Outline

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Outline

• 1. Tables as representations of data
• 2. Graphs
• Definition
• Components
• 3. Types of graph
• Bar
• Line
• Frequency distribution
• Scattergram

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Tables present data

• summarize data (no need to look at each
  individual data point).
• show numerical relationships in a matrix.

• advantage effect sizes computable
• disadvantage patterns in data more difficult to
  see than with graphs

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An example

• Stimulus size
• Small Medium Large
• Unfam 550 460 420
• Familiar 460 420 400
• 90 40 20

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2. Graphs Definitions

• Graphs are visual representations of a set of
  data points.

• Most graphs are two-dimensional, using Cartesian
  co-ordinate system (X and Y).
• Data are presented as a function relating X to Y.

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2. Graphs Definitions

• Graphs are visual representations of a set of
  data points.

Y1
X1
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2. Graphs Components

• X-axis shows independent variable.
• Y-axis shows dependent variable

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2. Graphs Components

• The slope of the function indicates how Y changes
  as X changes across a set of observations

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2. Graphs Components

• The intercept of the function indicates the value
  of Y when X 0

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3. Types of graphs

• Bar graphs.
• Line graphs
• Frequency distributions
• Scattergrams

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3a Bar Graphs

• Bar graphs
• Data represented as bars
• height indicates D.V.
• location along X axis indicates I.V.
• Use when data are categorical rather than
  quantitative.
• Example on next slide.

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Graph shows average for each of our samples
one of women and one of men
pairs of shoes owned
Women Men
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If The Economist had put the full line for
America in at the scale they used in their
original graph, it would have been 6 feet 10
inches long (roughly 20 times the length of the
line for Britain). By my rough interpolation,
Americans give almost 5 times as much in private
donations as the next 17 countries combined. That
information is hidden in the Economists original
graph.
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3b Line graphs

• Show D.V. as a function of I.V.
• Points show actual data
• Lines connecting points show interpolations

• Use when response varies continuously with I.V.
  but be careful about interpolation and
  extrapolation.

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3b Line graphs

• Interpolation inferring the Y value at an X
  between two known X values

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3b Line graphs

• Extrapolation inferring the Y value at an X
  beyond the range of X values for which you have
  data

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3b Line Graphs

• Spatial relationships illustrate quantitative
  relationships
• Slope
• Y-intercept

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3b Line Graphs

• Note the equation for a line
• Y ax b
• a slope and b intercept.

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Slope

• the rate of change in X with change in Y (or
  vice-versa).

• tells us how much change on Y scale is associated
  with a one-unit change on X
• slope can be positive or negative

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Intercept

• the value of Y when X 0, so that the line
  intercepts the Y axis.

• shows minimum (or maximum) value of Y

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3b Line Graphs

• Linear functions
• a unit change in X is associated with a unit
  change in Y.
• e.g., for each dollar, you get one chocolate bar.

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3b Line Graphs

• Non-linear functions
• amount of change in Y for a unit change in X
  depends upon where you are on X scale.
• e.g., the more chocolate bars you buy, the less
  each one costs.

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Performance
Arousal
The Yerkes-Dodson law relates arousal to
stimulation an example of a nonlinear function
in Psychology
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3c Frequency Distributions

• Show frequency with which different observations
  happen

• Y axis how many scores there are at each X
  value in the data set.

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3c. Frequency distributions

• Show how many scores occur in various ranges
  e.g.
• Range of scores
• 1 3 5
• 4 6 8
• 7 9 12
• 10 12 9
• 13 15 4

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Normal distributions
Y-axis measures frequency with which scores are
found
Observations near average are common.
Those at extremes are much less common
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3d - Scattergrams

• Show X-Y relation for individual cases
• That is, these show I.V. D.V. relation for
  cases

• E.g., on next slide, we see relationship between
  IQ (Y axis) and spatial ability (X axis)

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Intelligence test
Spatial ability
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3e Importance of Tables and Graphs

• A good graph or table helps you understand your
  results.
• Similarly, a good graph or table helps you
  explain your results to someone else.

• Consider the following three ways of presenting
  roughly the same information

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High frequency words are read faster than low
frequency words, but the difference is greater if
the words are irregular in spelling than if they
are regular in spelling.
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Typical average reading times (msec)
HF LF IRR 475 600 125 REG 450 500
50 25 100
IRR irregularly spelled words HF high
frequency REG regularly spelled words LF low
frequency
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Review

• Tables and graphs summarize data
• Tables allow quick computation of effect sizes

• Graphs use spatial relationships to show
  relationships among variables in the data
• Graphs show patterns in the data