For instance, we want to know whether freshmen with parents of BA degree are predicted to get higher GPA than those with parents without BA degree.

Transcription

1 DESCRIPTIVE ANALYSIS For instance, we want to know whether freshmen with parents of BA degree are predicted to get higher GPA than those with parents without BA degree. Assume that we have data; what information do we need to have at this point? A group of college freshmen Their GPA at the end of first year Whether they have parents Educational level of parents

2 DESCRIPTIVE ANALYSIS First task is to know the description of variables descriptive analysis Your variables are Interval/ordinal/nominal? Continuous/discrete? Why is it important? Your aim is to not only describe data but also find the association between variables. You have to choose adequate statistical process to find the meaning of association based upon characteristics of variables.

3 DESCRIPTIVE ANALYSIS First task is to know the description of variables descriptive analysis Quantitative variables have two key features to describe numerically The center of the data The variability/spread of the data Why do we need to understand both center and variability of the data?

4 DESCRIPTIVE ANALYSIS Typical setting of the data Row( 행 ) contains the observations for a particular subject Column( 열 ) contains the observations for a particular characteristics subject gen age high coll 1 m f f f M

5 DESCRIPTIVE ANALYSIS First task is to know the description of variables descriptive analysis Describing data with tables and graphs (quantitative or categorical variables) Numerical descriptions of center, variability, position (quantitative variables)

6 TABLES AND GRAPHS Frequency distribution: Lists possible values of variable and number of times each occurs Example: Student survey (n = 60) political ideology measured as ordinal variable with 1 = very liberal,, 4 = moderate,, 7 = very conservative

7 TABLES AND GRAPHS

8 TABLES AND GRAPHS HISTOGRAM : BAR GRAPH OF FREQUENCIES OR PERCENTAGES

9 NUMERICAL DESCRIPTIONS Let y denote a quantitative variable, with observations y 1, y 2, y 3,, y n a. Describing the center: Median: Middle measurement of ordered sample Mode: most frequently occurring value Mean: y y + y + + y Σy = = n n n i

10 NUMERICAL DESCRIPTIONS Which of mean, mode, and median is most appropriate concept to describe central tendency in following cases? 1. Quantitative or Categorical variable? 2. Ordered or Nominal variable? 3. Discrete or Continuous variable? What is an outlier and is its influence on mean, mode, and median? You need to overall spread, variability, and shape of distribution to better make sense the centrality of data.

11 DESCRIBING VARIABILITY Range: Difference between largest and smallest observations (but highly sensitive to outliers, insensitive to shape) Standard deviation: A typical distance from the mean The deviation of observation i from the mean is y y i

12 DESCRIBING VARIABILITY The variance of the n observations is s Σ( y y) ( y y) ( y y) = = n 1 n i 1 n The standard deviation is the square root of the variance,

13 DESCRIBING VARIABILITY Properties of the standard deviation: s 0, and only equals 0 if all observations are equal s increases with the amount of variation around the mean Division by n - 1 (not n) is due to technical reasons (later) s depends on the units of the data (e.g. measure euro vs $) Like mean, affected by outliers

14 BIVARIATE DESCRIPTION Categorical var s: show data using contingency tables Quantitative var s: show data using scatterplots Mixture of categorical var. and quantitative var. (e.g., number of close friends and gender) can give numerical summaries (mean, standard deviation)

15 BIVARIATE DESCRIPTION Scatter plot Happiness Very Pretty Not too Total Income Above Aver Average Below Aver Total

16 BIVARIATE DESCRIPTION contingency tables Happiness Very Pretty Not too Total Income Above Aver Average Below Aver Total

17 PRACTICE QUESTIONS : b, c, d