Descriptive statistics in social sciences

1. Developmental Research
Methods
Topic 4: Numerical Description
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2. Properties of Scales
• Measuring Variables
– Personality; IQ, etc
• Magnitude
– Size, Quantity
• Equal intervals
– Equal distance between
points in terms of concept
• Absolute zero
– This is nothing. Noting of
the property being
measured exists.
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3. Scales of Measurement
• Nominal
– Mutually exclusive
categories
• Ordinal
– Order of the numbers
mean something
The scale you are using – determines
what types of statistics you can do on the
data!
– Magnitude – but no zero
point and no equal
intervals
• Interval
– Magnitude
– Equal intervals
– No absolute zero
• Ratio
– Equal intervals and a true
zero point and magnitude
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4. Distributions
Allow you to see
how your data
looks
◦ Ranges or bins
(class interval)
◦ 10 or 20 ranges to
cover the entire
data set
You can see how
skewed the data is
Allows you to
decide what stat to
use
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5. Distributions
Mean Alcohol Consumption by Age
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5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
5 to
10
11 to
15
16 to
20
21 to
25
26 to
30
31 to
35
36 to
40
Average Drinks per Week
Age
mean alcohol
consumption

6. Distributions - Skew
mean alcohol consumption
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6
5
4
3
2
1
0
5 to
10
11 to
15
16 to
20
21 to
25
26 to
30
31 to
35
36 to
40
mean alcohol
consumption

7. Measures of central tendency
Mean
Median
◦ Insensitive to
extreme scores
mode
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8. Variation
Variability in your data
Range
Sum of the Squared Deviations from the
Mean
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9. Variance and Standard Deviation
Variance
Standard Deviation
or
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10. Standard scores
Z score
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11. Correlation
Relationship between two variables
No causation!
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12. Positive Correlation
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13. Negative Correlation
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14. No correlation
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