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

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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

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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