Psy2061 Research Methods Lab 2013 South University ✓ Solved

Page 1 Of 1 Psy2061 Research Methods Lab 2013 South Universitysteroi

Analyze a study investigating the effects of steroid usage, grip strength, aggression, and happiness, interpreting various statistical concepts including confidence intervals, experimental design, parameter vs. statistic, sampling distribution, and hypothesis testing based on multiple research scenarios.

Sample Paper For Above instruction

The research examining the relationship between steroid use and various physical and psychological outcomes offers an illustrative case study for understanding multiple statistical concepts critical to research methodology. The multifaceted nature of the study, incorporating both experimental and observational components, underscores the importance of clearly distinguishing between experimental designs, understanding confidence intervals, inferring population parameters from sample statistics, the shape and center of sampling distributions, and interpreting margin of error in polls.

Firstly, the study on steroid usage, grip strength, aggression, and happiness involves an investigator assigning participants. Clarifying the type of experimental design—whether it is a randomized comparative experiment or a matched pairs experiment—is fundamental. When the investigator allocates identical participants into different conditions, such as steroid use, and compares outcomes within the same individual (pre- and post-treatment), the design is a matched pairs experiment. Conversely, if participants are assigned randomly to different groups without pairing, it is a randomized comparative experiment. In the context of the provided description, if the investigators measured each individual's grip strength, aggression, or happiness before and after steroid use, it suggests a matched pairs design, which controls individual variability. However, if the study was set where participants were randomly assigned to steroid or non-steroid groups and outcomes compared between these groups, then it is a randomized comparative experiment.

When considering the effect of increasing the sample size from 75 to 500 participants on the confidence interval, statistical theory indicates that larger samples produce narrower intervals. This arises because the standard error decreases as the square root of the sample size increases, reducing the margin of error around the estimated mean difference or proportion. Mathematically, the confidence interval width is proportional to the standard error, which diminishes with increased sample size, making the interval more precise. Therefore, a sample of 500 participants would generate a narrower confidence interval, providing a more accurate estimate of the population parameter.

Transitioning to the BPA in canned soup study, which involves a crossover design, the study measures urinary BPA levels after consumption of canned versus fresh soup. The reported 95% confidence interval for the mean difference in BPA levels between treatments, 19.6 to 25.5 μg/L, provides a range of plausible values for this population parameter. The confidence interval does not include zero, implying a statistically significant increase in urinary BPA after canned soup consumption. This emphasizes the importance of understanding whether the interval includes zero to identify if the difference is statistically significant.

The question of whether the study is a randomized comparative experiment or a matched pairs experiment hinges upon the design specifics. Since each participant experienced both treatments (canned and fresh soup) with a period washout in between, this is a matched pairs design. This approach helps control individual variability, leading to more reliable estimates of the treatment effect.

Furthermore, increasing the sample size from 75 to 500 participants would generally produce a narrower confidence interval. Larger samples reduce the standard error, decreasing the range within which the true population mean difference lies with a given level of confidence.

In the context of the arrest study involving 7,335 young people, the proportion who had been arrested, 30%, is a statistic from a sample. Given a margin of error of 0.01, the plausible range for the true population proportion can be calculated by adding and subtracting the margin of error from the sample proportion, i.e., 0.30 ± 0.01, resulting in a range from 0.29 to 0.31. This interval accounts for sampling variability, providing a plausible range for the true proportion of young people who had been arrested by age 23.

Examining the question of whether the true proportion of arrests could be less than 25% with the given margin of error involves understanding that the interval 0.29 to 0.31 does not include 0.25. Therefore, it is unlikely that the true population proportion is as low as 25%, based on this data.

Similarly, the analysis of the statistics PhD programs demonstrates how sampling distribution shapes and centers are interpreted. Using the sample means from two different samples, the sample means are calculated exactly and denoted appropriately. The mean of the entire population of 82 graduate programs can be estimated by averaging all 82 enrollment numbers; this offers an understanding of population parameters.

Moreover, the sampling distribution of the sample means, if many samples are taken, tends to be approximately normal—symmetric and bell-shaped—regardless of the underlying population shape, given sufficiently large sample sizes due to the Central Limit Theorem. The distribution would be centered around the true population mean of enrollment across all programs, which can be estimated from the entire dataset.

In the context of the study on playing action video games, the confidence intervals for response time differences and accuracy scores serve to determine whether the groups differ significantly. Since the 95% CI for response time difference (-1.8 to -1.2 seconds) does not include zero and is negative, it indicates that game players are faster because their response times are significantly lower. Conversely, the CI for accuracy score (-4.2 to +5.8) includes zero, suggesting no significant difference in accuracy between game players and non-players. These interpretations highlight the importance of confidence intervals in hypothesis testing.

Finally, the poll data assessing opinions on "only one true love" and the election polling estimates involve calculating confidence intervals or margins of error to infer whether the true population parameters could be equal or differ. For example, the confidence interval for the difference in proportions who agree with the statement between males and females, based on the standard error, helps determine if the difference is statistically significant at a 95% confidence level. If the interval does not include zero, a significant difference exists; otherwise, the difference may be due to chance.

Similarly, in election polls, if the estimated support for a candidate exceeds 50% by at least the margin of error, it is likely that the candidate would win an actual election conducted at that time. If the interval overlaps 50%, the outcome is uncertain. The interpretation of confidence intervals and margins of error is crucial in decision-making processes in polling and election predictions.

In sum, these diverse scenarios underscore core principles in statistics: designing experiments appropriately, understanding the implications of sample size on confidence intervals, interpreting confidence intervals in terms of population parameters, and analyzing the shape and center of sampling distributions. Mastery of these concepts is vital for rigorous research and accurate inference across social and natural sciences.

References

  • Carwile, J., Ye, X., Zhou, X., Calafat, A., & Michels, K. (2011). Canned Soup Consumption and Urinary Bisphenol A: A Randomized Crossover Trial. Journal of the American Medical Association, 306(20), 2218–2220.
  • Green, et al. (2010). Improved probabilistic inference as a general learning mechanism with action video games. Current Biology, 20(September 14), 1.
  • Smith, A. (2011). Americans and Text Messaging. Pew Research Center.
  • American Mathematical Society. (2009). Data on enrollment obtained from Assistantships and Graduate Fellowships in the Mathematical Sciences.
  • Rock and Roll Hall of Fame. (2012). Inductees Data. rockhall.com/inductees/
  • USA Today. (2012). Study of Arrests Among Young People. https://www.usatoday.com/
  • Statistical Society of America. (2009). Enrollment Data in Statistics and Biostatistics PhD Programs.
  • Environmental Working Group. (2012). BPA and Food Safety Reports.
  • Pew Research Center. (2011). Mobile Phone and Text Messaging Study.
  • Data Science in Public Policy. (2010). Election Polling and Confidence Intervals.

Related Assignments