PUH 5302 Applied Biostatistics Course Learning Outcomes

PUH 5302, Applied Biostatistics 1 Course Learning Outcomes for Unit VI

Upon completion of this unit, students should be able to: formulate scientific questions into statistical hypotheses, distinguish between null and alternative hypotheses, model the steps involved in statistical hypothesis testing, and discriminate the significance of Type I and Type II errors.

This unit discusses the process involved in hypothesis testing, including data preparation, null and research hypotheses, the six-step process, and potential errors that could lead to incorrect conclusions. Scientific hypotheses are testable statements about phenomena or relationships that require verification. The process begins with formulating two opposing hypotheses about the population, one stating an association or effect, the other stating no association or effect.

The null hypothesis (H0) generally states what is currently believed or expected, and is assumed to be correct unless evidence suggests otherwise. The alternative hypothesis (H1), or research hypothesis, posits a relationship or effect that the researcher aims to support. For example, if one hypothesizes that 80% of adults would inform others if symptomatic with COVID-19, H0 would assert p = 0.8, while H1 would oppose this, such as p ≠ 0.8.

The hypothesis testing process involves six steps: (1) formulate the null hypothesis in statistical terms; (2) formulate the alternative hypothesis; (3) select the level of significance (commonly 0.05); (4) set the decision rule based on the test statistic, degrees of freedom, and critical value, and interpret the p-value in relation to α; (5) collect data and compute the test statistic; (6) make a conclusion to reject or fail to reject the null hypothesis based on the p-value.

Type I and Type II errors are inherent risks in hypothesis testing. A Type I error occurs when a true null hypothesis is wrongly rejected; its probability is set by the significance level α, often 0.05. A Type II error happens when a false null hypothesis is not rejected, with its probability denoted by β. The power of a test, 1-β, reflects its ability to detect a true effect when present. Larger sample sizes generally increase the power, reducing the risk of Type II errors.

The p-value quantifies the probability of observing a test statistic as extreme as, or more extreme than, the observed, assuming the null hypothesis is true. A lower p-value indicates stronger evidence against H0. If the p-value is less than α, H0 can be rejected; otherwise, the failure to reject H0 is considered a lack of sufficient evidence to support H1.

Understanding these concepts is fundamental in applying biostatistics to research, ensuring correct interpretation of data, and avoiding false conclusions that could impact public health policy or scientific understanding.

Paper For Above instruction

Hypothesis testing is a core component of biostatistics, enabling researchers to make informed decisions about the validity of scientific claims based on data. Its application bridges the gap between data collection and scientific inference, playing a vital role in public health, clinical trials, and epidemiological studies. This paper explores the essential aspects of hypothesis testing, emphasizing the formulation of hypotheses, the systematic six-step process, and interpretation of errors and p-values that influence research outcomes.

The Foundations of Hypothesis Testing

At the outset, the process begins with constructing a clear scientific hypothesis that is testable through statistical analysis. These hypotheses serve as the basis for decision-making and underpin the scientific method. The null hypothesis (H0) typically represents the status quo or a statement of no effect or association, while the alternative hypothesis (H1) reflects the researcher's claim or expectation for a significant effect or relationship. Formulating precise hypotheses is crucial because it determines the direction and nature of subsequent statistical testing (Fisher, 1925; Neyman & Pearson, 1933).

The Six-Step Hypothesis Testing Procedure

The process is methodical, standardized, and involves six critical steps. First, the null hypothesis is formulated in statistical terms, specifying the parameter in question. Second, the alternative hypothesis is formulated to challenge the null, proposing the expected effect or association. Third, the level of significance (α) is chosen—commonly 0.05—to determine the threshold for statistical significance (Merrill, 2022). Fourth, the appropriate test statistic is selected based on the data type and hypothesis, and the decision rule is established, involving critical values or p-values. Fifth, data are collected, and the test statistic is computed. Finally, the researcher interprets the p-value in relation to α, deciding whether to reject or fail to reject H0 (Lehmann & Romano, 2005).

Interpreting Errors and Significance

No hypothesis test is infallible; thus, understanding Type I and Type II errors is vital. A Type I error involves wrongly rejecting a true null hypothesis, which leads to false positives—a significant concern in clinical studies and public health interventions. The significance level α (often set at 0.05) controls for the chance of making a Type I error (Cohen, 1988). Conversely, a Type II error involves falsely retaining a false null hypothesis, leading to false negatives that could overlook meaningful findings (Koehler et al., 2017). The power of a test, or 1-β, indicates its ability to detect a true effect, and larger samples enhance this power, reducing the risk of Type II error.

The Critical Role of p-values

The p-value measures the probability of observing a test statistic as extreme as the one obtained, assuming the null hypothesis holds. When the p-value is less than α, the evidence is deemed sufficient to reject H0, indicating a statistically significant result (Nuzzo, 2014). However, reliance solely on p-values has been criticized, as they do not directly measure the probability that H0 is true. Recent research highlights misinterpretations and overemphasis on the 0.05 threshold, urging a more nuanced approach to statistical significance (Anderson, 2020).

Implications for Research and Practice

Proper application and interpretation of hypothesis testing are indispensable in evidence-based practice. Researchers must carefully formulate hypotheses, select appropriate testing procedures, and consider the potential for errors. Additionally, integrating confidence intervals and effect sizes can provide more informative insights than p-values alone (Cumming, 2014). Recognizing the limitations of hypothesis testing and striving for larger sample sizes, transparency, and replication can improve the reliability of scientific findings, especially in public health domains where misinterpretation may have serious consequences (Ioannidis, 2005).

Conclusion

Hypothesis testing remains a foundational tool in biostatistics, facilitating evidence generation and decision-making. Mastery of its steps, understanding of error types, and cautious interpretation of p-values are essential skills for researchers. As scientific inquiry advances, continuous refinement of statistical methods and critical appraisal of results will enhance the robustness and reproducibility of research outcomes, ultimately contributing to better health policies and scientific progress.

References

• Anderson, S. F. (2020). Misinterpreting p: The discrepancy between p values and the probability the null hypothesis is true, the influence of multiple testing, and implications for the replication crisis. Psychological Methods, 25(5), 596–609.
• Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Erlbaum.
• Cumming, G. (2014). The new statistics: Why and how. Psychological Science, 25(1), 7–29.
• Fisher, R. A. (1925). Statistical methods for research workers. Oliver and Boyd.
• Ioannidis, J. P. (2005). Why most published research findings are false. PLoS Medicine, 2(8), e124.
• Koehler, J. J., et al. (2017). Interpretation of hypothesis tests and confidence intervals. Journal of the American Statistical Association, 112(519), 185–193.
• Lehmann, E. L., & Romano, J. P. (2005). Testing Statistical Hypotheses (3rd ed.). Springer.
• Merrill, R. (2022). Principles and applications of biostatistics. Jones & Bartlett Learning.
• Neyman, J., & Pearson, K. (1933). On the problem of the most efficient tests of statistical hypotheses. Philosophical Transactions of the Royal Society A, 231, 289–337.
• Nuzzo, R. (2014). Scientific method: Statistical errors. Nature, 506(7487), 150–152.