ERP Lecture 2

18 flashcards · Other · by Daniel F.

1. Elements of Summary Statistics

   Number of observations Measures of central tendency mean: arithmetic mean, average influenced by extreme observations median: middle point when values are ranked in order of magnitude n even number then average of the two middle observations Mode: most frequent value More than one mode: bimodal, multimodal kurtosis, skewness, range Measures of variability variance standard deviation

2. central tendency in different measurement levels (data types)

   nominal variable: only mode is interesting ordinal variables: mode and median interesting interval / ratio: mean or median can be used, depending on skewness

3. Skewness

   shape, symmetry of the distribution is a normal distribution skewed left or right skew=0 symmetric -1 < skew < 1 slightly skewed outside that range: substantially skewed

4. Which measure of central tendency to use if interval/ratio variable is skewed vs not skewed

   not skewed: mean is skewed: median

5. Kurtosis

   shape, tailedness of distribution Degree to which scores cluster at the tails (heavy or light tails), compared to a normal distribution shape mesokurtic: kurtosis=3 Leptokurtic: heavy tails (maybe also) pointy (kurtosis>3) Platykurtic: light tails (maybe also) flatter (kurtosis<3)

6. Range of variables

   Range: maximum value - minimum value Interquartile range: Q3 - Q1 values ordered highest to lowest used to identify outliers

7. variance vs standard deviation

   Variance: the average of the squared differences between each data point and the mean Standard: deviation is the square root of variance, average deviation from the average

8. Standard deviation of normal distribution

9. Correlation

   any statistical relationship, whether causal or not, between two random variables

10. Correlation Coefficient

    r: Direction and strength of the relationship between two variables [-1, 1] sign and magnitude describes relationship r = +1 or -1: perfectly linearly correlated r = 0: No linear relationship Significance: Based on the correlation coefficient (r) and the sample size, “correlation significance” tells whether the correlation in population can be significantly different from zero or not

11. correlation vs causation

    Correlation does not say anything about the direction of causality Directionality problem: A and B can be correlated because A causes B or B causes A Third variable problem: A and B can be correlated not because A causes B, or B causes A, but some unmeasured third variable, C, causes both A and B.

12. Regression Analysis

    statistical method that helps to determine the strength and nature of the impact of one or more variables on a variable of interest Independent (explanatory) variable(s): Predictors; variable(s) that cause (predict or explain) a change in the variable of interest (Y) Dependent variable (Y): variable that is being influenced, its variance (its value) is explained by the changes in the independent variable(s) When x changes, what change can we expect in y?

13. bivariate regression vs multiple regression

    Bivariate Regression Equation: Y=b0+b1X+ϵ Y: Dependent variable (outcome) X: Independent variable (predictor) b0: Y-intercept (value of Y when X=0) b1: Regression coefficient (change in Y per 1-unit increase in X) A positive b indicates a direct relationship; negative = inverse ϵ: Error term Key metrics: R2: Proportion of variance in Y explained by X R-squared of 0.6 means that 60% of the variance in the dependent variable is explained by the independent variable(s). p-value: Significance of th…

14. OLS

    Ordinary least squares Minimize the distance between real observation and the fitted straight line Minimize the sum of squared deviations from the straight line Minimize the sum of the squared residuals

15. Interpreting regression coefficients

    sign, size, significance The regression coefficient 𝛽1 shows an estimate for the amount of change in 𝑦 (DV) due to a one-unit change in 𝑥1, c.p.

16. Interpreting logarithmic regression coefficients

    Level-Level: Y=β0+β1X A 1-unit increase in X → β1-unit change in Y Semi-log Level-Log: Y=β0+β1ln⁡(X) 1% increase in X → β1/100-unit change in Y Log-Level: ln⁡(Y)=β0+β1Xln 1-unit increase in X → 100β1% change in Y (exact: 100(eβ1−1)%100(eβ1−1)%) elasticity Log-log: ln⁡(Y)=β0+β1ln⁡(X) 1% increase in X → β1% change in Y (elasticity interpretation)

17. regression with dummy variable

    Indicates whether a condition is satisfied e.g. Citizenship (EU or non-EU) If you have m categories, include 𝑚 − 1 dummies, the omitted one is the base/reference category

18. Interpretation of regression coefficients of dummy variables

    The coefficient of a dummy variable represents the average difference in the dependent variable (Y) between the group where the dummy equals 1 and the group where it equals 0, c.p