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Lecture One

· Statistics:

· Descriptive:

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· What? Distribution of one variable (i.e., its center and dispersion); joint distribution of two variables (i.e., their relationship).

· How? Tabular, graphic, and numerical.

· Inferential:

· (Probability) sample population (of interest)

Sample statistic population parameter

· How? Confidence interval, hypothesis testing.


· Variable: things that vary. That is, different cases have different values. [draw data structure]


· Unit of analysis: what the statement/variable is about. To see why this matters, consider the following hypothetical example:

· Are female applicants less likely to get admitted than male applicants at the department level?

· Are female applicants less likely to get admitted than male applicants at the college level?




· Scale of measurement:

· Variables are always coded using numeric values, but values have different functions.

· Nominal: values are used for differentiation only. Race, gender, marital status, etc.

· Ordinal: ranking order of values is meaningful. Life satisfaction, level of support, etc.

· Interval: distance between values is meaningful. HDI, IQ, temperature, etc.

· Ratio: true zero, i.e., 0 means “none”. Income in dollars, number of children, etc.

· Usually, we call both interval and ratio variables continuous variables.

· Why important? It determines what technique to use.


· [optional] Reliability and validity issues:

· Reliability: consistency across repeated measurements.

· Validity:

· Construct validity: are we measuring what we want to measure?

· Internal validity: causality = association + temporal order + lack of spuriousness.

· External validity: generalizability.

· Reliability and construct validity are criteria for measurement evaluations.

· Internal and external validities are criteria used to evaluate research designs.

· There are more kinds of validities, which mean different things to different researchers.


· More on variable:

· Why variable? Population heterogeneity == the fundamental truth of social science.

· Essentialism vs. Population thinking: is variation REAL?

· Data structure: row == case, column == variable

· What method to use: depends on the scale of measurement/type of the variable(s)

· What it is about: unit of analysis

· Variables in relationship: independent variable (a.k.a. predictor, explanatory variable, exogenous variable) dependent variable (a.k.a. response, outcome, endogenous variable)


· Univariate description:

· The choice of methods (mainly) depends on the level of measurement.




· Frequency Table: title, frequency count ( f), relative frequency ( p), relative cumulative frequency

· Bar Chart: title, axes, labels, bars, (spacing b/w bars)

· Histogram: title, axes, labels, bars, (no spacing b/w bins), (class interval/bin width), (skewness)

· Contingency Table: cross-classification, cell counts, marginal totals, row/column percentages.

· To be continued…


· Bivariate relationship:

· Association: X is associated/correlated with Y.

· Influence: X has an impact on Y.

· Causality: X causes Y.

· (Randomized Controlled) Experiment: random assignment

· Observational Study: association/influence + temporal order + no spuriousness

· Important implication: association or influence ≠ causality

· A third variable Z might complicate the observed bivariate relationship b/w X and Y:

· Spuriousness: the observed XY relationship is due to a common cause Z.

· Interaction/specification/ modification: the observed XY relationship differs toward different groups of Z.

· Mediation/mechanism/intervening: th

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