ISB 208L Nature’s Numbers * Why Use Statistics? Statistics are sets of mathematical equations used to analyze what is happening in the world around us. Statistics also add confidence to the way we report our findings. Quiz Which of the following two graphs will have a greater standard deviation? Explain why. A B * Explain what a small standard error tells us about the averages (means) in comparison to all the values within that data set? Quiz * What Do Standard Errors Tell Us? Standard errors are calculations that show the accuracy of the population mean. Sometimes referred to as ‘Margin of Error’. Are these two data sets statistically similar or different? * Interpreting Standard Errors on Graphs Draw a horizontal line across the graph from each average’s error bar. If ranges overlap, then the differences in the averages are considered insignificant; that is, there is no statistically measurable difference between the two averages. If error bar ranges do not overlap, then the averages are considered significantly different, meaning there is sufficient data to suggest the values differ more than would be expected by chance alone. So what are we actually saying about the data. How would you communicate this to someone? * Graphs can be misleading! * Same Data with Errors Bars * Are these two data sets statistically similar or different? * * Today’s ObjectivesCollect Data & Create a Data TableCreate and Test a HypothesisCalculate & Plot Standard ErrorsAnalyze & Interpret Data Have fun with Madagascar Hissing Cockroaches! * Sexual Dimorphism (Males vs. Females) Sexual dimorphism is an observable difference between males and females of the same species. * Madagascar Hissing CockroachesThey live 2-3 years on average (sometimes up to 5!)They reach a size of 1.5 to 3 inches longThey are dark reddish brown to blackThey are hardy and docile and can easily be handled. Hissing cockroaches have a pair of modified spiracles (the tubes insects use for breathing) that they use to produce the hissing sound that inspired their name. * Testing a Hypothesis: I believe that only male hissing cockroaches hiss. Do not be afraid to handle the specimens, but they are living creatures so handle them carefully. Is this hypothesis Supported or Refuted?  Males have more pronounced ‘horns’ * Create a Sexual Dimorphism Hypothesis: Look at the last abdominal segment on the ventral side of both male and female cockroach at your table and create a hypothesis as to which has the longer abdominal segment. Decide as a group whether males or females will have a longer last abdominal segment on average – record your hypothesis on the worksheet. * We are going to measure sexual dimorphism based on the length of the last abdominal segment. 1. Measure (in millimeters) the length of the last abdominal segment on the ventral side of both male & female. 2. Repeat on ...

1. ISB 208L
Nature’s Numbers
*
Why Use Statistics?
Statistics are sets of mathematical equations used to analyze
what is happening in the world around us. Statistics also add
confidence to the way we report our findings.
Quiz
Which of the following two graphs will have a greater standard
deviation? Explain why.
A
B
*
Explain what a small standard error tells us about the averages
(means) in comparison to all the values within that data set?

2. Quiz
*
What Do Standard Errors Tell Us?
Standard errors are calculations that show the accuracy of the
population mean. Sometimes referred to as ‘Margin of Error’.
Are these two data sets statistically similar or different?
*
Interpreting Standard Errors on Graphs
Draw a horizontal line across the graph from each average’s
error bar.
If ranges overlap, then the differences in the averages are
considered insignificant; that is, there is no statistically
measurable difference between the two averages.
If error bar ranges do not overlap, then the averages are
considered significantly different, meaning there is sufficient
data to suggest the values differ more than would be expected
by chance alone.
So what are we actually saying about the data. How would you
communicate this to someone?

3. *
Graphs can be misleading!
*
Same Data with Errors Bars
*
Are these two data sets statistically similar or different?
*

4. *
Today’s ObjectivesCollect Data & Create a Data TableCreate
and Test a HypothesisCalculate & Plot Standard ErrorsAnalyze
& Interpret Data
Have fun with Madagascar Hissing Cockroaches!
*
Sexual Dimorphism (Males vs. Females)
Sexual dimorphism is an observable difference between males
and females of the same species.
*
Madagascar Hissing CockroachesThey live 2-3 years on average
(sometimes up to 5!)They reach a size of 1.5 to 3 inches
longThey are dark reddish brown to blackThey are hardy and
docile and can easily be handled.
Hissing cockroaches have a pair of modified spiracles (the tubes
insects use for breathing) that they use to produce the hissing

5. sound that inspired their name.
*
Testing a Hypothesis:
I believe that only male hissing cockroaches hiss.
Do not be afraid to handle the specimens, but they are living
creatures so handle them carefully.
Is this hypothesis Supported or Refuted?
Males have more pronounced ‘horns’
*
Create a Sexual Dimorphism Hypothesis:
Look at the last abdominal segment on the ventral side of both
male and female cockroach at your table and create a hypothesis
as to which has the longer abdominal segment.
Decide as a group whether males or females will have a longer
last abdominal segment on average – record your hypothesis on
the worksheet.
*

6. We are going to measure sexual dimorphism based on the length
of the last abdominal segment.
1. Measure (in millimeters) the length of the last abdominal
segment on the ventral side of both male & female.
2. Repeat on the cockroaches at each table.
3. Record the data on your the worksheet and calculate
statistics.
*
We are going to measure sexual dimorphism based on the length
of the last abdominal segment.
1. Interpret the graph you created to determine whether your
sexual dimporphism hypothesis was supported (holds true) or
refuted (does not hold true).
TURN IN: Your lab worksheet before leaving.
*
For Next Week
Red Cedar River investigations! We will go down to the river
and collect aquatic insects to make informed statements on the
water quality and pollution status of the river.
Homework/Prelab Assignment (posted in D2L)

7. *
VariabilityInformation about homogeneity or heterogeneity of a
sampleVariance (s2)
(5, 6, 8, 10, 12, 14, 15)
(8, 8, 9,10, 11, 12, 12)
(1, 2, 5, 10, 15, 18, 19)
(X1 – X)2 + (X2 – X)2 + … + (Xn – X)2
(n – 1)
S2 =
*
Standard Deviations = Square Root of Variance
s =
s2

8. *
Standard Error
s.e. =
s
n
*
Course
Summary/Reflection
Paper
ISB
208L
–
FA15
Paper
Description
and
Rubric

9. 1
Course
Summary/Reflection
Paper
–Due
Last
week
of
Regular
Class
(Project
Presentation
Day)
ASSIGNMENT
OBJECTIVES
AND
DESCRIPTION
(45
pts)
Everybody
studies,
learns
and
recalls
information
differently.
An

10. important
part
of
developing
these
skills
is
to
recognize
these
differences
and
reflect
on
your
own
individual
learning.
For
this
assignment,
you
will
reflect
on
your
own
individual
learning
in
the
form
of

11. a
reflection
paper.
A
reflection
paper
is
written
from
your
perspective
and
will
contain
your
thoughts
and
ideas
(you
will
not
be
using
the
internet
for
this
assignment).
There
are
five
topics
to

12. address
in
this
reflection
paper
(listed
below),
and
these
topics
are
based
on
the
course
goals
outlined
in
the
syllabus
and
highlighted
throughout
the
semester.
You
will
reflect
and
write
on
each
of

13. the
following
Reflection
Topics:
REFLECTION
TOPICS:
1)
Develop
and
practice
scientific
reasoning
and
analytical
thinking
in
order
to
make
more
informed
decisions.
Describe
a
lab,
lecture,
assignment,

14. or
aspect
of
this
course
that
you
feel
helped
accomplish
one
or
both
of
these
goals.
In
your
explanation,
state
the
specific
activity
and
provide
specific
examples
of
how
the
activity
helped
accomplish
the

15. goal(s).
If
you
do
not
feel
that
you
developed
or
practiced
scientific
reasoning
or
analytical
thinking
explain
why,
and
also
offer
a
suggestion(s)
that
would
have
helped
you
to
obtain
these
goals.

16. 2)
Communicate
effectively
to
diverse
audiences.
Describe
a
lab,
lecture,
assignment,
or
aspect
of
this
course
that
you
feel
helped
accomplish
this
goal.
In
your
explanation,
state
the
specific

17. activity
and
provide
specific
examples
of
how
the
activity
helped
accomplish
the
goal(s).
If
you
do
not
feel
that
you
developed
communication
skills
explain
why,
and
also
offer
a
suggestion(s)
that
would
have

18. helped
you
to
obtain
these
goals.
3)
Develop
teamwork
skills.
Describe
a
lab,
lecture,
assignment,
or
aspect
of
this
course
that
you
feel
helped
accomplish
this
goal.
In
your
explanation,
state

19. the
specific
activity
and
provide
specific
examples
of
how
the
activity
helped
accomplish
the
goal(s).
If
you
do
not
feel
that
you
developed
teamwork
skills
explain
why,
and
also
offer
a
suggestion(s)
that

20. would
have
helped
you
to
obtain
these
goals.
4)
Understand
the
role
of
science
as
an
important
part
of
your
daily
life.
Describe
a
lab,
lecture,
assignment,
or
aspect
of
this

21. course
that
you
feel
helped
accomplish
this
goal.
In
your
explanation,
state
the
specific
activity
and
provide
specific
examples
of
how
the
activity
helped
accomplish
the
goal(s).
If
you
do
not
feel
that

22. you
have
a
greater
appreciation
for
science
and
how
it
relates
to
your
daily
life
explain
why,
and
also
offer
a
suggestion(s)
that
would
have
helped
you
to
obtain
these
goals.

23. 5)
What
aspect
of
the
Water
Footprint
Calculator
Project
do
you
feel
you
learned
the
most
from,
and
why?
Or.
What
more
would
you
like
to
have
learned

24. during
this
project,
and
why?
Chose
one
of
these
two
topics.
FORMATTING
AND
GRADING:
Format:
The
paper
should
be
typed,
using
12pt
font,
and

25. single-­‐spaced.
There
is
no
minimum
required
number
of
pages
for
this
assignment;
however,
there
is
a
maximum
of
4
pages.
IMPORTANT:
Add
headers/titles
to
each
of
your
paragraphs
to
help
organize
your

26. thoughts.
For
example,
add
“Communicate
effectively
to
diverse
audiences”
at
the
beginning
of
that
particular
paragraph
or
section.
Grading:
The
total
assignment
is
worth
45pts.
The
grade
will

27. be
based
on
overall
spelling
and
grammar
(5pts
–3
to
5
spelling
or
grammatical
errors
2.5/5pts;
more
than
5
spelling
or
grammatical
errors
0/5pts),
and
substance
(8pts
each
topic;
40pts
total).
Substance

28. includes
your
understanding
of
the
material
(2pts),
how
your
thoughts
are
communicated
(2pts),
and
whether
your
thoughts
are
supported
by
specific
examples
(2pts)
to
specific
course
goals
(2pts).

29. Course
Summary/Reflection
Paper
ISB
208L
–
FA15
Paper
Description
and
Rubric
2
Submission:
All
papers
will
be
submitted
electronically
to
a
designated

30. Dropbox
in
D2L.
All
work
is
due
prior
to
the
beginning
of
your
last
regularly
scheduled
208L
class
period,
but
you
may
submit
your
work
earlier.
Your
instructor
may
also
require
a

31. hard-­‐copy
printed
and
brought
into
class
on
your
last
regularly
scheduled
208L
class
period.