1. Descriptive Statistics
Data - Quantitative observation of Behavior
What do numbers mean?
If we call one thing 1 and
another thing 2 what do
we mean?
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2. Properties of Measurement Scales 1. Difference – Nominal labels
2. Order – Ranking of value
3. Equal Intervals – Each numeric step is of
equal value.
*Addition & subtraction
Ratio – natural falling zero (zero means “none” of the quality being measured.
*multiplication and division
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3. Nominal Scales – Just name categories.
Categorical Scales
Nominal Scales – Just name categories.
- no order or arithmetic properties implied.
e.g., Sex 1 = male; 2 = female
Ordinal Scales – rank ordering but not equal
Intervals  no arithmetic properties.
e.g., Private, Lieutenant, Major, General
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4. 3. Interval Scale – Difference,Order and Equal Intervals. e.g., Temp
Continuous Scales
3. Interval Scale – Difference,Order and Equal Intervals.
e.g., Temp
Is 64 twice as warm as 32?
Does 0  mean there is no temperature?
Has addition and subtraction properties, (64 is as
much warmer than 62 as 65 is warmer than 63)
But not multiplication or division.
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5. Ratio Scales – have all arithmetic properties.
It is important to keep the limitations of the
Scale in mind when making conclusions.
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6. Frequency Distributions: Histogram
Abscissa (X-axis):
Dependant Variable
Ordinate (y-axis): Frequency
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7. E.g., 5 represents scores from 4.5 to 5.49.
Each number on the abscissa (X – axis) represents a range of which the reported number is the mid-point.
E.g., 5 represents scores from 4.5 to 5.49.
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8. Distribution of Scores
Symmetrical - scores evenly distributed around the mid-point of the distribution.
Skewed Distributions - scores pile up on one end of the curve.
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9. Measures of Central Tendency - Typical or Average Score
1. Mode - Most frequent score.
- can have more than one Mode (e.g., bimodal or Trimodal).
Fairly unstable - can be effected by one or two scores.
2,2,2,2,3,3,3,3,3,4,4,4,4,5,5 Mode = 3
2,2,2,2,2,3,3,3,3,4,4,4,4,5,5 Mode = 2
Can be used with any type of scale.
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10. 2. Median - Middle score, 50th Percentile
Uneven number of scores - just the mid-point.
E.g. 2,2,3,4,4,5,6,6,7 Median =
When even number
- add 2 middle scores and divide by 2
2, 2, 3,4, 4,5,6, 6, 7, 7 Median =
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11. Medians can not be used with Nominal Data. Medians are fairly stable.
Insensitive to extreme scores.
E.g, 2,2,3,4,4,5,6,6,7 Median = 4
2,2,3,4,4,5,6,6,20 Median is still 4.
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12. 3. Mean - Arithmetic Average. X = (SX)/N = Sum of all the scores
number of scores.
Requires an Interval or Ratio scale.
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13. In a symmetrical, unimodal, distribution the Mode, Median and Mean will all be the same. When the distribution is skewed, or contains some deviant scores, these three measures can be very different.
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14. IE(DS)

15. In the News
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16. Measures of Dispersion
Range - Difference between the highest and lowest category = 9
Strongly effected by extreme scores.
Must be at least ordinal scale.
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17. Deviation Scores (Interval or Ratio)
Total of each score minus the mean.
Problem: This will always be zero.
Total above mean (+ scores) will always
equal total below the mean (- scores).
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18. Uses a mathematicians trick! All squared numbers are positive.
Variance
Uses a mathematicians trick!
All squared numbers are positive.
Variance = deviation scores squared
Number of scores
Sum now does not equal zero.
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19. Problem: Most people do not think in Squares.
i.e., 16 is only twice as dispersed as 4.
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20. Standard Deviation (s) - square root of variance.
4 compared to 16
2 compared to 4
Average amount that scores deviate from the mean.
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21. Most measures fall on a normal curve - most frequent score is mean
- as scores get more extreme they are less frequent
- symmetric distribution
- asymptotic
Standard Deviations
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