Scales of Measurement

1
Scales of Measurement

• Ratio
• All properties of an interval scale absolute
  zero point
• Can form ratios of the values
• that have meaning
• Examples
• Temperature in Kelvin
• Reaction time
• Weight
• Height

2
Types of Data

• Why does knowing the level of measurement/type of
  data matter?
• Type of data dictates the allowable statistical
  analyses
• Assumptions
• Psychology Interval data assumption

3
Data Presentation

• Graphs
• Allows you to see data
• Usually better than a table
• Use the graph suited to the scale of the data

4
Data Presentation

• Axes
• Two types
• Vertical y-axis usually characteristic of
  scores is plotted along
• Horizontal x-axis scores are plotted along
• Choose suitable units

5
Data Presentation

• Axes
• y-axis should be about 2/3 to ¾ of the length of
  the x-axis to avoid distortion
• If axes do not intersect at 0, use breaks
• Each axis should be labeled and the title should
  be short and explicit

6
Data Presentation

• Axes

7
Data Presentation Types

• Pie chart
• No axes
• Use if dealing with percents 100
• Pieces represent percentages of the whole pie
• Use with qualitative (categorical data)

8
Data Presentation Types

• Pie chart

9
Data Presentation Types

• Bar graph
• Use with qualitative data
• Frequencies per level/category
• Bars do not touch

10
Data Presentation Types

• Bar graph

11
Data Presentation Types

• Histogram
• Use with quantitative data
• Frequency per level/category
• Arrange categories in numerical order
• Bars touch to show continuity
• Too few or too many categories can distort the
  shape of the distribution
• Never group scores so that one could fall into
  two categories

12
Data Presentation Types

• Histogram

13
Data Presentation Types

• Line Graph
• Use when graphing experimental results
• Typically, when have two or three variables

14
Data Presentation Types

• Line Graph

15
Data Presentation

• Line Graph

16
Data Presentation Types

• Scatterplot
• Use with two variables
• Helps to see the relationship between the two

17
Data Presentation Types

• Scatterplot

18
Data Presentation Types

• Stem Leaf Plot
• Stem/leaf drawing
• If turn 90 degrees, will get a histogram

19
Data Presentation Types

• Stem Leaf Plot

Starting Salary Stem-and-Leaf Plot for GENDER
Female Frequency Stem Leaf 2.00
1 . 33 6.00 1 . 678999 20.00
2 . 00000000001123334444 15.00 2
. 556666666788999 12.00 3 .
000000333344 3.00 3 . 567 1.00
Extremes (gt49000) Stem width 10000 Each
leaf 1 case(s)
20
Data Presentation Types

• Stem Leaf Plot

Starting Salary Stem-and-Leaf Plot for GENDER
Male Frequency Stem Leaf 1.00
0 . 8 1.00 1 . 0 9.00
1 . 567888889 15.00 2 .
000023333334444 13.00 2 .
5556667778889 16.00 3 .
0000011123334444 1.00 3 . 5
1.00 4 . 1 Stem width 10000 Each
leaf 1 case(s)
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Data Presentation Types

• Stem Leaf Plot

Males Females 8 0
0 1 33 98888765 1 678999
444433333320000 2 00000000001123334444
9888777666555 2
556666666788999 4444333211100000 3
000000333344 5 3 567
1 4 4 9
22
Data Presentation Types

• Frequency Distribution
• Represents scores and their frequencies
• Frequency number of time the score occurs
• Symbolized by f
• Distribution any organized set of data
• Table
• List scores in order with lowest score at the
  bottom of the table

23
Data Presentation Types

• Frequency Distribution Types
• Simple
• Shows number of times each score occurs in a set
  of data

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Data Presentation Types

• Simple Frequency Distribution Example
• Raw Scores

25
Data Presentation Types

• Simple Frequency
• Distribution Example

26
Data Presentation Types

• Frequency Distribution Types
• Relative frequency distribution
• Proportion of total number of scores that occur
  in each interval
• Symbolized by rel. f
• Formula for a scores relative frequency

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Data Presentation Types

• Relative
• Frequency
• Distribution
• Example

28
Data Presentation Types

• Frequency Distribution Types
• Cumulative frequency distribution
• Number of scores that fall at or below a
  particular score
• Symbolized by cf
• To compute, add simple frequencies for all scores
  below the score with the frequency for the score

29
Data Presentation Types

• Cumulative
• Frequency
• Distribution
• Example

30
Data Presentation Types

• Frequency Distribution Types
• Cumulative percentage distribution
• Percentage of scores the fall below the at or
  below a particular score
• Can find by dividing the cumulative frequency by
  the total number of scores and multiplying by 100

31
Cumulative Percentage Distribution Example