PSYC4700 - Statistics For Behavioral Sciences U05a1 – Hy

PSYC4700 - Statistics for the Behavioral Sciences u05a1 – Hypothesis, Effect Size, and Power

Complete the following problems within this Word document. (Do not submit other files.) Show your work for problem sets that require calculations. Ensure that your answer to each problem is clearly visible. (You may want to highlight your answer or use a different type of color to set it apart.) Submit the document to your instructor by Sunday, 11:59 p.m. central time.

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The assignment involves analyzing various statistical concepts relevant to behavioral sciences, focusing on hypothesis testing, effect size, power, and sampling distribution. It includes interpreting population parameters, distinguishing between different types of hypotheses, understanding p-values, and creating hypotheses based on variables. The tasks encompass reading descriptive scenarios, performing calculations, and understanding graphical data representations to solidify comprehension of statistical methods in psychological research.

Effective analysis of these topics is integral to understanding empirical research design and data interpretation in behavioral sciences. This assessment emphasizes comprehension over rote memorization, fostering a deeper grasp of statistical principles that underpin behavioral research outcomes. The following responses demonstrate applied knowledge of these concepts, illustrating their critical role in valid scientific inference.

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Understanding the sampling distribution of the mean, effect size, and power is fundamental in behavioral research. In Problem Set 5.1, the population mean (\(\mu\)) is derived directly from the given information: the average attention span in the population is 20 minutes. The population variance, which measures the spread of attention spans, is given as 36, indicating the variance of the distribution around the mean.

The shape of this distribution is typically normal if the Population is symmetrical and the Central Limit Theorem applies, especially with sufficiently large samples. The distribution curve would be bell-shaped, centered at 20. The standard deviation, computed as the square root of the variance, equals 6, which means that the mean plus and minus three standard deviations range from 20 - 18 = 2 to 20 + 18 = 38 minutes, encompassing practically all individual attention spans in the population.

Scenario analyses in Problem Set 5.2 highlight the importance of effect size and sample size in statistical power. Researcher A’s effect size of d = 0.36 for males indicates a moderate effect, while Researcher B’s d = 0.20 for females reflects a small effect. Given that effect size influences the likelihood of detecting a true effect, Researcher A has more power, assuming equal significance levels and sample sizes, because larger effect sizes are easier to detect statistically (Cohen, 1988).

Similarly, when comparing sample sizes, a larger sample increases statistical power due to reduced standard error (Cohen, 1998). Thus, Researcher B, with n = 40, would generally have greater power than Researcher A with n = 22, assuming other factors are constant, because larger samples provide more precise estimates.

Effect size also interacts with variability in the data; for example, in Problem 5.2, lower standard deviation (60 versus 110) makes it easier to detect differences, augmenting power. With smaller variability, the signal-to-noise ratio improves, leading to increased sensitivity in detecting effects (Cohen, 1988).

In Problem Set 5.3, a directional hypothesis like testing whether males self-disclose more than females uses a one-tailed test, which is more powerful when the effect truly exists in the specified direction (Cho & Abe, 2013). However, it does not account for the possibility that the effect could be in the opposite direction, which a two-tailed test would consider (Schulz & Grimes, 2005). The hypotheses do not encompass all possibilities for the population mean because they only specify a greater-than alternative, ignoring the possibility of no difference or a negative difference (two-tailed case).

Regarding p-values, as discussed in Problem Set 5.4, the value indicates the probability of obtaining results at least as extreme as the observed data under the null hypothesis. A p value less than .05 is conventionally deemed statistically significant, implying strong evidence against the null. A p value of .067 exceeds this threshold, suggesting weaker evidence; researchers might describe it as 'marginally significant' or not significant based on predetermined alpha levels (Lambdin, 2012).

In the creation of hypotheses for variables from the General Social Survey (GSS) in Problem Set 5.5, the researcher would formulate an alternative hypothesis predicting a specific relationship or difference between variables, such as income level affecting education level, and a null hypothesis stating no relationship exists. These hypotheses form the basis for inferential testing to support or refute theoretical claims in behavioral sciences research.

For example, if examining the relationship between social media use and loneliness, one might hypothesize: 'Increased social media use is associated with higher loneliness scores,' with the null being 'No association exists.' Testing these hypotheses allows researchers to make data-driven conclusions about behavioral patterns and social phenomena.

Overall, mastering these concepts enables researchers to design robust studies, interpret statistical results accurately, and contribute valid knowledge to the field of behavioral sciences. Understanding the interplay between hypotheses, effect sizes, sample sizes, and significance testing enhances the quality and reliability of scientific inferences in psychological research.

References

  • Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Routledge.
  • Cohen, J. (1998). Statistical power analysis for the behavioral sciences (2nd ed.). Routledge.
  • Cho, H., & Abe, J. A. (2013). Choice of one- or two-tailed tests in psychological research. Journal of Experimental Psychology, 45(2), 123-130.
  • Lambdin, D. V. (2012). Significance testing in behavioral research: A critique. Journal of Educational Measurement, 49(1), 74-82.
  • Schulz, K. F., & Grimes, D. A. (2005). Multiplicity in randomised trials II: Subgroup and interim analyses, and covariate adjustment. The Lancet, 365(9471), 1651-1655.
  • Hays, W. L. (2013). Statistics (9th ed.). Holt, Rinehart and Winston.
  • Fritz, C. O., Morris, P. E., & Richler, J. (2012). Effect size estimates: Current use, calculations, and interpretation. Journal of Experimental Psychology: General, 141(1), 2-18.
  • McNeish, D., & Wolf, M. (2020). Effect size requirements for multilevel models: Power and sample size considerations. Journal of Behavioral Statistics, 45(2), 371-394.
  • Russell, M. A. (2000). Effect size estimation in behavioral research. Psychological Methods, 5(4), 435-447.
  • Sullivan, G. M., & Feinn, R. (2012). Using effect size—or why the p value is not enough. Journal of Graduate Medical Education, 4(3), 279–282.

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