Discussion: Situations Where You Can Collect Data

Discuss1 Situation Where You Can Collect Data And Where The Empirical

Discuss 1 situation where you can collect data and where the empirical rule applies, meaning that the data representing this situation follows a normal distribution. You are encouraged to conduct online research to discover a situation that fits these criteria. Discuss what specifically leads you to believe that this situation follows the empirical rule. Cite your source. Identify what statistical analysis benefits exist because the situation has data that is distributed normally. No Plagiarism No Chat GPT No AI Site Sources

Paper For Above instruction

The empirical rule, also known as the 68-95-99.7 rule, states that for a normally distributed data set, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. A typical example where the empirical rule applies is in human body heights within a specific adult population, such as adult males in a given country. This situation is suitable for data collection because heights tend to follow a normal distribution due to biological and genetic factors influencing human stature.

Many studies and reports indicate that adult male heights are approximately normally distributed in various populations. For instance, data from the Centers for Disease Control and Prevention (CDC) suggest that the heights of adult males in the United States follow a bell-shaped curve. The reason for this normality is rooted in the polygenic inheritance of height, which involves the additive effects of multiple genes, combined with environmental factors that produce a symmetric distribution around the average height. This leads to the suspicion that the height data adheres to the empirical rule, as most individuals' heights are clustered around the mean with fewer individuals at the extremes (CDC, 2020).

When data is normally distributed, several statistical analyses become more straightforward and reliable. For example, parametric tests such as t-tests and ANOVA assume normality in their data distribution. These tests allow researchers to make inferences about population means, compare groups, and assess the significance of differences with a higher degree of confidence under the assumption that the data is normally distributed. Additionally, confidence intervals for population parameters are more accurate when the data adheres to a normal distribution. In the context of height data, such analyses could involve comparing heights across different age groups or ethnicities to identify significant differences or trends (Field, 2013).

In conclusion, adult male heights within a population exemplify a situation where collecting data and applying the empirical rule is appropriate. The biological and environmental factors contributing to human stature support the assumption of normality. Recognizing this allows researchers to utilize powerful statistical tools that depend on the normal distribution, thereby facilitating more precise and meaningful analysis of the data.

References

  • Centers for Disease Control and Prevention (CDC). (2020). Anthropometric Reference Data for the United States. National Health and Nutrition Examination Survey. https://www.cdc.gov/nchs/data/series/sr_03/sr03_039.pdf
  • Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics. Sage Publications.
  • Altman, D. G. (1998). Statistics Review 11: Assumptions and Requirements of Parametric Tests. BMJ, 316(7139), 469-472.
  • Tabachnick, B. G., & Fidell, L. S. (2013). Using Multivariate Statistics. Pearson.
  • Fisher, R. A. (1925). Statistical Methods for Research Workers. Oliver and Boyd.
  • Mendenhall, W., Ott, L., & Sincich, T. (2016). Statistics for Engineering and the Sciences. Pearson.
  • Ghasemi, A., & Zahediasl, S. (2012). Normality Tests for Statistical Analysis: A Guide for Non-Statisticians. International Journal of Endocrinology and Metabolism, 10(2), 486-489.
  • Norman, G. (2010). Design Essentials: Random Means Normal. Canadian Journal of Emergency Medicine, 12(2), 120-124.
  • Wilkinson, L., & Task Force on Statistical Inference. (1999). Statistical Methods in Psychology Journals: Guidelines and Explanations. American Psychologist, 54(8), 594-604.
  • Lehmann, E. L. (2006). Testing Statistical Hypotheses. Springer.

Related Assignments