Scattergrams Scatterplots

1
Scattergrams(Scatterplots)

• Chapter 9
• SPSS Holcomb
• EDLD 6333 F07

2
Scattergrams

• Learning Objectives
• Define scattergram
• Understand uses of scattergrams
• Learn connection of scattergrams w/ correlation
  coefficients
• Identify when to use a scattergram
• Learn how to create a scattergram in SPSS

3
Scattergrams cont.

• Learning Objectives cont.
• Be able to interpret a scattergram for
• Strength
• Direction
• Linearity
• Learn to format a scattergram for APA reports

4
Definition of Scattergrams

• Definition of Scattergrams
• A scattergram is
• Also known as a scatter diagram
• Also known as Scatterplots (for rest of ppt too)
• A figure
• A summary of bivariate data (2 variables)
• Shows the visual relation (correlation) b/w two
  variables X Y
• Visually shows if there is a relationship b/w two
  sets of data

5
Example of a Scatterplot

• http//regentsprep.org/Regents/math/data/scatter.h
  tm

More explanation to come this is just an
example to help visualize what a scatterplot may
look like
A visual representation of two sets of data (two
variables)
6
Definition of Scatterplots cont.

• Definition of Scatterplots cont.
• A scatterplot is
• A figure that represents 2 interval/ratio
  variables
• Reminder Scale is interval/ratio (measurement on
  a scale)
• Reminder A variable is the trait/characteristic
  that varies among the participants in the study
• A scatterplot has 2 axes
• One for each variable

7
Definition of Scatterplots cont.

• Definition of Scatterplots cont.
• A scatterplot has
• Scores for each participant are represented by a
  single dot on the figure
• Patterns of the dots indicate direction of the
  relationship b/w the variables
• Patterns of the dots indicate strength of the
  relationship b/w the variables

8
Uses of Scatterplots

• Uses of Scatterplots
• Scatterplots can be used to
• Determine if one event affects another
• Determine relationships (correlation) between
  sets of data gathered
• Scatterplots are not used
• With Likerts
• Even if Likert is interval/ratio

9
Scatterplots w/ Correlation Coefficients

• Scatterplots w/ Correlation Coefficients
• Correlation
• A correlation coefficient is the single numerical
  value used to describe a relationship
• A scatterplot is the statistical figure showing
  the relationship

10
Scatterplots w/ Correlation Coefficients cont.

• Scatterplots w/ Correlation Coefficients cont.
• Scatterplots go w/ Pearson r Correlation
  Coefficients
• More on Person r in next chapter
• A scatterplot should be done before calculating
  the correlation coefficient
• A scatterplot reveals nature of relationship of
  the two variables studied
• Scatterplot is the statistical figure that shows
  relationship

11
Creating a Scatterplot

• To Create a Scatterplot
• Follow procedures for adding variables in
  Variable View data in Data View
• Reminder SPSS Version 15 uses Legacy

12
Creating a Scatterplot cont.

• To Create a Scatterplot cont.
• After data for two variables has been entered
• Click on Graphs
• Click on Scatter/Dot
• Click on Define
• The default is Simple Scatter

13
Creating a Scatterplot cont.

• To Create a Scatterplot cont.
• Before choosing variables for X Axis Y Axis
  determine
• Predictor variable
• When 1 variable is intended to predict another
• Ex SAT Verbal Score
• Also known as the Independent Variable
• Use Predictor variable for X Axis
• Horizontal axis on a scatterplot

14
Creating a Scatterplot cont.

• To Create a Scatterplot cont.
• Before choosing variables for axes determine
• Variable being predicted
• Also known as Criterion Variable or Outcome
  Variable
• The variable being predicted
• Ex Freshman GPA
• Also known as the Dependent Variable
• Use for Y Axis
• Vertical axis on a scatterplot

15
Creating a Scatterplot cont.

• To Create a Scatterplot cont.
• Before choosing variables for axes determine
• If no prediction is involved either variable can
  be placed on X or Y axis

16
Creating a Scatterplot cont.

• To Create a Scatterplot cont.
• In the Simple Scatterplot dialog box
• Click on 1st variable (Predictor/IV)
• Click on arrowhead to left of X Axis box
• Variable should show in X Axis box
• Click on 2nd variable (Predicted/DV)
• Click on arrowhead to left of Y Axis box
• Variable should show in Y Axis box
• Click OK

17
Interpreting a Scatterplot

• Graph Interpretation
• Reminder
• A scatterplot provides a visual of the
  relationship b/w 2 variables
• Assists with prediction of possible correlation
• Predictor variable is on the X Axis (Horizontal)
• Criterion (Dependent) variable is on the Y Axis
  (Vertical)
• Unless no prediction is involved then either
  variable on either Axis

18
Interpreting a Scatterplot cont.

• Graph Interpretation cont.
• Important characteristics of graph
• Each dot on scatterplot represents the 2 scores
  for the 1 participant
• Scores are from the 2 variables chosen
• Dot is participant location on graph between
  the 2 axis is the combination of the 2 scores

19
Interpreting a Scatterplot cont.

• Graph Interpretation cont.
• Important characteristics of graph
• If dots form patterns
• If dots form a pattern that rises from the
  lower-left corner to the upper-right corner
  pattern is called a positive or direct
  relationship

20
Interpreting a Scatterplot cont.

• Scatterplot w/ a Positive or Direct Relationship
• http//www.statcan.ca/english/edu/power/ch9/scatte
  rgraphs/scatter.htm

21
Interpreting a Scatterplot cont.

• Scatterplot w/ a Positive or Direct Relationship
  2nd Example
• http//www.statcan.ca/english/edu/power/ch9/scatte
  rgraphs/scatter.htm

22
Interpreting a Scatterplot cont.

• Graph Interpretation cont.
• Important characteristics of graph
• If dots form patterns
• If dots form a pattern that rises from the
  upper-left corner to the bottom-right corner
  pattern is called a negative or inverse
  relationship

23
Interpreting a Scatterplot cont.

• Scatterplot w/ a Negative or Inverse Relationship
• http//www.statcan.ca/english/edu/power/ch9/scatte
  rgraphs/scatter.htm

24
Interpreting a Scatterplot cont.

• Graph Interpretation cont.
• Important characteristics of graph
• If dots form a clear pattern
• If dots are not scattered and follow a clear
  pattern the relationship may be strong
• A correlation coefficient can help determine
  strength of relationship (Chapter 10)

25
Interpreting a Scatterplot cont.

• Scatterplot w/ a Strong Relationship
• http//www.statcan.ca/english/edu/power/ch9/scatte
  rgraphs/scatter.htm

26
Interpreting a Scatterplot cont.

• Graph Interpretation cont.
• Important characteristics of graph
• Spread of Data
• If there is scatter concentrated
• If dots do not form a straight line but are
  somewhat scattered on the graph
• Even with scatter the direction of the pattern
  may be clear
• This may indicate that the relationship is not
  perfect

27
Interpreting a Scatterplot cont.

• Scatterplot w/ a concentrated Scatter Pattern
• http//www.statcan.ca/english/edu/power/ch9/scatte
  rgraphs/scatter.htm

28
Interpreting a Scatterplot cont.

• Graph Interpretation cont.
• Important characteristics of graph
• Spread of Data
• If there is data is wide spread
• If dots do not form a straight line but are
  widely scattered on the graph
• This indicates that there is no relationship

29
Interpreting a Scatterplot cont.

• Scatterplot w/ a wide spread Scatter Pattern
• http//www.statcan.ca/english/edu/power/ch9/scatte
  rgraphs/scatter.htm

30
Interpreting a Scatterplot cont.

• Graph Interpretation cont.
• Important characteristics of graph
• If dots generally follow a straight line
• If you can draw a straight line the overall
  pattern of the dots follow the line then the
  relationship is linear
• Also known as a perfect direct linear
  relationship
• Knowing if relationship is linear is important
  b/c stats for correlation coefficients help
  describe linear relationships (Chapter 10)

31
Interpreting a Scatterplot cont.

• Scatterplot w/ a Perfect Linear Relationship
• http//www.statcan.ca/english/edu/power/ch9/scatte
  rgraphs/scatter.htm

32
Interpreting a Scatterplot cont.

• Graph Interpretation cont.
• Important characteristics of graph
• If dots form a pattern curved or round
• Example of a nonlinear or curvilinear
  relationship
• Probably there is no relationship
• Probably no correlation will be done

33
Interpreting a Scatterplot cont.

• Scatterplot w/ a Curvilinear Relationship
• http//forrest.psych.unc.edu/research/vista-frames
  /help/lecturenotes/lecture11/overview.html

Strongly positive but Curvilinear
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Interpreting a Scatterplot cont.

• Graph Interpretation cont.
• Important characteristics of graph
• If a dot (or dots) are very far outside the
  pattern
• Called outliers
• Outliers are values so different in scores from
  the other scores
• Outliers are not random chance but scores so very
  far out from other scores in the distribution of
  scores

35
Interpreting a Scatterplot cont.
Outlier

• Scatterplot w/ a an Outlier
• http//www.statcan.ca/english/edu/power/ch9/scatte
  rgraphs/scatter.htm

36
Stats Humor

• http//davidmlane.com/hyperstat/humorf.html

37
Formatting for Scatterplots in APA

• Formatting Scatterplots for APA
• Scatterplots are figures
• Figure number should be in italics
• Follow figure number with a caption (the
  descriptive title)
• APA dictates figure number caption are placed
  below figure

38
Describing Scatterplot in APA

• Wording to Describe Findings of Scatterplot
• Describe direction
• Describe strength
• Describe relationship of variables
• Description also includes value of the
  corresponding correlation coefficient
• Symbol is r (lower case r with italics on the r)
• Ex The scatterplot in Figure 9.10 indicates
  that there is a strong, linear, direct
  relationship between SAT Verbal scores and
  freshman GPA (r .83).

39
Conclusion

• A scattergram (or scatterplot) is a
  diagram/figure
• Scatterplots show if there is a relationship b/w
  2 variables
• Interval/ration variables are used in
  scatterplots
• Scatterplots help determine need to run Pearson r
  Correlation Coefficients

40
Conclusion cont.

• Interpretation of the visual representation of
  the scores for the participants helps identify
  type of relationship strength for the 2
  variables
• Different types of direction, strength, spread
  of data possible
• When writing description of scatterplots in APA
  include the corresponding correlation coefficient