Quantitative Data Analysis

Social Research Methods 2109 & 6507

Spring, 2006

March 6 2006

Quantitative Analysis: convert data to a numerical form and

statistical analyses

• quantification (量化 ): the process of converting data to a numerical format (將資料轉換成數字形式 )

Quantification of Data

• Develop codes and a codebook

• Coding data (資料編碼 )

• Data entry (資料輸入 )

• Data file construction (資料檔的建立 )

• Statistical Analyses

Quantitative Data Analyses

• Univariate analyses (單變量分析 ): a single variable– Distributions, central tendency, dispersion, su

bgroup comparisons

• Bivariate analyses (雙變量分析 ): the analysis of two variables

• Multivariate analyses (多變量分析 ): analyzing more than two variables simultaneously

Univariate Analysis

• Distributions (分配 )– Frequency distribution (can use a graph)

• Central tendency (the form of an average) (集中趨勢 )– The arithmetic mean (算數平均數 )– The mode (the most frequently occurring attrib

ute) (眾數 ) – The median (the middle attribute in the ranked

distribution of observed attributes) (中位數 )

Univariate Analysis

• Dispersion (離差 ): the way values are distributed around some central value (ex: an average)– The simplest measure: the range– Standard deviation: an index of the amount of

variability

Examples of Dispersion

Please note: some calculations are not suitable to all variables

• Continuous variables (quantitative variables) (連續變數 ): a variable whose attributes form a steady progression– Ex: age

• Discrete variables (qualitative variables) (間斷變數 ): a variable whose attributes are separate from one another, or discontinuous – Ex: gender– Nominal or ordinal variables

Bivariate Analysis

• Explanatory bivariate analyses: consider causal relationships (考慮兩個變數的因果關係 )

• Explanatory or Independent Variables vs. Response or Dependent Variables

Measures of association

• The basic idea: proportionate reduction of error (PRE) (消減錯誤的比例 )

• If you know the relationship between the two variables, you will make fewer errors in guessing values of one variable if you know values of the other.

• Today: focus on correlation (相關係數 )

A Scatterplot (散佈圖 ): display the relationship between two quantitative variables measured on the s

ame individuals (能顯示二量化變數的關係 )

Looking at a scatterplot

• Look for direction, form, and strength of the relationship

• Direction (方向 ): – Positive association (正相關 )– Negative association (負相關 )

Looking at a scatterplot

• Form (形式 ): what shape or pattern?–直線 ? 曲線 ? 集中 ? 分散 ?

• Strength: the points in the scatterplot lie to a simple form (a line or a curve?) (圖中各點多接近一直線或曲線 ?)

Outlier (極端值 ): an individual obs. falling outside the overall pattern of the graph

The correlation coefficient (r)

• Correlation (r): a measure of the strength and direction of the linear relationship between two quantitative variables (二量化變數直線關係的強度及方向 )

• r can take on values from -1 to 1

Facts about correlation:

• A positive value of r: a positive association• A negative value of r: a negative association• r closer to 1 or -1: stronger association• r = 0 : no association• r : measures the strength of linear association• r (y, x) = r (x, y)• r: sensitive to outliers

Examples of correlations

More about correlations

• How big is a correlation?

No hard and fast rule

• In general: abs(r) >0.7--- strong association

• But in social sciences, r is usually not strong in terms of its value (< 0.7)

Formula of the correlation coefficient

To get r in SPSS:

• 分析 (A) →相關 (C) →雙變量

相關

1 .661**. .000

474 474.661** 1.000 .474 474

Pearson 相關 ( )顯著性 雙尾

個數Pearson 相關

( )顯著性 雙尾個數

EDUC ( )教育程度 年

SALARY 目前薪資

EDUC 教育( )程度 年

SALARY 目前薪資

0.01 ( )在顯著水準為 時 雙尾 ，相關顯著。**.

Conclusions about correlation:

• Scatterplots: the first step when considering the association between two quantitative variables

• r: summarize the strength of linear association

• Distinct (but related) to the slope of the regression line