantially lower.
Marepalli Rao, Ph.D. (Committee Chair)
Tesfaye Mersha, Ph.D. (Committee Member)
Roman Jandarov, Ph.D. (Committee Member)
47 p.
Biostatistics

Recommended Citations

Citations

  • Yang, L. (2024). Sample Size Calculation in Simple Linear Regression under Two Scenarios [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1721233071853519

    APA Style (7th edition)

  • Yang, Li. Sample Size Calculation in Simple Linear Regression under Two Scenarios. 2024. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1721233071853519.

    MLA Style (8th edition)

  • Yang, Li. "Sample Size Calculation in Simple Linear Regression under Two Scenarios." Doctoral dissertation, University of Cincinnati, 2024. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1721233071853519

    Chicago Manual of Style (17th edition)

ucin1721233071853519
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© 2024, some rights reserved.Creative Commons License Sample Size Calculation in Simple Linear Regression under Two Scenarios by Li Yang is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by University of Cincinnati and OhioLINK.