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Displaying Categorical Data

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... (for categorical data) are bar charts and pie charts. ... Contingency Tables. ... Know the difference between a qualitative and quantitative variable. – PowerPoint PPT presentation

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Title: Displaying Categorical Data


1
Displaying Categorical Data
  • Chapter 3

2
Data and Dirty Laundry
  • Laundry needs to be separated into loads for a
    machine to handle it.
  • Laundry should be sorted by color (and other
    factors potentially) for best results.
  • Data likewise needs to be organized into
    manageably small clusters or portions.
  • Data likewise needs to be sorted in some
    specific, useful way for best results.

3
Where to Start When Analyzing Data
  • Step 1 Draw a picture.
  • Humans are a visual species, and by seeing the
    data we are better able to think about it.
  • Step 2 Draw a picture.
  • With a properly selected picture, we are better
    able to demonstrate our reasoning and our
    process.
  • Step 3 Draw a picture.
  • Once a conclusion has been reached it is often
    best expressed as a picture.
  • Note On some problems step 1, 2, and 3 might
    each require their own pictures.

4
Frequency Vocabulary
  • Frequency The number of times a value occurred.
  • Relative Frequency The number of times a value
    occurred divided by the total number of cases
    collected.
  • Often expressed as a percent.
  • Frequency Table A table that displays
    frequencies.
  • Relative Frequency Table A table that displays
    relative frequencies.

5
Step 1 Draw a Picture
  • With categorical data, we want to start with a
    frequency chart.
  • Your book gave you some examples, but we will use
    some hypothetical favorite color data.

6
Step 1 Draw a Picture
Color Frequency
Black 2
Blue 20
Green 14
Pink 8
Purple 5
Red 5
Yellow 6
Color Frequency
Blue 20
Green 14
Pink 8
Yellow 6
Purple 5
Red 5
Black 2
Vs.
7
Frequency vs. Relative Frequency
  • With a small data set like 60, these raw counts
    are not a problem.
  • If you had a data set where 1472 people
    contributed a favorite color, you would generally
    be better off getting the relative frequency.

8
Frequency vs. Relative Frequency
Color Frequency
Blue 20
Green 14
Pink 8
Yellow 6
Purple 5
Red 5
Black 2
Color Frequency
Blue 33.3
Green 23.3
Pink 13.3
Yellow 10
Purple 8.3
Red 8.3
Black 3.3
Vs.
9
Step 2 Draw a Picture
  • If all you are doing is describing the data, then
    a frequency table or relative frequency table
    will cover steps 1 and 2.
  • The same picture that helps you think about what
    is going on also helps to show what is going on.
  • We will come back to what happens when you are
    doing more than just describing data.

10
Step 3 Draw a Picture
  • Even if you are describing the data with a
    frequency chart to show what is going on, you
    should use an additional picture to showcase your
    findings.
  • Two popular choices (for categorical data) are
    bar charts and pie charts.
  • Bar charts are best when the categories can be
    put in some sensible order, such as months.
  • They can basically always be used
  • Pie charts are best when the categories do not
    have a natural order, such as colors.
  • Pie charts can only be used when your data adds
    up to 100 of the data

11
Bar Charts and Pie Charts
  • Bar charts are super crazy easy on Excel once you
    get the hang of it.
  • Pie charts are also easy.
  • Creating a pie chart by hand is much trickier
    than a bar chart, so if you are having to work by
    hand you might do a bar chart instead of a pie
    chart.

12
Step 1 Draw a Picture
  • When we want to look at the relationship between
    two variables, we will use a contingency table
    instead of a frequency chart.
  • A contingency table is a table where the rows are
    categories for one variable and where the columns
    are categories for the other variable.

13
Contingency Table
  • Once we have determined the columns and the rows,
    we fill the table with the frequencies.
  • Each value represents the frequency of the
    category for that row happening at the same time
    as the category for that column.

14
Contingency Table
  • Next we will total each row and total each
    column.
  • Then we will total the whole table.
  • To do this we total the row totals and total the
    column totals to make sure they match.

15
Contingency Tables
  • Relative values get trickier.
  • In a frequency table, there is only one total.
  • In a contingency table there is a row total and a
    column total and a table total.

16
Example Time!
  • If you missed class today, this was the really
    sad part to miss.
  • You should get notes from someone who was here.

17
Assignments
  • Read Chapter 3 for tomorrow if you havent
    already.
  • The Chapter 1-3 Quiz will be Friday.
  • Chapter 3 5, 9, 19 (This is the first half,
    more will be added before a due date is set)
  • Chapter 2 homework is due tomorrow.
  • Problems 2-7, 25, 26
  • I will not be actively lecturing over the Area
    Principle. Instead, if you have questions about
    it, you should bring those tomorrow so that when
    I ask Are there any questions about the Area
    Principle? you have a good answer.
  • I will not answer the question, What even is the
    Area Principle?
  • Nor will I answer any of its ilk.

18
More Unsupporting Cast
  • On yesterdays episode we talked about Mr.
    Cheeseburger and then need for ridiculously
    levels of clarity.
  • Today we will focus on the Casual Observer, the
    Hasty Generalizer and the Exemplar, which might
    seem like the same at first, but are actually
    three very differently flawed archetypes.
  • They do, however, have in common that they come
    to their conclusions far too easily.

19
The Casual Observer
  • This phrase normally refers to a person who is
    looking at the situation, but does not have any
    particularly strong background in what is going
    on and who does not look any deeper than what is
    on the surface.
  • We are using it to refer to someone who does
    exactly that with exactly the same restrictions.
  • Casual Observers are easily swayed by misleading
    pictures and misinformation because they are only
    looking at what is immediately available.

20
The Casual Observer
  • The reason it is important to be aware of these
    observers is that the reason we must be concise
    is because if we take yawn-worthy lengths of time
    to get to our true point, some people will have
    totally tapped out by then.
  • We need to get to our points in a timely manner
    so that a casual observer gets the information
    before they would otherwise give up.

21
The Hasty Generalizer
  • A hasty generalization is when a person assumes
    that something which is/seems true in some
    situation is also actually true in many, if not
    all, similar situations.
  • The person I refer to here is a little different
    than that, though.
  • In this context I am referring to a person who
    just wants you to get to the conveniently
    digested point, not really caring how you got
    there, so they can get on with their day.

22
The Hasty Generalizer
  • Such a person will typically latch on the first
    solid point you make and assume that the rest of
    what you said is meaningless, unless a better
    point comes along.
  • At which point they tend to abandon the original
    point in favor of the new one.
  • It is important to be complete while being
    concise in order to get around this. Your entire
    point needs to be visible in a relatively concise
    and clear manner for someone trying to breeze
    through it to get the full effect.

23
The Exemplar
  • Normally an exemplar would be someone who has
    done things in a way that sets a superior example
    for others to follow.
  • In this case, though, I am referring to a person
    who fixates on a specific example of something
    happening, and assumes that it is way more
    important than it is.
  • Interestingly enough, that is actually closer to
    a hasty generalization, most of the time, than it
    is to anything else.

24
The Exemplar
  • For example, this person assumes that 9 out of
    10 dentists approving of a particular dental
    product means that 1 of them did notand that it
    should be closely investigated as to exactly why.
  • This kind of person also assumes that there is
    genuine scientific controversy as to the
    existence of global warming because there are
    scientists which are unconvinced.
  • This kind of person might get pulled over once
    for running a stop sign and then immediately
    decides that cops will always pull you over for
    running stop signs.

25
The Exemplar
  • This sort of person tends to believe that one
    rather unlikely example should hold just as much
    weight as the ongoing, consistent outcomewhich
    is the opposite of that example.
  • It is very important that we address any and all
    unusual results in our efforts to avoid someone
    taking them and running with them,
    metaphorically, which means taking time to
    explore possible reasons that strange results
    occurred.

26
Quiz Bulletpoints
  • Know what T-S-T stands for and what each one
    means.
  • Know how to identify the 5 Ws and How in a
    study.
  • Know the difference between a qualitative and
    quantitative variable.
  • Know how to find percentages from a contingency
    table.
  • Know the area principle.
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