Chapter 1 2: Stats Starts Here

1
Chapter 12 Stats Starts Here

• Statistics has a reputation as hard, and
• Statistics courses are not necessarily chosen as
  fun electives, but
• Statistics can be fun! Learning to think clearly
  with data will open your eyes to seeing the world
  more clearly

2
What Is (Are?) Statistics?

• Statistics (plural) are particular calculations
  made from data.
• As we will see in Chapter 2, Data are values with
  a context.
• Statistics (the discipline) is a way of
  reasoning, a collection of tools and methods..
• Statistics is about variation.
• All measurements are imperfect, since there is
  variation that we cannot see.
• Statistics helps us to better understand the
  real, imperfect world in which we live.

3
Think, Show, Tell

• There are three simple steps to doing Statistics
  right
• first. Know where youre headed
  and why.
• how you calculated your result.
  Graphical display are often useful here, too.
• what youve learned. You must
  explain your results so that someone else can
  understand your conclusions- even someone who
  hasnt taken this class.

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Mis-Use of Statistics is Common.
Understanding Statistics requires more than just
memorizing formulas and plugging numbers in it
involves THINKING

• What is the misunderstanding here?
• What is the likely underlying story?

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Not Your Typical Math Class

• Emphasis will be on understanding the problem,
  applying the right method, and helping others
  understand your analysis
• The good news not a lot of formulas to memorize,
  compared to your typical math class
• The bad news (for some) Statistics involves
  thinking, including deciphering word problems,
  figuring out what information is relevant, doing
  reality checks to see if your answer makes
  sense, and communicating your results effectively

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In Summary Chapter 1

• Statistics can be (and is) fun!
• Statistics gives us a way to work with the
  variability in the world around us and
  communicate conclusions to others.
• Statistics can be mis-interpreted

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Chapter 2- Data What Are Data?

• Data can be numbers, record names, or other
  labels.
• Not all data represented by numbers are numerical
  data (e.g., 1male, 2female).
• Data are useless without their context

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The Ws

• To provide context we need the Ws
• Who
• What (and in what units)
• When
• Where
• Why
• and HoW
• of the data.
• We dont always get all the Ws, but the answers
  to who , what and why are essential.

9
Data Tables

• The following data table (Amazon book purchases)
  clearly shows the context of the data presented
• Notice that this data table tells us the What
  (column) and Who (row) for these data.

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Who

• The Who of the data tells us the individual cases
  for which (or whom) we have collected data.
• Individuals who answer a survey are called
  respondents.
• People on whom we experiment are called subjects
  or participants.
• Animals, plants, and inanimate subjects are
  called experimental units.
• Sometimes people just refer to data values as
  observations and are not clear about the Who.
• But we need to know the Who of the data so we can
  learn what the data say!

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What and Why

• Variables are characteristics recorded about each
  individual.
• The variables should have a name that identify
  What has been measured.
• To understand variables, you must Think about
  what you want to know.

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What Qualitative vs. Quantitative

• A categorical (or qualitative) variable names
  categories and answers questions about how cases
  fall into those categories.
• Categorical examples gender, race, ethnicity
• A quantitative variable is a measured variable
  (with units) that answers questions about the
  quantity of what is being measured.
• Quantitative examples age (years), income (),
  height (inches), weight (pounds)

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What with Why (cont.)

• The questions we ask about a variable (the Why of
  our analysis) shape what we think about and how
  we treat the variable.

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What with Why Ordinal Variables

• Example In a student evaluation of instruction
  at a large university, one question asks students
  to evaluate the statement The instructor was
  generally interested in teaching on the
  following scale 1 Disagree Strongly 2
  Disagree 3 Neutral 4 Agree 5 Agree
  Strongly.
• Question Is interest in teaching categorical or
  quantitative
• We sense an order to these ratings, but there are
  no natural units for the variable interest in
  teaching. These are ordinal variables.
• With an ordinal variable, look at the Why of the
  study to decide whether to treat it as
  categorical or quantitative.

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Counts Count

• When we count the cases in each category of a
  categorical variable, the counts are not the
  data, but something we summarize about the data.
• The category labels (shipping methods) are the
  What
• The individual purchases counted are the Who.

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Counts Count (cont.)

• When we focus on the amount of something, we use
  counts differently. For example, Amazon might
  track the growth in the number of teenage
  customers each month to forecast CD sales (the
  Why).
• The What is teens,
  the Who is months,
  and the
  units are
  number of
  teenage customers.

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Identifying Identifiers

• Identifier variables are categorical variables
  with exactly one individual in each category.
• Examples Social Security Number, ISBN, FedEx
  Tracking Number, Student ID
• Dont be tempted to analyze identifier variables.
• Example Do students with high ids get better
  grades?

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Where, When, and How

• We need the Who, What, and Why to analyze data.
  But, the more we know, the more we understand.
• When and Where give us some nice information
  about the context and maybe the applicability of
  the data!
• Example Comparing tuition rates across
  universities with samples from 2006 mixed in with
  samples from 1986 is unfair.
• Comparing home energy usage to determine how
  green people are when some people live in
  Michigan and some people live in San Francisco
  may be unfair.
• How the data are collected can make the
  difference between insight and nonsense.
• Example results from Internet surveys are often
  useless
• The first step of any data analysis should be to
  examine the Wsthis is a key part of the Think
  step of any analysis.
• And, make sure that you know the Why, Who, and
  What before you proceed with your analysis.

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What Can Go Wrong?

• Dont label a variable as categorical or
  quantitative without thinking about the question
  you want it to answer.
• Just because a variables values may be numbers
  does not make it quantitative.
• Always be skepticaldont take data for granted.

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What have we learned?

• Data are information in a context.
• The Ws help with context.
• We must know the Who (cases), What (variables),
  and Why to be able to say anything useful about
  the data.
• We treat variables as categorical or
  quantitative.
• Categorical variables identify a category for
  each case.
• Quantitative variables record measurements or
  amounts of something and must have units.
• Some variables (Ordinal Variables) can be treated
  as categorical or quantitative depending on what
  we want to learn from them.

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Examples

• Determine as many Ws as possible (mention if
  they are explicitly given or if can be inferred),
  and specify whether variables are qualitative or
  quantitative, and if quantitative, what are the
  units of measure
• Book problem 21 In 2002 Consumer Reports
  published an article evaluating refrigerators,
  listing 41 models and giving brand, cost, size
  (cu ft.) estimated annual energy cost, overall
  rating and brand repair history ( of
  refrigerators requiring repairs over 5 years).

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Additional Example

• Determine as many Ws as possible (mention if
  explicitly given or if can be inferred), and
  specify whether variables are qualitative or
  quantitative, and if quantitative, what are the
  units of measure
• 3 Owing to several major ocean spills by
  tankers, Congress passed the 1990 Oil Pollution
  Act, which requires all tankers to be designed
  with thicker hulls. Further improvements in the
  structural design of a tank vessel have been
  proposed since then, each with the objective of
  reducing the likelihood of a spill. To aid in
  this development, a 1995 article in Marine
  Technology reported spillage amounts and causes
  of punctures for 50 recent tanker spills in
  oceans.

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Example Old Test Question

• Katherine was hired as a 2006 summer intern by
  Johnson Johnson at their research center in
  Rouen, France to study U.S. consumer spending
  habits on skincare products. Here is all the data
  she recorded from conducting phone interviews,
  via a machine that randomly dials numbers in the
  415 area code.
• Describe the data by identifying all the Ws
  that are given or can be inferred.
• Who (and how many cases?)
• What (list all variables, say if they are
  qualitative or quantitative, and provide the
  units when appropriate)
• When
• Where (be specific!)
• Why
• How