Designing Social Inquiry

STATISTICAL METHOD

Jaechun Kim

The Role of Statistics

One of the most preferred (quantitative) methods, but it is not

necessarily superior to the qualitative method…

The central logic of quantitative and qualitative methods are the

same – message of KKV…

Two Types of Statistics

Descriptive Statistics – enables the researcher to summarize and

organize data in an effective and meaningful way…

Inferential Statistics – allows the researcher to make inferences.

Allow us to test the hypotheses...

Descriptive Statistics

The purpose of descriptive statistics is to inform the audiences of the major characteristics of the data you collected …

Using Graphs to Describe Distribution pie graphs; bar graphs; chart. etc.

Measures of Central Tendency (MCT)

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…

Measure of Dispersion – conveys the information about the distribution of the data… 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 Add up the deviation of each observation

from the mean and divide it by the number of observation.

Standard Deviation Square root of the variance…to put it in the original units of

measurement… What does small SD mean??

Variance 2, 4, 6, 8 Squaring average deviation

Types of frequency distributions Symmetrical distribution Skewed distribution

What is “Normal Distribution”?

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

Inferential Statistics

Two Variable Linear Regression (Bivariate Analysis) 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 )

* 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 )

Y X

Washington D.C 133.7 1609.

West Virginia 24.4 138

The Principle of Least Squares

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

R Square

Proportion of variation explained

since

total variationr² = 1 -

Unexplained variation

total variationr² =

Explained variation

we have

Multivariate Analysis (Multiple Regression)

An extension of bivariate analysis p.35. three dimensional graph!

Simpson’s Paradox

See my example… Sometimes considering only aggregate data can

be highly misleading. Outcome at the subdivision level should be also examined.

Regression fallacy

Regression toward the mean pp. 56-60