Lesson 1.1.1 The Statistical Analysis Process 1/Students/PDF/lesson_1... · “Is astrology real, or is it just random? ... their zodiac sign was 0.40. ... The Statistical Analysis
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INTRODUCTION What is statistics? Why do we study statistics? Statistics is about using data (or numeric observations about the world) to answer questions. Before
scientists created statistics and before people used data, they would make arguments about how the world
worked based on opinions and hunches. A lot of times these arguments were wrong. For example,
hundreds of years ago, people argued the earth was the center of the universe. Looking at data allowed us
to start making better conclusions. Through science, we saw that the earth goes around the sun, not the
other way around. But science and mathematics weren’t enough, because sometimes data were really
messy. Things often don’t happen the same way every time. And sometimes what looks like a trend is
actually due to random chance. So to understand the data in the world, scientists developed statistics. Using
statistics they could know whether something that seemed to happen some of the time was actually true, or
if it was just random.
There are lots of things you might want to know about the world--things that statistics can help you answer.
It could help you in your job. As a faculty member i may want to know whether a new teaching method
works better for my students. Or if you worked for a medicine company, you may want to know whether a
new medicine can help people who have cancer. Statistics can also help you understand society so we can
have a better democracy. Politicians and news organizations conduct surveys and polls in order to find out
what voters are concerned about and who might win an election. Statistics can help you know whether the
results of surveys and polls tell you something new, or whether the news story is overblown.
In addition, when you buy things statistics can help. You probably hear news stories about how oatmeal or
red wine are good for your health and hydrogenated oils are bad for you. You might wonder: how do
researchers know this? And how certain are they? Certainly not every person who drinks red wine lives to
old age, and not every person who eats those oils dies immediately. With all the complexity in the real
world, how do we know whether the relationship between some food and your health is real or imaginary?
Statistics can help you do just that.
In general, in statistics, we formulate a question that we want answered--like about the impact of a
medicine or the health effects of a food. Then we don’t just argue about it in theory. We gather data from
the real world and then we summarize the data so we can see if the result we’re expecting is there, or if it
isn’t. In addition, statistics gives us the tools to know how confident we are that our answer is correct.
Today we are going to think about this with a question that lots of people wonder but that we hardly ever
use real data to answer. “Is astrology real, or is it just random?” Signs of the Zodiac and Personality Traits The table below lists the four steps in this process.
Steps in a Statistical Investigation
1. Ask a question that can be answered by collecting data.
2. Decide what to measure and then collect data.
3. Summarize and analyze the data.
4. Draw a conclusion and communicate the results.
Can a person’s birthday determine his or her personality traits, like being kind or being jealous? In this task,
you will try to figure out whether personality characteristics are determined by a person’s birthday. Your
instructor just gave you a list of personality traits. These traits are in birthday groups. Each birthday group
has 3 sets of personality traits. Only 1 set actually goes with that birthday group according to the zodiac
calendar. The other 2 sets are not associated with the zodiac or astrological sign for those birthdays.
Look for your birthday on the handout. Read the 3 sets of personality traits for your birthday group. Pick
the set of personality traits that you think matches your own personality. Of course, none of the sets will
match your personality perfectly, so just pick the set that describes your personality the best.
10 You can repeat the process of getting “by chance” outcomes a large number of times. This will
help you understand what kinds of match proportions are consistent with picking cards at
random.
First, write the class proportion from Task 2 in the following table under Trial 1. Second, work
with your classmates to repeat the process of picking cards until you have proportions for 10
trials.
When you are done, fill in the table below with the proportions of the students who picked “match.” (Note: “Observed Proportion” means the proportion we see from the data we collected in each trial.)
Trial Observed Proportion
1
2
3
4
5
6
7
8
9
10
11 Your professor constructed a dotplot which shows the observed “Match” proportions for the 10
trials where the students picked one of three choices at random.
A What was the smallest match proportion observed? B What was the largest match proportion observed?
+++++ This lesson is part of STATWAY™, A Pathway Through College Statistics, which is a product of a Carnegie Networked Improvement Community that seeks to advance student success. Version 1.0, A Pathway Through Statistics, Statway™ was created by the Charles A. Dana Center at the University of Texas at Austin under sponsorship of the Carnegie Foundation for the Advancement of Teaching. This version 1.5 and all subsequent versions, result from the continuous improvement efforts of the Carnegie Networked Improvement Community. The network brings together community college faculty and staff, designers, researchers and developers. It is an open-resource research and development community that seeks to harvest the wisdom of its diverse participants in systematic and disciplined inquiries to improve developmental mathematics instruction. For more information on the Statway Networked Improvement Community, please visit carnegiefoundation.org. For the most recent version of instructional materials, visit Statway.org/kernel.
+++++ STATWAY™ and the Carnegie Foundation logo are trademarks of the Carnegie Foundation for the Advancement of Teaching. A Pathway Through College Statistics may be used as provided in the CC BY license, but neither the Statway trademark nor the Carnegie Foundation logo may be used without the prior written consent of the Carnegie Foundation.