Dealing with Data

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Dealing with Data

1. Coding
2. Descriptive Statistics
3. Measures of Central Tendency
4. Measures of Variability

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Dealing with data

• Analysis of quantitative data is a complex field
  of knowledge
• Analysis starts from coding and cleaning data
• Coding- reorganizing raw data into a format that
  is machine readable (easy to analyze using
  computers)

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Coding

• Can be simple clerical task when the data are
  recorded as numbers on well-organized recording
  sheets
• Can be difficult when a researcher wants to code
  answers to open-ended survey questions

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Open-ended questions

• Open-ended questions are questions that encourage
  people to talk about whatever is important to
  them. They are the opposite of closed-ended
  questions that typically require a simple brief
  response such yes or no.
• Open-ended questions invite others to tell their
  story in their own words.

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Closed-ended vs. Open-ended

• Did you have a good relationship with your
  parents? (yes/no)
• Tell me about your relationship with your parents.

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Codebook

• Set of rules stating that the certain numbers are
  assigned to variable attributes
• Codebook is a document describing the coding and
  the location of data variables in a format that
  computers can use
• For example, a researchers codes males as 1 and
  females as 2

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Computer file
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The first thing to do

• Descriptive analysis
• Possible Outliers/Entry Errors/Missing cases

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Outliers

• A scatterplot can show any outliers in the data
  set

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Outliers

• "Rare" event syndrome. Another reason for
  outliers is the "rare" event syndrome--extreme
  observations that for some legitimate reason do
  not fit within the typical range of other data
  values. Such unusual observations might include
• a 70 degree day in January in Oregon
• a 500 point rise/drop in a stock market index
• an unusually high score on an aggressiveness
  scale for a troubled child
• All these events may be quite unusual, but
  they're still part of the overall picture

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What Should You Do About Them?

• Effectively working with outliers in numerical
  data can be a rather difficult and frustrating
  experience
• Neither ignoring nor deleting them at will are
  good solutions
• If you do nothing, you will end up with a model
  that describes essentially none of the
  data--neither the bulk of the data nor the
  outliers

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What Should You Do About Them?

• Transformation
• Deletion
• Accommodation

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Transformation

• Transforming data is one way to soften the impact
  of outliers since the most commonly used
  expressions, square roots and logarithms, shrink
  larger values to a much greater extent than they
  shrink smaller values
• However, transformations may not fit into the
  theory of the model or they may affect its
  interpretation. Taking the log of a variable does
  more than make a distribution less skewed it
  changes the relationship between the original
  variable and the other variables in your model.
  In addition, most commonly used transformations
  require non-negative data or data that is greater
  than zero, so they are not always the answer

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Deletion

• Only as a last resort should you delete outliers,
  and then only if you find they are legitimate
  errors that can't be corrected, or lie so far
  outside the range of the remainder of the data
  that they distort statistical inferences. When in
  doubt, you can report model results both with and
  without outliers to see how much they change

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Accommodation

• One very effective plan is to use methods that
  are robust in the presence of outliers
• Nonparametric statistical methods fit into this
  category and should be more widely applied to
  continuous or interval data

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Descriptive Statistics

• Describe numerical data
• Can be categorized by the number of the variables
  involved
• Univariate
• Bivariate
• Multivariate

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Univariate statistics (males and females)

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Males only
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Females only
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Using graphs

• A graph is a visual representation of a
  relationship between, but not restricted to, two
  variables
• A graph generally takes the form of a
  two-dimensional figure
• Although, there are three-dimensional graphs
  available, they are usually considered too
  complex to understand

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What is a graph?

• A graph commonly consists of two axes called the
  x-axis (horizontal) and y-axis (vertical)
• Each axis corresponds to one variable.
• The axes are labeled with different names
• The place where the two axes intersect is called
  the origin. The origin is also identified as the
  point (0,0).

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Parts of a graph
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A good graph

• accurately shows the facts
• grabs the reader's attention
• has a title and labels
• is simple and uncluttered
• clearly shows any trends or differences in the
  data
• is visually accurate (i.e., if one chart value is
  15 and another 30, then 30 should appear to be
  twice the size of 15).

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Why use graphs when presenting data?

• Graphs
• are quick and direct
• highlight the most important facts
• facilitate understanding of the data
• can convince readers
• can be easily remembered

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When is it not appropriate to use a graph?

• The data are very dispersed Division of votes
  for the major political parties, in a federal
  election, Anytowne

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When is it not appropriate to use a graph?

• there are too few data (one, two or three data
  points) Figure 12. Number of students enrolled
  in Greenfield Secondary School

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When is it not appropriate to use a graph?

• the data are very numerous Figure 13. Number of
  students taking English as a second language at
  West High School,

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When is it not appropriate to use a graph?

• The data show little or no variations Figure
  14. Number of young adults who exercise at least
  once weekly, by age, 1996 to 2002

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Types of graphs

• Histograms
• Bar charts
• Pie charts
• Dot charts
• Line graphs
• Scatterplots

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Histogram

• A histogram is the graphical version of a table
  which shows what proportion of cases fall into
  each of several or many specified categories of
  one variable

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Histographs

• A histograph, or frequency polygon, is a graph
  formed by joining the midpoints of histogram
  column tops
• These graphs are used only when depicting data
  from the continuous variables shown on a
  histogram
• A histograph smoothes out the abrupt changes that
  may appear in a histogram, and is useful for
  demonstrating continuity of the variable being
  studied

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Distribution of salaries for the Acme Corporation
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Bar charts

• A bar chart is used to graphically summarize and
  display the differences between groups of data
  (or several variables)

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Disadvantage of vertical bar graph

• One disadvantage of vertical bar graphs, is that
  they lack space for text labeling at the foot of
  each bar
• When category labels in the graph are too long,
  you might find a horizontal bar graph better for
  displaying information

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Horizontal bar graphs

• The horizontal bar graph uses the y-axis
  (vertical line) for labeling
• There is more room to fit text labels for
  categorical variables on the y-axis.

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A double or group horizontal bar graph

• Similar to a double or group vertical bar graph,
  and it would be used when the labels are too long
  to fit on the x-axis

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Stacked bar graphs

• The stacked bar graph is a preliminary data
  analysis tool used to show segments of totals
• The stacked bar graph can be very difficult to
  analyze if too many items are in each stack
• It can contrast values, but not necessarily in
  the simplest manner

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Example

• Triathlon, percentage of time spent on each
  event, by competitor

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A split bar graph

• Is a better choice for displaying information
  than a double pie chart
• The key point in preparing this type of graph is
  to ensure that you are using the same scale for
  both sides of the bar graph

Earnings in Utopia, by sex
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Pie Charts

• A pie chart is a circle graph divided into
  pieces, each displaying the size of some related
  piece of information
• Pie charts are used to display the sizes of parts
  that make up some whole.

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Example

• The pie chart below shows the ingredients used to
  make a sausage and mushroom pizza. The fraction
  of each ingredient by weight is shown in the pie
  chart below
• Note that the sum of the decimal sizes of each
  slice is equal to 1 (the "whole" pizza")

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Area Chart
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Dot graphs

• The simplest ways to represent information
  pictorially

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Line graphs

• Line graphs are more popular than all other
  graphs combined because their visual
  characteristics reveal data trends clearly and
  these graphs are easy to create
• Line graphs, especially useful in the fields of
  statistics and science, are one of the most
  common tools used to present data

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Line graphs

• A line graph shows how two variables are related
  by drawing a continuous line between all the
  points on a grid

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Using correct scale

• When drawing a line, it is important that you use
  the correct scale. Otherwise, the line's shape
  can give readers the wrong impression about the
  data

Number of guilty crime offenders, Grishamville
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Scatterplots

• In science, the scatterplot is widely used to
  present measurements of two or more related
  variables
• It is particularly useful when the variables of
  the y-axis are thought to be dependent upon the
  values of the variable of the x-axis (usually an
  independent variable).

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Scatterplots

• Car ownership in Anytowne, by household income

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Scattered data points
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Data widely spread
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Measures of Central Tendency

• Measure of the center of the frequency
  distribution
• Mean
• Median
• Mode

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Mean

• The mean of a list of numbers is also called the
  average. It is found by adding all the numbers in
  the list and dividing by the number of numbers in
  the list.
• Example Find the mean of 3, 6, 11, and 8.
• We add all the numbers, and divide by the number
  of numbers in the list, which is 4.
• (3  6  11  8)  4  7
• So the mean of these four numbers is 7.

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Mean

• Mean is strongly affected by change in extreme
  values
• 3, 6, 11, 8, and 50
• Mean 15.6

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Median

• Is the middle point
• It is also the 50th percentile, or the point at
  which half the cases are above it and half below
  it
• The median of a list of numbers is found by
  ordering them from least to greatest
• If the list has an odd number of numbers, the
  middle number in this ordering is the median
• If there is an even number of numbers, the median
  is the sum of the two middle numbers, divided by 2

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Median

• Example
• The students in Bjorn's class have the following
  ages 29, 4, 3, 4, 11, 16, 14, 17, 3. Find the
  median of their ages. Placed in order, the ages
  are 3, 3, 4, 4, 11, 14, 16, 17, 29
• Median11

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Median

• The students in Bjorn's class have the following
  ages 4, 29, 4, 3, 4, 11, 16, 14, 17, 3
• Find the median of their ages. Placed in order,
  the ages are 3, 3, 4, 4, 4, 11, 14, 16, 17, 29
• The number of ages is 10, so the middle numbers
  are 4 and 11, which are the 5th and 6th entries
  on the ordered list. The median is the average of
  these two numbers
• (4  11)/2  15/2  7.5

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Mode

• The mode in a list of numbers is the number that
  occurs most often, if there is one.
• Example The students in Bjorn's class have the
  following ages 5, 9, 1, 3, 4, 6, 6, 6, 7, 3
• Find the mode of their ages
• The most common number to appear on the list is
  6, which appears three times.
• The mode of their ages is 6.

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Measures of Variation

• Another characteristic of a distribution
• Spread, dispersion, or variability around the
  center
• Two distributions can have identical measure of
  central tendency but differ in their spread about
  the center

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Example

• Seven people are at the bus stop in front of a
  bar
• Their ages are 25 26 27 30 33 34 35
• Bothe median and mean are 30
• At a bus stop n front of an ice-cream store,
  seven people have identical median and mean, but
  their ages are 5 10 20 30 40 50 55
• The ages in the second group are spread more from
  the center, or distribution of ages has more
  variability

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Variability

• In city X, the median and mean family income is
  25,000 and it has zero variation (every family
  in this city has income exactly 25,000)
• City Y has the same median and mean family
  income, but 95 percent of its families have
  income of 12, 000 per year and 5 percent have
  incomes of 300,000 per year
• City X has perfect income equality, while there
  is great inequality in city Y.

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Measures of Variation

• Range
• Percentiles
• Standard Deviation

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Range

• It consists of the largest and smallest scores
• In our examples with people at the bus stop
• Range 1 35-2510
• Range2 55-540

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Percentiles

• Tells the score at a specific place within the
  distribution
• Median is the 50th percentile
• 25th and 75th percentiles are often used
• 25th percentile is the score at which 25 percent
  of the distribution have either that score or a
  lower one

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Standard Deviation (SD)

• It is based on the mean that gives an average
  distance between all scores and the mean
• People rarely compute SD by hand

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Results with two variables

• Bivariate relationship
• First step Seeing the relationship
• The Scattegram is graph with points plotted on a
  coordinate plane
• Correlation (association)

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Correlation

• A correlation is a single number that describes
  the degree of relationship between two variables

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Example
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Bivariate Tables

• Contingency table is formed by cross-tabulating
  two or more variables
• Constructing percentaged tables
• Usually computers do that
• We need to learn how to read them
• The row and column percentages let a researcher
  address different questions

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