Tables & Graphs. Outline 1. Tables as representations of data 2. Graphs * Definition * Components 3....
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Transcript of Tables & Graphs. Outline 1. Tables as representations of data 2. Graphs * Definition * Components 3....
Tables & Graphs
Outline
1. Tables as representations of data
2. Graphs* Definition* Components
3. Types of graph* Bar* Line* Frequency distribution* Scattergram
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
An example
Stimulus size
Small Medium Large
Familiar 460 420 400
Unfam 550 460 420
90 40 20
Effect sizes (msec)
Data in msec
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 represented as a function relating X to Y.
2. Graphs – Components
X (horizontal) axis = independent variable.
Y (vertical) axis = dependent variable
X
Y
2. Graphs – Components
Bars or lines Bars indicate
height of function at levels of I.V.
X
Y
2. Graphs – Components
Bars or lines Lines indicate
what happens to D.V. at points on I.V. between observations (interpolation)
X
Y
3. Types of graphs
A. Bar graphs.
B. Line graphs
C. Frequency distributions
D. Scattergrams
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.
# pairs of shoes owned
Female Male
Graph shows average # for each of our samples – one of women and one of men
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.
3b – Line Graphs
Spatial relationships illustrate quantitative relationships
SlopeY-intercept
3b – Line Graphs
Note the equation for a line:
Y = ax + b
a = slope and b = intercept.
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
Y
654321
Positive slope – as Y gets Negative slope – as Y getslarger, X gets larger. larger, X gets smaller.
Y
654321
X X
Y
654321
X
Zero slope – no relation between X and Y.
Intercept
the value of Y when X = 0, so that the line intercepts the Y axis.
shows minimum (or maximum) value of Y
Y
654321
X
Y-Intercept
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.
Y
654321
X
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.
The Yerkes-Dodson law relates arousal to stimulation – an example of a nonlinear function in Psychology
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.
3c. Frequency distributions
Show how many scores occur in various ranges
Range # of scores
1 – 3 54 – 6 87 – 9 1210 – 12 913 – 15 4
Normal distributions
Observations near average are common.
Y-axis measures frequency with which scores are found
Those at extremes are much less common
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)
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:
“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.”
HF LF
IRR 475 600 125REG 450 500 50
25 100
IRR = irregularly spelled words HF = high frequencyREG = regularly spelled words LF = low frequency
Typical average reading times (msec)
HF LF
IRR
REG
RT
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