Analyzing Statistical Results

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Analyzing Statistical Results

• Lesson 3-8

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Statistics, Data Analysis, and Probability 2.3
2.5

• SDAP 2.3 Analyze data displays and explain why
  the way in which the question was asked might
  have influenced the results obtained.
• SDAP 2.5 Identify claims based on statistical
  data and, in simple cases, evaluate the validity
  of the claims.

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Key Vocabulary
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Justified

• to show something to be just (fair) or right
• An act
• A claim
• A statement

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As we learned, sampling techniques affect
results. The way we ask questions affect
results, too.
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Part IThe way we word questions can affect the
results we get.
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Do you think that all sixth graders should have a
minimum of three hours of homework a night?
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Should students practice the math skills they
learn and get feedback the next day on how well
they are doing?
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You were just asked the same question twice but
it was worded differently.
Do you think that all sixth graders should have a
minimum of three hours of homework a night?
Should students practice the math skills they
learn and get feedback the next day on how well
they are doing?
Why did the first question get a different
reaction than the second one?
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When we ask question for statistical purposes,
and we want representative results, we need to
take persuasive words out of the question.

• People tend to feel strongly toward questions
  when the following kinds of things are mentioned
  
• Having freedoms taken away
• Forcing them to do something
• Any kinds of adjectives (positive or negative)

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The best statistical questions make the person
you are asking stop and thinkand make them feel
like they will not be judged for either choice.
We call these questions neutral or fair.

• Do you support or oppose
• Are you for or against
• Eliminate adjectives
• Eliminate persuasive words that make a person
  feel pressured to answer the question the way you
  want them to

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Lets practice

• Which statistical question is worded in a way
  that will get genuine results?

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Are you in favor of restricting excessive
gasoline consumption?
Gut reaction Of course!
Most neutral
Do you favor or oppose gasoline rationing?
Do you want gasoline rationing to limit your
driving freedom?
Gut reaction NO!
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Do you favor the construction of a new California
freeway to cut down on traffic jams?
Gut reaction Of course!
Do you want your tax money spent on the
construction of another freeway?
Gut reaction NO!
Most neutral
Do you support or oppose the construction of
another freeway?
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Should residents of Rancho Cucamonga recycle
paper?
Most neutral
Should residents of Rancho Cucamonga be forced to
recycle paper every week?
Gut reaction NO! I dont want to be FORCED to do
anything!
Should residents of Rancho Cucamonga pay to
recycle paper?
Gut reaction Pay? NO! I dont have any extra
money
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Part IIIs this claim justified by the
statistics?
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Sometimes we are persuaded to believe or
disbelieve thingseven when the data is not
justified.

• You know the population is too big, but the
  sample is not defined.
• Graphs are made incorrectly to misrepresent data
• Questions are unfairly worded and therefore,
  answers provided were biased (always check to see
  who is providing or paying for the data)

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Population too big, but sample not defined
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Studies have shown that Zow quenches thirst in 4
out of 5 people who drink it.

• Based on this statistic, which claim is
  justified?
• Ann drank Zow so she isnt thirsty anymore
• She might be the 1 person whose thirst was not
  quenched.
• Zow is good for peoples health
• There is no information related to this question!
• 4 out of 5 people love the taste of Zow
• No! Just because you drink something, does NOT
  mean you love it! Maybe that is all that was
  availabel and you were desperate!
• Zow will likely quench Davids thirst
• Probably. It is wet. 4 out of 5 people who drank
  it said it quenched their thirst.

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We found that 88 of those who use Head Set
Shampoo have clean and silky hair. So, using Head
Set Shampoo will make your hair clean and silky.

• NOT JUSTIFIED
• What about the 12 who do not have clean and
  silky hair?
• Did people have clean and silky hair before using
  this shampoo?
• How was this data gathered?

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Is this claim justified? Why or why not? What
kind of a sample did they use?
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Data in graphs is often misread because the
person reading it does not understand how to read
it correctly
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Reading a table how was the data gathered?

• Notice that the percents do not add up to 100.
  Each person was asked each of these questions
  and how they answered one of the questions has
  NOTHING to do with their answer to another one.
• One person could fit into every one of these
  categoriesor none at all!

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Both graphs represent the number of new clients
signed up each month at Excelsior Realty. Which
graph is misleading? Why?

• The first graph is missing increments 0-30. It
  makes it seem that there are very few new clients
  at all.

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The graphs show the number of honor-roll students
in each grade at Ferndale Middle School. Which
graph is most accurate? What makes the other one
inaccurate?

• The first graph is most accurate. The bars go up
  in intervals of 10 from the beginning to the end.
• The second graphs vertical axis starts at 58,
  and then continues with intervals of one.

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The graphs show the number of students receiving
A's in each grade at Glenwood Middle School.
Which graph is most accurate? What makes the
other one inaccurate?

• The second graph does not show any dramatic
  differences, but it is most accurate.
• The first graph has a break between 0-60. The
  rest of the intervals are in increments of 1. If
  the entire graph were shown, then this would be a
  VERY tall graph!

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Questions were unfairly worded and therefore,
answers provided were biased

• Always check to see who is providing you with the
  data
• This is especially true during election time!
• Who made the commercials?
• Who paid for the commercials?
• What is their bias (which point of view do they
  come from)?
• Religious groups have definite points of view
• Pro-groups and Anti-groups have their own agenda
  (animal rights, energy supporters, professional
  unions, etc.)

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For more interesting websites on political
advertizing, visit the following

• The Living Room Candidate
• By Museum of the Moving Image
• FactCheck.org
• Funded by the Annenberg Foundation, a
  non-partisan group

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Helpful Links
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Some Helpful Links

• University of North Carolina Statistics
• Statistics often flawed in reports by media, MIT
  researcher warns