The concepts of accuracy and precision are not always easy to grasp. Here are two sets of studies: (a) The mass of a secondary weight standard is determined by weighing it on a very precise balance under carefully controlled laboratory conditions. The average of 18 different weight measurements is taken as the weight of the standard. (b) A group of 10,000 males between the ages of 50 and 55 is surveyed to ascertain a relationship between calorie intake and blood cholesterol level. The survey questionnaire is quite detailed, asking the respondents about what they eat, smoke, drink, and so on. The results are reported as showing that for men of comparable lifestyles, there is a \(40 \%\) chance of the blood cholesterol level being above \(230 \mathrm{mg} / \mathrm{dL}\) for those who consume more than 40 calories per gram of body weight per day, as compared with those who consume fewer than 30 calories per gram of body weight per day. Discuss and compare these two studies in terms of the precision and accuracy of the result in each case. How do the two studies differ in ways that affect the accuracy and precision of the results? What makes for high precision and accuracy in any given study? In each of these studies, what factors might not be controlled that could affect the accuracy and precision? What steps can be taken generally to attain higher precision and accuracy?

Step by step solution

01

Understand precision and accuracy

Before comparing the studies, we need to understand the concepts of precision and accuracy. Precision refers to how close the measurements are to each other, while accuracy refers to how close the measurements are to the true value. In a study, high precision means the measurements are consistent, while high accuracy indicates that the measurements are reliable and close to the actual value.

02

Analyze Study (a)

In study (a), a secondary weight standard is being measured using a highly precise balance under controlled laboratory conditions. 18 different measurements are taken, and their average is used as the weight of the standard. In this study, the precision is likely to be high because it is carried out under strictly controlled conditions using a precise balance. However, the accuracy of the study might be affected by factors such as small variations in the measuring instrument, errors in taking measurements, or variations in environmental conditions.

03

Analyze Study (b)

In study (b), a large survey of 10,000 males is conducted to analyze the relationship between calorie intake and blood cholesterol level. The survey includes a detailed questionnaire, and the results are reported as a risk percentage for high cholesterol levels based on calorie consumption. In this study, the precision might be affected due to the large sample size and variations in the responses from the participants. The accuracy could be affected by factors such as generalization, bias in responses, or errors in data collection.

04

Compare the studies

Study (a) is likely to have higher precision compared to study (b) due to the controlled conditions and the use of a precise balance. However, accuracy could be affected by measurement errors in study (a) or biases and errors in data collection in study (b).

05

Steps to attain higher precision and accuracy

To attain higher precision and accuracy in any study: 1. Ensure proper calibration of measuring instruments 2. Use controlled conditions to minimize variations in the measurements 3. Increase sample size to reduce the impact of individual errors 4. Use unbiased methods of data collection 5. Test for any assumptions made during data collection or statistical analysis 6. Use reliable sources of information/data In study (a), to improve accuracy, ensure the balance is calibrated regularly and environmental factors are controlled. In study (b), enhance the accuracy and precision by using a more representative sample, controlling for potential biases, and using multiple data sources to validate the findings.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!