Quantitative Data Analysis Social Research Methods 2109 & 6507 Spring, 2006 March

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, subgroup 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 attribute) ( 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 same 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) > 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

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