Measurement and accuracy (data-based)

Overview

To start the semester we will consider how scientists measure and quantify the natural world. We will learn foundational quantitative (mathematical) skills and concepts that will appear throughout the semester. We'll use these tools and concepts to consider climate data, including a recent climate change study on hurricane intensity. 

Background

Measurement:  Accuracy & Precision [4:52]

Measurement systems:  TedED: Why the metric system matters [5:07]  &  BBC Earth Lab: A fun guide to Imperial measurements [2:50]

U.S. Metrication:  Decades TV: U.S. metrication [2:24]  &  U.S. Metric Board 1981 PSA [0:59]  &  U.S. Office of Education 1978 cartoon commercial [1:00]

Unit conversions for climate data:  The story behind the Fahrenheit [5:23] 

Notation: Scientific notation [4:14]  &  Significant figures [5:03]

Article for concept application: Measurement of long-term climate trends (hurricanes) with evolving technology

Introduction

What image comes to mind when you read the word scientist? For many people, it’s a laboratory scientist with a lab coat, protective eyewear, and latex gloves. This image is frequently portrayed in textbooks, advertisements, and TV shows. This is a very specific type of scientist, one who studies microscopic objects like cells, enzymes, and DNA. However, there are many other types of scientists working in a variety of settings, using a variety of technologies, studying objects ranging from molecules to the entire planet. This semester, you’ll learn how the field of ecology blends many scientific disciplines, as well as their tools and technologies, to study all living organisms on our planet.  

The term scientist wasn't actually coined until 1834 when it was created to describe one brilliant woman, Mary Somerville, who broke the mold held at the time by “men of science”. Whereas her predecessors had largely focused their attention within one discipline, Mary Somerville was a self-taught mathematician who harmonized the fields of astronomy, geology, and biology into a single, interdisciplinary, and visionary form. Read the linked article to begin learning more about her life and her legacy. 

Ecologists today integrate many scientific disciplines, tools, and technologies to study the diversity of life on this planet. Whether it’s microbes under Antarctic ice or common cranes (birds) migrating over Mt. Everest, ecologists are driven by two key motivations: 1) describing the abundance and distribution of organisms on the planet, and 2) understanding the relationships among organisms and their environments. In this class, you’ll explore some of the most common ways ecologists measure and quantify these aspects of the natural world.  

A critical part of science is collecting data, which requires measurement.  Measurement is also critical to various other human enterprises, including trade, taxation, and construction.  Although various measurement systems exist, commonalities exist.  Most nested systems, meaning smaller standards (units) are used to measure smaller items.  For example, we use inches to measure height and miles to measure distances among cities.  They are also standardized, meaning at some level (ranging from local to global) people agree on what a measure means.  These traits are critical to making measurements useful.  

Measurement systems: metric & Imperial

Think about some of the beverages you might have had recently. Perhaps you bought a 12-ounce water, a half-gallon of milk, a medium coffee, or a 2-liter soda. All of these measurements are exact amounts except one – a medium coffee can only be defined relative to the small and large sizes. You might also recognize that liter is a metric unit (also called International System of Units) whereas ounce and half-gallon are Imperial units (also called English Units or U.S. Customary Units). This makes it cumbersome to compare amounts, as anyone will know that's ever had to convert recipes in the kitchen. 

When there are multiple systems with which to measure things, it creates confusion. Watch the background video "BBC Earth Lab" for a humorous summary of this confusion! Different measuring standards cause problems not just for science but also for governance, trade, taxation, construction, clothing, and many other industries and systems. In fact, in 1998 a miscalculation between metric and Imperial units caused the $200 million Mars Climate Orbiter to crash into the red planet before it was ever used!

The good news is there is one global standardized measurement system – the metric system. Watch the "TedEd" background video for some perspective on this. Follow that up with the three short background videos on U.S. metrication attempts over the years. Then, use the table below of metric prefixes to answer the following questions.

5.  Whereas Imperial units are based on a power of 12, the metric system is based on a power of ________. This makes the metric system much simpler to convert between small and large numbers.

6.  Rank these common metric prefixes from smallest to largest: tera-, centi-, kilo-, micro-, milli-, nano-.

7.  Although the U.S. is officially a metric country for international commerce, most of the nation uses Imperial units. What would be some benefits to officially switching over to the metric system?

Conversions within and between measurement systems: climate data

It’s important to be able to convert numbers within measurement systems (e.g., liters to milliliters) as well as between measurement systems (e.g., liters to gallons). This occurs often for climate data in the U.S., where scientific organizations use metric but the rest of the country uses Imperial. As a fun challenge, consider switching a weather app on your phone to metric units and see what it's like to experience the world in a different measurement system! 

For temperature, metric values are recorded in Celsius and Imperial values are recorded in Fahrenheit. Watch the background video on "The story behind the Fahrenheit". Then examine these equations for converting between Fahrenheit and Celsius, and answer the following questions by making the calculation (don't just do an internet search): 

°C = (°F – 32) * (5/9)                                    °F = (°C) * (9/5) + 32

8.  Average human body temperature is 98.6°F. What is this in Celsius?     _________________

9.  Water boils at 100°C. What is this in Fahrenheit? _________________

10.  Thinking about climate change, scientists and many global leaders have stated goals to keep 21st century temperature rise below 2°C.  What is this in Fahrenheit? _______________

For precipitation (rainfall & snowfall), metric values are recorded in millimeters or centimeters, and Imperial values are recorded in inches.   How do we convert between these units?

There are many different ways and methods that can help you convert from one unit to another.  Here we demonstrated one method known as dimensional analysis that may help keep things organized. First, identify the things you know - the number and unit you are given, as well as the unit you want to convert to. Next, the things you need to know to help you solve the problems - this may involve one or more conversions that were listed above. Now, we have to organize these conversions for calculations. Start with creating the diagram shown below, note that the vertical lines may be more or less depending on the number of conversions you are using.

We will continue this method by using this example question: convert 2.18 hours to seconds. 

• In the far left upper box, write down the number and unit you were given.

• Without knowing how many seconds are in an hour off the top of your head, the conversion from hours to seconds is through minutes because 

1 hour = 60 minutes

1 minute = 60 seconds

• We will fill out the boxes in the second column with the conversion from hour to minutes. We want to cancel out hours to get minutes and since hours is in the top box, we will write hours in the bottom box of the second row and minutes in the top box. Make sure the numbers of the conversions follows the corresponding units.

• To determine which unit belongs in which box, remember this: when you take one unit and divide it by the same unit, that unit cancels out. 

• If the question was asking to convert to minutes, the placement of all the necessary conversion factors is complete. This is because the unit, hour, would be cancelled out, leaving minutes as the only unit left.

• Moving on from minutes to seconds, we add the second conversion in the boxes of the third column following the same idea of the previous step. We want to cancel out minutes to get seconds, therefore we will put minutes in the bottom box and seconds in the top.  

• What is left to do is the calculation, multiply all the numbers in the top boxes and divide by all the numbers in the bottom boxes. Make sure to cancel out the matching units, leaving unit not cancelled out which should also be the unit you are trying to convert to. Write your answer in the far right upper box. 

  • Note that for all the individual columns (60 min/1 hour; 60 seconds/1 minute)  the top and bottom components are equivalent - you are simply multiplying your original amount by 1!

Using this approach and the information provided,  answer the following questions:

1 inch = 2.54cm   

11.  In an average month, New York City receives approximately 3.5 inches of precipitation. How many centimeters is this?_____________  How many millimeters is this?_____________

12.  A little farther north in Albany, an average month sees approximately 76.2 mm of precipitation. How many inches is this?____________ How similar is this to NYC’s precipitation, and what factors might influence the similarity/difference between the two cities? 

Scientific notation & significant figures

While metric prefixes allow us to easily talk about familiar numbers, scientific notation is the preferred way of writing extremely large and extremely small numbers. An example of scientific notation would be 3.25 x 105 , where 3.25 is called the coefficient. When this number is expanded from scientific notation, it would be 325,000 (the decimal was moved 5 places to the right and filled with zeros). Alternatively, the number 3.25 x 10-5 would be expanded to 0.0000325 (the decimal was moved 5 places to the left and filled with zeros).   

We can also convert into scientific notation. For example, the number 1,234,567 written in scientific notation would be 1.23 x 106. By comparison, the number 0.0004567 would be written as 4.57 x 10-4. 

As noted above, The first number in scientific notation is called the coefficient. It only has digit to the left of the decimal.  The number of digits contained in the coefficient depends on significant figures and other factors.  The term “significant figures” means the number of digits that carry meaningful information. 

• Example 1: 5.6789 contains 5 significant figures. 

• Example 2: 8.60792 contains 6 significant figures. 

• Example 3: 0.0044 contains 2 significant figures due to leading zeros

The second number is called the base and is always the number 10.  The third number is the exponent. It is always a whole number (integer).  Positive numbers mean we are expressing a large number (decimal moves to the right for standard form).  Negative numbers mean we are expressing a small number (decimal moves to the left for standard form).

Whether you’re converting from scientific notation or into scientific notation, there are simple rules to follow:

• Converting out of scientific notation: If the exponent is positive, move the decimal to the right. If the exponent is negative, move the decimal to the left.

To learn more, watch the background videos on "Scientific Notation" and "Significant Figures". Then convert the following numbers into scientific notation with 3 significant figures:

13.  123,456              _________________

14.  149,599,728    _________________

15.  0.0008193        _________________

Convert the following numbers out of scientific notation:

16.  5.09 x10-2         _________________

17.  6.80 x 104          _________________

18.  3.16 x 10-7        _________________

Concept application: climate change data

Considering all of the topics and skills you’ve just learned, read the background story on measurement of long-term climatic data. This story is a journalist’s summary of a recent peer-reviewed article on global increases of hurricane intensity. Pay particular attention to the paragraph starting with “The main hurdle we have for finding trends is…”.  Answer the following questions:

19.  In your own words, what is the overall finding of this research study?

20.  In your own words, what is the main hurdle they faced for finding trends?

21.  Is this hurdle an issue of accuracy, precision, or both?

For a follow-up, you can also read an article by NASA that explains the need and ability to adjust long-term temperature datasets before combining them.