Learning Goals
During this activity, you will:
- Utilize standardized scores and the Empirical Rule to determine if an observation is unusual.
- Compare two observations by calculating and comparing z-scores.
Click on a skill above to jump to its location in this activity.
What Is Unusual?
In a medical study, many observations are made in an effort to obtain a data sample representative of the population from which it was taken. In this activity, you’ll see how standardized scores and the Empirical Rule can be used to determine if an observation is usual or unusual.
Around the world, pharmaceutical companies conduct clinical trials to evaluate the safety and efficacy of their drugs. Clinical trials are research studies performed on people and are aimed at evaluating if a new drug is safe and effective. People who participate in clinical trials are volunteers.
question 1
video placement
[Intro video: In this activity, we’ll use the landscape of a medical study to learn how the Empirical Rule can help us identify unusual observations of a quantitative variable. We’ll also compare two observations by calculating and comparing their standardized scores. Data collected during medical studies tends to form a bell-shaped, unimodal distribution, with a large number of observations located near the mean and equal numbers of values further from the mean falling off to either side. [voice over the empirical rule image from What to Know 4E]. Under these conditions, we know that almost all the observations in the distribution fall within three standard deviations from the mean. This lets us set an exact threshold for how far away from the mean an observation can be located for us to consider it unusual. But human clinical trials require people willing to participate. They are costly and take a great deal of time to gather the appropriate data, even decades to study the effects of a drug over an entire lifespan. Can you think of a good alternative to having human volunteers participate in clinical trials? How about using mice instead? In this activity, we’ll explore a medical study involving mice as we learn to apply the Empirical Rule and standardized scores.]
Mice are often used in medical studies to evaluate the effects of chemicals and pharmaceuticals. One reason for this is that scientists know a lot about the genome of a mouse. They are bred in labs to be identical, so the only thing different between them is the treatment. Mice also have short lifespans, which allows scientists to model the effects of a drug over their entire lifespan (about [latex]800[/latex] days). It is much more difficult to understand the effects of a drug over the lifetime of a human.
Consider a study concerned with learning how a drug or a treatment affects the body. The toxicity of a chemical and its impact on vital organs is of interest when assessing the effects of a chemical treatment. A standard method used to measure the level of toxicity in an organ is to use the organ’s weight.[1]
- Sellers, R. S., Mortan, D., Michael, B., Bindhu, M., Roome, N., Johnson, J. K., Yano, B. L., Perry, R., & Schafer, K. (2007). Society of toxicologic pathology position paper: Organ weight recommendations for toxicology studies. Toxicologic Pathology. 35(5), 751-755. https://doi.org/10.1080/01926230701595300 ↵
- What is a genome? (2017, January 6). Yourgenome. Retrieved from https://www.yourgenome.org/facts/what-is-a-genome ↵
- Definition of toxicity. (2021, March 29). RxList. Retrieved from https://www.rxlist.com/toxicity/definition.htm ↵
- Lazic, S. E., Semenova, E., & Williams, D. P. (2020, April 20). Determining organ weight toxicity with Bayesian causal models: Improving on the analysis of relative organ weights. National Center for Biotechnology Information. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7170916/ ↵
