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Quantitative Data Analysis

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.

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Quantitative Data Analysis

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  1. Quantitative Data Analysis Social Research Methods 2109 & 6507 Spring, 2006 March 6 2006

  2. 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)

  3. 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

  4. 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

  5. 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)

  6. 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

  7. Examples of Dispersion

  8. 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

  9. 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

  10. 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)

  11. 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)

  12. 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)

  13. 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?)

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

  15. 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

  16. 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

  17. Examples of correlations

  18. 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)

  19. Formula of the correlation coefficient

  20. To get r in SPSS: • 分析(A) →相關(C) →雙變量

  21. 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

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