Question

The article "The Largest Last Supper: Depictions of Food Portions and Plate Size Increase Over the Millennium" (International Journal of Obesity [2010]: 1-2) describes a study in which each painting in a sample of 52 paintings of The Last Supper was analyzed by comparing the size of the food plates in the painting to the head sizes of the people in the painting. For paintings that were painted prior to the year \(1500,\) the estimated average plate-to-head size ratio was smaller than this ratio for the paintings that were painted after the year \(1500 .\) Is the inference made one that involves estimation or one that involves hypothesis testing?

Short answer

The inference is one that involves estimation rather than hypothesis testing.

Step-by-step solution

Understanding the Context and the Question

In this study, researchers looked at 52 paintings of The Last Supper and observed changes in plate-to-head size ratios according to the era of the painting. They found that, generally, this ratio was smaller in paintings done before 1500 than in those done after. The question is whether this is an example of estimation or hypothesis testing.

Define Estimation and Hypothesis Testing

Estimation is a statistical method that approximates calculated values based on observed data, while hypothesis testing involves making an assumption (hypothesis) about a population parameter and then testing the validity of that hypothesis using evidence from sample data.

Analyzing the Inference in the Context

The inference made in this study is that plate-to-head size ratios in these paintings changed over time. However, the study does not test a specific hypothesis - for example, that this ratio increased by a specific percentage over time period. Instead, the inference basically refers to an observed trend in the sample data.

Categorizing the Inference

Given that the researchers simply identified a pattern in the data without validating a specific claim regarding population parameters, the inference they made is more likely related to the concept of estimation rather than hypothesis testing.

Key concepts

Estimation in Statistics

Estimation plays a vital role in statistics when we seek to determine an unknown parameter of a population based on sample data. It's like trying to guess the weight of a suitcase by lifting it rather than using a scale. Statisticians use estimations to infer population characteristics without having to collect information from every individual member of that population.

In the context of art analysis, estimation can help us understand historical trends, such as the changing food portion sizes in paintings over time. By estimating the plate-to-head size ratio in a sample of artwork, researchers are tackling the problem much like a tourist might estimate the height of a landmark using a familiar object, like a pen, as a reference.

In the case of the analysis of 'The Last Supper' paintings, estimation provides a grasp of the average change in the plate-to-head size ratio across time periods. This process does not involve making firm assumptions upfront as in hypothesis testing but rather provides an educated guess about the ratio based on available samples.

Hypothesis Testing

Hypothesis testing is the detective work of statistics, where we start with a suspicion (the hypothesis) and look for evidence in our data to support or refute it. Imagine a student claiming that studying with music leads to better test scores. To validate this, their peers might conduct an experiment to test this hypothesis by comparing scores from music-listening studiers to those who study in silence.

In scientific research, including art analysis, hypothesis testing often involves establishing a null hypothesis, which is a default statement that there is no effect or no difference, and an alternative hypothesis, which is what the researcher expects to find. After gathering data, statistical tests determine whether the results significantly contradict the null hypothesis, suggesting that the alternative hypothesis may be true. The study's inference of varying plate-to-head size ratios over time could lend itself to hypothesis testing if the researchers were testing a precise claim, such as 'The plate-to-head size ratio increased by 20% after 1500 compared to before 1500.'

Plate-to-Head Size Ratio Analysis

The intriguing plate-to-head size ratio analysis examines the relationship between the depicted plate size and the head size of figures in artwork, providing an indirect measurement of perspective, perception, and possibly, societal tendencies over time. It's akin to gauging the economic condition of a society by the attire of the people in historical photographs.

By measuring the plates relative to the heads in 'The Last Supper' paintings, researchers can explore trends in how food and abundance are represented visually. This can reflect cultural tendencies, like the increase in portion sizes or changes in artistic style. For educational purposes, art students and historians might be interested to know not only the findings but also how such analyses contribute to a broader understanding of art history and its relation to social changes.

Plate-to-head size ratio analysis is a meticulous process that must take into account the varying styles of painters, the differences in plate and head sizes over the course of history, and the renderings of perspective in artwork, further complicating the estimation process. Such an analysis is beneficial not only for art critics but can also enhance our understanding of the intersection between art, culture, and the evolution of social habits.