Displaying Categorical Data

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Displaying Categorical Data

• Chapter 3

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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.

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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.

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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.

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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.

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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.
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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.

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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.
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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.

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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

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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.

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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.

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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.

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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.

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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.

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Example Time!

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

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.