Download Descriptive Statistics

Designing Social Inquiry
STATISTICAL METHOD
Jaechun Kim
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The Role of Statistics
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One of the most preferred (quantitative) methods, but it is
not necessarily superior to the qualitative method…
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The central logic of quantitative and qualitative methods are
the same – message of KKV…
Two Types of Statistics
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Descriptive Statistics – enables the researcher to summarize
and organize data in an effective and meaningful way…
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Inferential Statistics – allows the researcher to make
inferences. Allow us to test the hypotheses...
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Descriptive Statistics
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The purpose of descriptive statistics is to
inform the audiences of the major
characteristics of the data you collected …
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Using Graphs to Describe Distribution
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pie graphs; bar graphs; chart. etc.
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Measures of Central Tendency (MCT)
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Mode : The category that appears most frequently in
your data
Median : Divides the distribution into two equal parts;
Positional measure
e.g. 6,9,11,12,16,18,21,24,30
Mean (Average)
Sum of all of the observations divided by the total
number of observations; Most frequently used MCT…
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Measure of Dispersion – conveys the
information about the distribution of the
data…
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e.g. 8,8,9,9,10,10,10,10,10,11,11,11,12,12
4,5,6,7,8,9,10,10,11,12,13,14,15,16
Average Deviation
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Add up the deviation of each observation
from the mean and divide it by the number of
observation.
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Variance
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2, 4, 6, 8
Squaring average deviation
Standard Deviation
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Square root of the variance…to put it in the original
units of measurement…
What does small SD mean??
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Types of frequency distributions
Symmetrical distribution
 Skewed distribution
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What is “Normal Distribution”?
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One particular type of symmetrical
distribution
Properties of Normal Distribution
1. Symmetrical and bell-shaped
 2. Mean and the median coincide at the center of
the distribution
(mean and the median have the same value, falls
exactly on the center)
 3. It presupposes infinite number of observations
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Inferential Statistics
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Two Variable Linear Regression (Bivariate
Analysis)
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Definition:
The method of specifying the nature of a
relationship between two interval variables using a
linear function
My example
* Y= Size of the police force in 51 states of the US
(number of the police officers employed per
10,000 population)
* X= Crime rate (number of crimes reported to the
policy per 100,000 population )
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Y
X
Washington
D.C
133.7
1609.
West Virginia
24.4
138
* Y= Size of the police force in 51 states of the US
(number of the police officers employed per 10,000 population)
* X= Crime rate
(number of crimes reported to the policy per 100,000 population )
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The Principle of Least Squares
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The fitted line is chosen so as to minimize the
sum of the squares of the residuals
Minimize, ∑ e²i,
- That is, minimize ∑ (Yi – Ŷi)²
Figure of bivariate regression
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R Square
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Proportion of variation explained
since
Unexplained variation
r² = 1 total variation
we have
Explained variation
r² =
total variation
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Multivariate Analysis (Multiple
Regression)
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An extension of bivariate analysis
p.35. three dimensional graph!
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Simpson’s Paradox
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See my example…
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Sometimes considering only aggregate data can
be highly misleading. Outcome at the subdivision
level should be also examined.
Regression fallacy
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Regression toward the mean
pp. 56-60