Doctorate Level Questions No Plagiarism Paraphrase Th 087852

Doctorate Level Questions No Plagiarismparaphrase The Conten

Question One: How is sample size related to statistical tests and outcomes? Give a specific example. Why is it important to plan the sample size before collecting data?

Sample size plays a critical role in determining the validity and reliability of statistical tests and their outcomes. A sufficiently large sample enhances the statistical power of a study, increasing the likelihood of detecting a true effect when it exists (Cohen, 1988). Conversely, an inadequate sample size can lead to Type II errors—failing to reject a false null hypothesis—resulting in potentially misleading conclusions. For example, in a clinical trial evaluating a new drug’s efficacy, having too few participants might fail to reveal a real therapeutic benefit, whereas a larger sample size could produce statistically significant results, confirming efficacy. Planning the sample size beforehand ensures the study is appropriately powered, optimizing resource use, minimizing risks of Type I and Type II errors, and ensuring the findings are generalizable (Biau, Kernéis, & Porcher, 2008). Methodological rigor in sample size calculation safeguards the integrity and credibility of research outcomes.

Question Two: Fill in the following for a possible study with one independent variable (IV) with two conditions/treatments and a dependent variable (DV) that is measured on a continuous scale (interval or ratio): Independent variable = ______________ Condition A = ______________ Condition B = ______________ Dependent variable = _______________ How do you know this DV is measured on a continuous scale? How would you word the null hypothesis for your sample study? How would you word the alternative hypothesis for your sample study? What alpha level would you set to test your hypothesis? Why?

In designing this study, the independent variable (IV) could be "Type of Exercise," with Condition A as "Aerobic Exercise" and Condition B as "Resistance Training." The dependent variable (DV) might be "Cardiovascular Endurance," measured using VO2 max values, which are continuous because they can take any value within a range and are measured on an interval scale (Shephard, 2001). The null hypothesis (H0) states there is no difference in cardiovascular endurance between the two exercise conditions: H0: μA = μB. Conversely, the alternative hypothesis (H1) posits that a significant difference exists: H1: μA ≠ μB. An alpha level of 0.05 is typically selected for hypothesis testing, balancing the risk of Type I error with statistical rigor (Fisher, 1950). This threshold indicates a 5% probability of rejecting the null hypothesis when it is actually true, maintaining scientific precision.

Paper For Above instruction

Understanding the relationship between sample size and statistical outcomes is fundamental in research methodology. The sample size critically influences statistical power, which is the probability of detecting an actual effect if it exists. A larger sample provides more precise estimates, reduces sampling error, and increases the likelihood of achieving statistically significant results (Cohen, 1988). For instance, in psychological research, studying the effect of a new intervention on anxiety levels, an adequately powered sample—say, 100 participants per group—can detect smaller effect sizes with high confidence. On the other hand, a small sample may lead to inconclusive results, often due to increased variability and reduced sensitivity to true effects (Biau, Kernéis, & Porcher, 2008). Therefore, pre-study planning for sample size—using power analysis—helps optimize resource use, ethical considerations, and the overall validity of findings (Faul et al., 2007). It ensures the study can meaningfully test the hypotheses while minimizing both Type I and Type II errors.

Moving to study design, when considering an experiment examining the effects of different exercise modalities on cardiovascular fitness, clear operational definitions are essential. The independent variable could be "Type of Exercise," with two conditions: aerobic exercise and resistance training. The dependent variable, measured continuously, might be "VO2 max levels," a standard indicator of cardiovascular endurance, which are interval data because they are numerical and capable of taking any value in a range (Shephard, 2001). The null hypothesis asserts no difference exists in VO2 max between the two groups, expressed as H0: μA = μB. The alternative hypothesis states that there is a difference, H1: μA ≠ μB. An alpha level of 0.05 is typical, meaning there is a 5% chance of a Type I error—incorrectly rejecting the null when it is true (Fisher, 1950). This threshold strikes a balance between sensitivity and specificity in hypothesis testing, providing responsible standards for interpreting results and ensuring scientific rigor.

References

  • Biau, D. J., Kernéis, S., & Porcher, R. (2008). Sample size calculation in clinical research. Clinical Orthopaedics and Related Research, 466(9), 2282-2291.
  • Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Routledge.
  • Fisher, R. A. (1950). Statistical methods for research workers. Oliver and Boyd.
  • Faul, F., Erdfelder, E., Buchner, A., & Lang, A. (2007). Statistical power analyses using GPower 3.1: Tests for correlation and regression analyses. Behavior Research Methods*, 39(2), 175-191.
  • Shephard, R. J. (2001). VO2 max and physical activity participation. Medicine and Science in Sports and Exercise, 33(6), 851-857.

Related Assignments