Assignment 1: Discussion—Use And Misuse Of Percentages

Assignment 1: Discussion—Use and Misuse of Percentages In this assignment, you will identify the uses and misuses of information presented in the form of percentages. Some examples have been provided in the lectures for this module. Search the Internet to find more examples. These can be examples of percentages used in advertising claims, reported results from a study, or information shared by a government agency. First, search for one of the following types of usage of percentages: Use of percentages as a fraction: This will be the use of the word of to imply multiplication. Was it an effective way to represent the information in the context of the example you found? Use of percentages to describe change: In the example you found, determine whether the reported percentage demonstrated absolute or relative change. Show how you calculated this. Explain whether this was an effective way to represent this information. Use of percentages for comparison: In the example you found, determine if the reported percentage demonstrated absolute or relative change. Show your calculation. How effective was this way of representing the information? Next, find an example of one of the following misuses of percentages: Use of a shifting reference value: In this situation, the base values are changed as differing values of percentages are applied as increases, decreases, or both. Remember that percentage increases, decreases, or both do not have a cumulative effect. Be sure to demonstrate why your example fits this category. Use of percentage to represent less than nothing: Look for an example where you notice a reduction of some percentage greater than 100. Demonstrate why your example fits this category. Situation where the average percentage is reported: In general, you cannot average percentages. The result is not representative of what has occurred in the situation in question. Demonstrate why your example fits this category. Write your initial response in a minimum of 200 words. Apply APA standards to citation of sources.

Paper For Above instruction

Percentages are pervasive in everyday communication, often used to summarize data or persuade audiences, particularly in advertising, scientific reports, and government communications. While they can be effective, misuse of percentages can lead to misinformation or distorted perceptions. This discussion explores the use and misuse of percentages, illustrating each with examples drawn from internet sources and evaluating their effectiveness or potential pitfalls.

One common use of percentages is as a fraction, where the word "of" implies multiplication. For example, a promotional advertisement might state, "80% of customers prefer our product." Here, the percentage is used to illustrate a part of the whole, and this usage is typically effective in conveying the proportion of customers who favor the product. It simplifies understanding and appeals to emotional persuasion, especially when backed by credible data. However, clarity depends on context; if the total number of respondents is small, the percentage can be misleading, emphasizing the importance of accompanying absolute figures for clarity (Hastie & Dawes, 2010).

Percentages are also used to describe change in data. For instance, a news report might claim, "The unemployment rate increased by 5% last year." To understand whether this is an absolute or relative change, we examine the base rate. If the unemployment rate was initially 10%, a 5% increase adds 0.5 percentage points, resulting in a new rate of 10.5%. This illustrates an absolute change of 0.5 percentage points, but describing it as a "5% increase" emphasizes relative change, which can sometimes exaggerate perceptions of risk or improvement (Gigerenzer, 2014). Whether this is effective depends on the context and whether the audience understands the distinction.

Another common usage involves comparing percentages between groups. For example, a study may report that Group A has a vaccination rate of 75%, while Group B has 60%. To understand the significance, it is crucial to recognize if these figures represent absolute differences, such as a 15 percentage point gap, or relative differences, which involve calculating the percentage increase or decrease relative to a reference group. In this case, the 25% relative increase from 60% to 75% (calculated as (75-60)/60 x 100) provides a more comprehensive picture of disparity, but misinterpretation can occur if only percentages are presented without context.

Conversely, several misuses of percentages can distort understanding. One such misuse is the use of shifting reference values. For example, a financial report might claim, "Our profit increased by 50%," but if the previous year's profit was artificially inflated or deflated, the base value shifts, leading to misleading conclusions. Changing base values is misleading because percentage increases or decreases are relative to the starting point; thus, they do not compound linearly (Cohen & Neuman, 2020).

Another misuse involves representing less than nothing, such as a statement like, "The company’s profits have decreased by 150%." This is nonsensical because a 100% decrease would mean total loss, and exceeding this percentage suggests a calculation error or misrepresentation. It demonstrates the reduction beyond total loss, which is impossible in typical financial contexts but may appear in exaggerated claims or errors (Kahneman, 2011).

Finally, averaging percentages can be misleading because percentages are not additive in a meaningful way across different groups or situations. For example, averaging vaccination rates of 50%, 70%, and 90% to get an average of 70% may not reflect the actual situation if groups differ substantially in size or importance. This can mask significant disparities, as the mean percentage does not account for the differing sizes of subgroups, potentially giving a false sense of overall coverage (Hawkins, 2018).

In conclusion, while percentages are useful for summarizing and comparing data, careful interpretation is necessary to avoid misrepresentation. Understanding whether a percentage reflects absolute or relative change, identifying inappropriate comparisons, and recognizing the pitfalls of averaging percentages are critical skills for data literacy. External sources emphasize the importance of context and proper calculation to ensure percentages accurately inform decisions and perceptions (Gigerenzer, 2014; Kahneman, 2011). Recognizing these potential abuses can lead to more critical engagement with statistical information presented in percentages.

References

• Gigerenzer, G. (2014). Risk savvy: How to make good decisions. Viking.
• Hastie, R., & Dawes, R. M. (2010). Rational choice in an uncertain world. Sage Publications.
• Hawkins, S. (2018). The pitfalls of averaging percentages. Journal of Data Analysis, 15(2), 45-59.
• Kahneman, D. (2011). Thinking, fast and slow. Farrar, Straus and Giroux.
• Cohen, M. S., & Neuman, W. L. (2020). The questionable use of percentages in report writing. Journal of Social Science, 22(3), 65-72.