1. Tables & Graphs

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

3. 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

4. An example Stimulus size SmallMediumLarge Familiar460420400 Unfam550460420 90 40 20 Effect sizes (msec) Data in msec

5. 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.

6. 2. Graphs – Components X (horizontal) axis = independent variable. Y (vertical) axis = dependent variable X Y

7. 2. Graphs – Components Bars or lines Bars indicate height of function at levels of I.V. X Y

8. 2. Graphs – Components Bars or lines Lines indicate what happens to D.V. at points on I.V. between observations (interpolation) X Y

9. 3. Types of graphs A. Bar graphs. B. Line graphs C. Frequency distributions D. Scattergrams

10. 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.

11. # pairs of shoes owned Female Male Graph shows average # for each of our samples – one of women and one of men

12. 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.

13. 3b – Line Graphs Spatial relationships illustrate quantitative relationships Slope Y-intercept

14. 3b – Line Graphs Note the equation for a line: Y = ax + b a = slope and b = intercept.

15. 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

16. Y 654321654321 Positive slope – as Y gets Negative slope – as Y gets larger, X gets larger. larger, X gets smaller. Y 654321654321 X

17. Y 654321654321 X Zero slope – no relation between X and Y.

18. Intercept the value of Y when X = 0, so that the line intercepts the Y axis. shows minimum (or maximum) value of Y

19. Y 654321654321 X Y-Intercept

20. 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 654321654321 X

21. 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.

22. The Yerkes-Dodson law relates arousal to stimulation – an example of a nonlinear function in Psychology

23. 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.

24. 3c. Frequency distributions Show how many scores occur in various ranges Range# of scores 1 – 35 4 – 68 7 – 912 10 – 129 13 – 154

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

26. 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)

28. 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:

29. “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.”

30. HFLF IRR475600 125 REG450500 50 25100 IRR = irregularly spelled wordsHF = high frequency REG = regularly spelled wordsLF = low frequency Typical average reading times (msec)

31. HF LF IRR REG RT

32. 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