EPPL 612
Unit: Epistemology – How Do We Know What We Know?
Bitto & Goff
Lesson #5: Salty Seas
(Descriptive Statistics and the Stochastic Nature of Data Collection)
(plus a proposed “Lesson 5A” on graphing data)
PURPOSE & OVERVIEW:
In this lab, students will explore a handful of different methods for estimating the salinity
of seawater, and this will be the occasion for developing an understanding of the
inherently stochastic nature of data collection and for learning how to perform basic
statistical descriptions such as mean, variance, and standard deviation. A key message is
that “true” parameters can NEVER be known; instead, we can only estimate them.
Consequently we require special statistical methods to help us gauge the confidence with
which we can accept our estimates – a concept that will be developed in the next several
lesson/lab activities. (Note the conceptual connection between this message and the
opening lesson on appearances vs. actuality. Once again we must ask: How do we know
what we know?)
INTENDED AUDIENCE: Advanced secondary science course or summer program for
gifted and high-achieving students.
ESSENTIAL QUESTIONS:
 If all we ever have are estimates of unknowable parameters, then how can we
gauge the degree of confidence that our estimates warrant? In other words, how
shall we gauge the credibility of the inferences that we draw from less-thanperfect estimates?
KEY CONCEPTS:
 Unknowable parameters vs. imperfect estimates (stochastic or “noisy” nature of
all data collection)

Descriptive statistics (mean, variance etc.) as estimates of unknowable
parameters

Measures of central tendency vs. measures of dispersion
OBJECTIVES – After this lesson, students will be able to:
 Identify definitions, descriptions, and/or instances of natural science and its truth
claims striving to be: quantitative (vs. qualitative, usually) and probabilistic.

Calculate basic descriptive statistics: mean, mode, median, range, variance, and
standard deviation for a given set of data.

Recognize the distinction between appearances, which can be deceiving, and
reality “out there” (= realism). Similarly, recognize the stochastic nature of all
data collection, such that all we can ever get are estimates of unknowable
parameters, hence the need for replication, statistics, and probabilistic gauges of
statistical confidence (as opposed to “proof”). Also, apply all of this in their own
data analyses, scientific investigations, and evaluations/critiques of others’
research. (See details below under both Process and Content Goals.)
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EPPL 612
Unit: Epistemology – How Do We Know What We Know?

Bitto & Goff
Analyze data graphically and statistically, including the calculation of descriptive
statistics; the construction and interpretation of professional-looking graphs with
appropriate scales, “best fit” curves, and error bars; and the selection, application,
and interpretation of appropriate inferential statistics for testing null and
alternate hypotheses – all by way of current technology/computer software.
Concept Goals
Goal 1
Goal 2
x
Process Goals
Goal 1
Goal 2
x
Content Goals
Goal 1
Goal 2
Principles of Gifted Education at Work:
 Integrates key concepts, unifying themes, and fundamental principles with
advanced content and sophisticated skills

Contributes to holistic, systemic coherence

Invokes higher order thinking/reasoning and cultivates good habits of mind

Involves complex, multi-dimensional, sophisticated undertakings

Tackles meaningful matters of substance, authenticity, and depth, cultivating
expertise that approaches that of real world professionals

Calls for authentic inquiry and investigation

Integrates technology

Calls for collaboration with peers of similar readiness and ability
Vocabulary:
 Quantitative vs. Qualitative

“Noise”

Measures of central tendency: mean, median, mode

Measures of dispersion: range, variance, standard deviation
Materials:
 Documents: “Salty Seas” (lab guide for students), instructions for each method (to
be posted at each station), graphs for hydrometer and conductivity stations

Jug of homemade seawater (~15-20 ppt). Hydrometer(s), thermometer(s), CBL
with conductivity probe (or comparable probeware), refractometer, titration
kit(s), balances, hotplates, safety goggles, evaporating dishes, tongs, wire gauze,
graduated cylinders, beakers, flasks, droppers.
PROCEDURES
Introduction/Hook:
Recall that science is empirical, grounded in sensory
observations. Ideally – though not always – scientific
TEACHER NOTES
Note: make the salinity
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EPPL 612
Unit: Epistemology – How Do We Know What We Know?
data is quantitative rather than qualitative:
Bitto & Goff
slightly less than 20 ppt.
Quantitative = Expressed in numerical measures.
Whenever possible, a scientist collects observations
that are quantitative rather than qualitative, so that
she can manipulate the data mathematically, graph
the results, and perform statistical tests.
Qualitative = Expressed in purely descriptive terms
(e.g., adjectives) rather than numerical quantities
Quantitative measurements enable us to graph and run
statistical operations that allow us to spot patterns in
nature that we’d otherwise miss. This lab will break us
into this side of Science. Distribute “Salty Seas: Five
Methods for Estimating Salinity” and describe the
procedure.
Learning Activities:
Two Day Procedure: Pairs or trios of students will travel
to five different stations at which they will estimate the
salinity of a single stock sample of seawater using these
methods: evaporation, titration, hydrometer,
refractometer, and conductivity. They will then combine
their data and calculate basic descriptive statistics both
by hand and in Excel. Students will then evaluate the
pros and cons of each method, and consider matters of
accuracy and variability in collecting data.
Notice that there was only ONE jug of seawater, and yet
different methods yielded difference estimates.
Moreover, the SAME methods yielded different estimates
upon replication. Key message: All data is inherently
“noisy,” and we can NEVER know the “true” or “real”
salinity of the sample. All we ever have are estimates
...and that’s why we need statistics! (An idea that we
will flesh out in the lessons and labs to come…)
The number of stations
needed will depend upon
class size. The evaporation
procedure takes the most
time and so requires multiple
stations. The titration
station is second longest, so
at least two stations are
desirable. The other three
stations are brief. NOTE: Not
all student teams will
complete all 5 procedures,
but try to allow time for
them to do at least 3 or 4.
Grouping:
Students should work in teams of two or three. Probably
no need for special grouping strategies.
Closure/Debriefing:
Analyze the statistics together and go over the
interpretation questions. Reemphasize the big message
about stochasticity and the utter unknowability of
“true” parameters …all we ever have are estimates.
Make explicit the connection, here, to our earlier
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EPPL 612
Unit: Epistemology – How Do We Know What We Know?
Bitto & Goff
lessons on appearances vs. actuality, healthy
skepticism, etc. So the next question is, how can gauge
how confident we can be in the accuracy of our estimates
and the inferences that we draw therefrom?
Homework:
Calculate descriptive stats and answer written questions for homework, if necessary.
Ancillary Lesson/Assignment – “Lesson 5A”
This would be a logical occasion on which to give students practice with graphing data (a
skill that they will cultivate throughout the year on numerous lab activities and class
investigations, in preparation for their independent research projects.) The teacher can
use the accompanying documents to develop an ancillary lesson on graphing both by
hand and in Microsoft Excel. There are three files on making “best fit” curves by hand: a
tutorial with examples of Do’s and Don’ts, plus a pair of practice problems. Students can
do this independently (e.g., for homework). There is also a guide for making good
scientific graphs in Excel. NOTE: The directions here refer to earlier versions of Excel, 2003
and prior. The 2007 and subsequent versions of Excel made major changes to the graphing
mechanisms. Therefore, while this document’s general advices and principles still hold, the
Excel instruction will have to be updated.
Differentiation
 Choice: n/a
 Resources: n/a
 Products: n/a
 Tiering, Compacting, etc.: n/a (however, this lab involves some very high order
concepts and some fairly sophisticated data collection and analysis)
Differentiation for:
 ELL: The hands-on and computational nature of this activity are ELL-friendly.
 Twice-Exceptional: n/a
 Highly Gifted: n/a
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