Colorado State University — Pueblo, Fall 2016
Math 156, Introduction to Statistics, Section 1
[In Physical Space]
Course Schedule & Homework Assignments
Here is a link to the page of common
comments on graded assignments.
Here is a link back to the course syllabus/policy page.
This schedule is will be changing very frequently, please check it at
least every class day, and before starting work on any assignment (in case the
content of the assignment has changed).
Below, we refer to the text Introduction to Statistics, hosted by
Saylor Academy, as SIS. The book was
originally written by Douglas S. Shafer and Zhiyi Zhang, both of the University
of North Carolina, and is released under a
Creative Commons
Attribution-NonCommercial-ShareAlike 3.0 Unported
(CC BY-NC-SA 3.0 license.
Here
is an on-line version of this book, while here is a PDF of the full book
(and here is a local copy) and
here is a DOCx, either of which can be downloaded and saved, printed, or
searched.
If you see the symbol
below, it means that class was videoed and you can get a link by e-mailing me.
Note that if you know ahead of time that you will miss a class, you should
tell me and I will be sure to video that day for you.
When there is a reading assignment, please read the named section(s) before
that day.
Homework for a particular day is due that day, either in class or
handed in at my office by 3pm.
Your e-mail address. (Please give me one that you actually check
fairly frequently, since I may use it to contact you during the
term.)
Your year/program/major at CSUP.
What you intend to do after CSUP, in so far as you have an idea.
Past math classes you've had.
The reason you are taking this course.
Your favorite mathematical subject.
Your favorite mathematical
result/theorem/technique/example/problem.
Anything else you think I should know (disabilities, employment
or other things that take a lot of time, etc.).
[Optional:] The name of a good book you have read
recently.
Please do this some time Monday. But as some direct incentive: I will
only enter your name into my gradebook and give you your Homework
Late Passes when I get this e-mail, so you really need to
do this assignment as soon as possible. [By the way, just to be fair,
in case you are interested, here is a
version of such a self-introductory e-mail with information as I would
fill it out for myself.]
Some content we discussed, terms defined:
individuals, population, sample
variables, measurements
categorical [also called qualitative] and
quantitative
some big picture discussion of what the whole subject of
statistics is about
Hand in BI1. This will be an unusual one: write down two or
three things you were surprised about in the organization of this
course. Be specific, mention types or numbers or formats of some
assignments, etc.
Discussion of ASEs (see more below, next Monday). First is due soon!
Some content we discussed, terms defined:
the notation $\sum x$, or $\sum_{i=1}^n x_i$
measure of central location [of some quantitative data]:
[sample] mode
sample mean $\overline{x}$ and population mean
$\mu$
Quiz 1 today
Hand in HW1: SIS §1.1: 16, SIS §1.3: 4, SIS §2.1: 4, 8, 14 [in 14, add: What kind of graphical representation(s) of this data can you make? Sketch it (them)!]
Hand in BI2 (on an idea from Wednesday's class or readings)
Here is an example of the kind of thing we
are looking for. (The "critique" in this example is very friendly and
positive — which is actually unsurprising, since the source is a
famously careful and impartial research organization — while
yours may not be as positive (e.g., sometimes it is fun to find
a published statistic which is full of errors!).
Some content we discussed, terms defined:
examples of means, e.g., computing from data frequency
tables
means are very sensitive to outliers [not a phrase used in
the book, but very important nonetheless]
[sample] median $\widetilde{x}$
shape of a histogram: symmetric, and
skewed right or left
the sample variance $s^2$ and
sample standard deviation $s$, unfortunately still very
sensitive to outliers
the population variance $\sigma^2$ and
population standard deviation $\sigma$, unfortunately still
very sensitive to outliers
how to compute variances and standard deviations with electronic
tools
discussion of importance of variability in data; what it means
for the variance (standard deviation) to be 0.
Many web pages describe how to use your favorite calculator to do
statistical computations. If you have a TI-84, for example,
this
is a good reference for variance, standard deviation, and IQR. If you
have another calculator, just use your favorite search engine to look
for "compute standard deviation on a calculator name." You can
also find many smartphone apps, some probably free, on your favorite
app store. And finally, if you search for "online standard deviation
calculator," you will find many web pages which will do these kinds of
computations for you on whatever Internet-connected device you have.
Hand in BI4 on something from Monday's class or something new
from the reading SIS §2.2
the interquartile range [IQR] — which is a measure of
the variability of a dataset which is
insensitive to outliers!
This page (which we have seen before) explains how to compute IQRs on a
TI-84, if that's your calculator. If you have a different
calculator, just use your favorite search engine to look for
"compute IQR on a calculator name" or "compute quartiles on a
calculator name." You can also find many smartphone apps,
some probably free, on your favorite app store. And finally, if you
search for "online IQR calculator" or "online quartile calculator"
you will find many web pages which will do these kinds of
computations for you on whatever Internet-connected device you have.
a specifically data-driven organization, such as one of the
following [descriptions below, when in quotation marks and
italics are taken from the respective site's
self-description]
FiveThirtyEight
[FiveThirtyEight is an on-line journalism site which applies
careful research and thoughtful statistical modeling to
current stories in politics, economics, science, "life", and
sports. It was founded by Nate Silver, who has done
statistical analysis for sports betting and also predicted
state-by-state the outcomes in the last several presidential
elections with incredible accuracy.]
The Pew Research
Center ["Pew Research Center is a nonpartisan fact
tank that informs the public about the issues, attitudes and
trends shaping America and the world. It conducts public
opinion polling, demographic research, media content analysis
and other empirical social science research. Pew Research
does not take policy positions."]
The Gapminder
Foundation ["Gapminder is a non-profit venture –
a modern 'museum' on the Internet – promoting
sustainable global development and achievement of the United
Nations Millennium Development Goals."]
the Gallup polling
organization ["Gallup delivers forward-thinking
research, analytics, and advice to help leaders solve their
most pressing problems. Combining more than 75 years of
experience with its global reach, Gallup knows more about the
attitudes and behaviors of the world's constituents,
employees, and customers than any other organization."]
Hand in BI6 (on an idea from Friday's class or readings)
Today [Monday] is the last day to drop classes without a grade
being recorded.
Hand in BI8 (on an idea from Wednesday's class or readings)
Hand in HW3: SIS §2.4: 12, 14, 26, 32, and a supplemental problem which we will call 2.4.S1 which is Are there any outliers in the data for problem 32?, and SIS §2.5: 8, 24
Quiz 3 today [on quartiles, the five-number summary, boxplots,
the IQR, z-scores, the 1.5IQR rule for outliers, and the empirical
rule — also known as the 68-95-99.7 rule]
complement of a subset [event], notation $E^c$,
translation into English: not
Venn diagrams
probability rule for complements
intersection of sets [events], notation $A\cap B$,
translation into English: and
union of sets [events], notation $A\cup B$,
translation into English: or
Hand in BI9 (on an idea from Friday's class or readings)
Hand in ASE3. See above, here and
here, for the required parts of an
ASE (the second of those explanations above also has a list of
a few sites you could go to in order to find materials for an
ASE, although of course something you are interested in yourself
would probably be much more fun). Please look for something which
mentions variability, standard deviation, and/or
outliers.
mutually exclusive events, notation $\emptyset$ for the
empty set
the book's Probability Rule for Mutually Exclusive
Events is somewhat inaccurate: while it is true that
if events $A$ and $B$ are mutually exclusive, then $P(A\cap
B)=0$, it is not true that if $P(A\cap B)=0$ then $A$ and
$B$ are necessarily mutually exclusive.
additive rule of probability
the conditional probability $P(A\mid B)$ of event $A$
given event $B$
Hand in BI10 (on an idea from Monday's class or readings)
Hand in BI12 (on an idea from Friday's class or readings)
Hand in ASE4. Please try to find something which mentions
probability, maybe even conditional probability, and/or
independence [for events], if possible.
Test I in class today. Make sure you are comfortable with
the material outlined on this review sheet.
Don't forget your calculator, or other favorite electronic
device!
There was a delay with grading midterm I -- sorry! As a consequence,
it's best to start new material today and come back to the midterm on
Wednesday. So:
Skim the following background, examples of ethically questionable
experiments:
Nazi doctors experimented on human subjects during the Holocaust.
It is very hard to read about this horror. But — despite the
denials of some deranged quacks even today — it really did
happen, and We Must Never Forget, as is said. If you want
to look into this, search a bit on the Internet, or read a few
articles in Wikipedia on the subject.
Some content we discussed, terms defined: Ethical experimental
design is now a major subject of study. Major organizations have made
statements of principles in this area, for which you might look
at this Wikipedia page or other articles to which it refers. In this
large, nuanced field, we will take as basic at least the following
four required components of ethical experimentation on human
subjects:
Informed Consent: Note that true informed consent is more
difficult than it might seem at first. In particular, economic or
other constraints on potential experimental subjects might make it
very hard for them to refuse. Also, being truly informed does mean
that subjects are aware of all possible consequences and outcomes,
good and bad, of the experimentation.
"Do No Harm": This, also, can be tricky. Some
inconvenience to a subject might be considered small harm contrasted
with a potentially large benefit from running the experiment through
to its conclusion. But the principle insists that we confront this
issue and always err, to the extent we can, on conservative views of
what might harm the experimental subjects. This principle is
related, therefore, to the Hippocratic Oath taken by physicians, which contains the
requirement First do no harm.
Note also that paying attention to this issue sometimes requires
that an experiment be interrupted early, if preliminary data show
that one treatment or another in the experiment is doing harm to
some of the subjects.
Anonymity/Confidentiality: This again is based on respect for
the autonomy of experimental subjects, that they should be able to
control the release of information about themselves. The default,
therefore, is that subjects' identities must be kept confidential
when the experimental results are announced. The easiest way to do
this, although often not the way it is actually done, is for the
subjects actually to remain anonymous during the entire experiment.
Institutional Review Board [IRB] (or FDA)
oversight: The IRB is an external board which checks that the
principles of ethical experimental design are being followed in
each case. The IRB must be approached, in advance, regarding
any experimentation that has human subjects, for approval when the
organization (university, company, research lab, etc.) gets
any US Federal support. Failure to do so can result in all future
such funding being cut to that organization. See this Wikipedia article.
In the US, the Food and Drug Administration (FDA) has oversight of
medical products and drugs, some of which includes detailed control
of the clinical experiments done to validate them.
:
Test I post-mortem.
Hand in BI17 on basics of experimental ethics.
:
Skim The Belmont Report (or even this Wikipedia summary), a famous and important report
giving Ethical Principles and Guidelines for the Protection of Human
Subjects of Research, as its subtitle says.
Hand in BI18. This is a special one: please write a paragraph
about how you think Test I went for you. Are you perfectly content
with how it turned out? If not, what do you think was the cause of the
trouble? And what can you do next time to make things better?
Yes, we do have class today, even though it is the federal
holiday celebrating the arrival of Christopher Columbus in the New
World. (Not so clear why we celebrate him: his idea of how big the
world is was wildly off the mark (unlike the quite accurate estimate
produced by Eratosthenes in the 3rd century BCE); he never
actually made it to the North American continent; he brought back from
his very first trip some of the indigenous people he met as slaves;
etc., etc.)
Read this page which discusses some
basics of experimental design.
Some content we discussed, terms defined:
observational studiesvsexperiments
bias
control groups
randomization [to prevent bias]
The Placebo Effect
blinding and particularly double-blind experiments
RCTs
Hand in BI19 (on an idea from Friday's class or readings)
Hand in ASE6, which is a special one: read
this articleand any other sources you find on the same subject which are
useful (such as the research report in the Proceedings of the
National Academy of Sciences to which there is a link in that first
article), and then do as detailed an ASE as you can on this
topic, containing all the usual parts. Also include a section in
this ASE discussing the ethics of this study. Use
the ethical criteria we discussed in class and which are in the readings
from last week. As a consequence, this ASE will probably be a
fair bit longer than usual.
Quiz 7 today [on experimental design, basics of the sampling
distribution of the mean, and SRSs]
Hand in BI21 (on an idea from Wednesday's class or readings)
Hand in HW7:
Suppose I am curious if people learn as well when they read
books on a screen (such as a phone, computer, or e-reader) as
they do when they read the same book on paper. Describe in a
sentence or two (or three...) an observational study I
might do on this topic, and then, separately,
an experiment.
For the observational study, think of a lurking variable which
might be confounded with the variable of the study you proposed.
People who eat lots of fresh fruits and veg have lower rates of
colon cancer than people who don't eat those things. One ideas is
that certain vitamins in these foods have a preventative effect
for cancer. To test this, a researcher got 1000 people who were
at risk of colon cancer and divided them into a group which got a
vitamin supplement every day and another group which got a placebo.
The experiment was performed double-blind.
After four years of this study, it was found that there was
almost no difference in colon cancer rates.
Was that an observational study or an experiment?
Explain very concretely how the experiment was (should have
been) done: groups chosen, pills given, results processed,
etc.
The experimental result in the previous problem was surprising
because it is really a fact that people who eat the fruit and veg
which have those vitamins do have lower rates of colon cancer.
Suggest some lurking variables which might explain this observation.
Since the experiment found no difference in colon cancer rates,
one of the lurking variables you suggest might be the real cause
of the beneficial effect of eating fruits and veg, rather than
just the vitamins, as our disappointed experimenter above was
hoping.
the idea of a confidence interval, particularly the meaning
of its confidence level [very important!]
the large-sample confidence for the population mean
the margin of error of a confidence interval
the critical values used in the formulæ for
confidence intervals
Hand in BI22 (on an idea from Friday's class or readings)
Hand in ASE7. See if you can find a source which describes
its experimental design, mentioning a few of the terms we have used
in our discussions of this topic. Then do a usual ASE which talks
about individuals, populations, variables, methods, etc., and
then also includes a critique of the stated experimental design.
the sample size needed for a particular margin of error in
a CI for a population mean
the sample size needed for a particular margin of error in
a CI for a population proportion
the most conservative estimate (of that sample size
for proportions)
Hand in BI25 (on an idea from Friday's class or readings)
Hand in ASE8. Try to find one about a confidence interval for
a population mean or average (same thing). It can help to look for
the phrase "margin of error." Be careful not to get a source
which is about a confidence interval for a percentage (like election
data often is, for example), since that is not a CI for a mean (means
are not percentages).
:
Read SIS §8.1 but skip
the sections called The Rejection Region and Standardizing
the Test Statistic; in the section Two Types of Errors,
only read the definition of the two types, skip the "level of
significance of the test"
Some content we discussed, terms defined:
the null hypothesis $H_0$ and alternative $H_a$ of
a test of hypotheses ... also called a test of
significance and hypothesis test
our null hypotheses $H_0$ are (always!) of the form
$H_0$: parameter = value
our alternative hypotheses $H_a$ can have the form
$H_a$: parameter ≠ value, called a
two-tailed test; or
either
$H_a$: parameter < value or
$H_a$: parameter > value
both called one-tailed tests
conclusions we make: "reject $H_0$" or
"fail to reject $H_0$"
what could go wrong? there are two types of errors we could
make:
a Type I error, when we reject the $H_0$ even though it
is true, and
a Type II error, when we fail to reject the $H_0$ even
though it is false
Hand in BI26 (on an idea from Monday's class or readings)
:
Read SIS §8.2 looking
mostly for the definition of the test statistic and the examples; read
this page for details of how we will do
the tests in this class.
Some content we discussed, terms defined:
test statistic or $z$-statistic
$p$-value of a test [this is very important, and
you will be expected to understand and to be able to explain
this concept]
significance level
Hand in BI27 (on an idea from Wednesday's class or readings)
Quiz 9 today [on confidence intervals for the population
proportion, finding the sample size needed for a given margin of error,
and/or some basic ideas/terms from hypothesis testing]
Hand in HW9: SIS §7.3: 6, 20 [hint: "point estimate" here is another way of saying "sample
proportion"]; SIS §7.4: 2, 4, 16;
SIS §8.1: 2.
Read, if you like, SIS §8.3
— that is the book's description of the material we've already
seen on this page. New material to read
for today is SIS §8.4, or
this page for our version of this.
Some content we discussed, terms defined:
Always start a hypothesis test by stating the population, RV,
parameter of interest, and null and alternative hypotheses
$H_0$ and $H_a$
formulæ for the test statistic in a hypothesis for a
population mean $\mu$ in the case of
known population standard deviation $\sigma$: the
test statistic is a $z$-statistic, with formula
$z=\frac{\overline{X}-\mu_0}{\sigma/\sqrt{n}}$; you
compute the $p$-value with the standard Normal table (based
upon what kind of alternative hypothesis you have); this whole
test is then called a "$Z$-Test".
unknown population standard deviation: the
test statistic is a $t$-statistic, with formula
$t=\frac{\overline{X}-\mu_0}{s/\sqrt{n}}$, where $s$ is the
sample standard deviation; you compute the $p$-value with the
appropriate part of a table of Student's $t$-Distribution
depending upon the degrees of freedom $df=n-1$ and in the
direction determined by the kind of alternative hypothesis
you have); this whole test is then called a "$T$-Test".
Hand in BI28 (on an idea from Friday's class or readings)
Hand in ASE9. Try to find one about a confidence interval for
a population proportion -- there should be tons of these in coverage of
the presidential election. It can help to look (again) for the phrase
"margin of error." Be careful not to get a source which is
about a confidence interval for a population mean; proportions will
often be expressed as percentages, remember.
Hand in BI30 (on an idea from Wednesday's class or readings)
Quiz 10 today [on confidence intervals for the population mean
with known and/or unknown population standard deviation and/or for the
population proportion; particular attention on the logic and structure
of hypothesis test and the meanings of $p$-values]
Hand in HW10: In these problems, always use the
$p$-value approach of the descriptions in the web pages for our
class: one,
two,
three, and
four. Problems to do are
SIS §8.2: 8, 14;
SIS §8.4: 12, 18; and
SIS §8.5: 12, 14.
shape, strength, and direction of a
relationship visible in a scatterplot
[linear] correlation coefficient, some properties
Hand in BI31. This is another special one: think about the
previous special BI18. Did the same thing happen? Did you
manage to make the change you contemplated? Did it have the desired
effect? What do you think you could do next time?
Hand in BI32 (on an idea from Friday's class or readings)
Hand in ASE10: this is a "free-range" ASE: pick a topic that
interests you, a nice article or webpage or whatever, which has a clear
bit of statistical content, and write up an ASE as we've been doing
all semester. [So be sure to clearly talk about the population,
variable[s], parameter[s], sample, methods, etc.] If you want
to do one which has a scatterplot and/or mentions correlation, that
would be great [but is not required, since we've just started talking
about this material].
Really, read this page, it has lots of useful
information about the content of this unit of the course.
Some content we discussed, terms defined:
continuing with topics started on Wednesday, and on
this page.
Hand in BI34 (on an idea from Wednesday's class or readings)
No quiz today because this material [on scatterplots, the
correlation coefficient, and least squares regression lines] will be
tested in the [fairly short] midterm following our Thanksgiving Break.
Here is a video with some
specific suggestions about reviewing for this Test III; it is not all
that much more than is in the review sheet
and the other page on this material written
specifically for this class, but if you like to hear the suggestions
spoken out loud, by all means watch
the video.
:
Test III in class today. Make sure you are comfortable with
the material outlined on this review sheet.
Don't forget your calculator, or other favorite electronic
device!
Today is the last day to hand in any late work for credit, even
with Homework Late Passes.
Please also hand in any unused Homework Late Passes you have left,
for course extra credit.
:
Test III post-mortem will be sent by email! If you do not get an
email with links to videos explaining how to do the Test III problems,
inquire further (by email) about it. But there will be
no in-person class.
Make sure you drop by GCB314 at some point to pick up any graded work
for which you may be waiting.
Hand in BI35, a special one: what do you intend to do for the
next few days to enable you to do the best you possibly can on the
final exam for this class? Be specific!
below, it means that class was videoed and you can get a link by e-mailing me.
Note that if you know ahead of time that you will miss a class, you should
tell me and I will be sure to video that day for you.