Outline

1. Tables as representations of data2. 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 sizeSmallMedium Large

Unfam 550 460 420

Familiar 460 420 400 90 40 20

Effect sizes (msec)

Reaction times 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 presented as a function relating X to Y.

2. Graphs – Definitions

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

X

Y

X1

Y1

2. Graphs – Components

• X-axis shows independent variable.

• Y-axis shows dependent variable

X

Y

Origin: X = 0 and Y = 0

2. Graphs – Components

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

X

Y

a

b

Slope = ab

2. Graphs – Components

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

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

Women Men

Graph shows average # for each of our samples – one of women and one of men

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 Economist’s original graph.

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

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

X

Y

3b – Line graphs

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

X

Y

3b – Line Graphs

• Spatial relationships illustrate quantitative relationships

– Slope– Y-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

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

Arousal

Per

form

ance

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 – e.g.:

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)

Spatial ability

Inte

llige

nce

test

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