Data and Sampling

Question 1

What are data?

Answer 1

Observations/measurements of some phenomenon of interest
A dataset is a collection of realisations of random variables

Question 2

What can the index of a data point indicate?

Answer 2

The set for cross sectional data, the time for time series or panel data

Question 3

What are the types of data?

Answer 3

Numeric, grouped, or categorical
Data sets can be cross-sectional, time series, or some combination (panel data tracks a group over time, repeated cross-sectional data take different random samples)

Question 4

What can be included in summary statistics?

Answer 4

Measures of central tendency, measures of dispersion, other measurements of the distribution, measures of relationship between the variables

Question 5

What measures of central tendency are there?

Answer 5

Mean, median (50th percentile), mode, geometric mean (nth root of the product of the data, doesn’t work with negative data)

Question 6

What measures of dispersion are there?

Answer 6

Standard deviation, range, interquartile range

Question 7

What are some other measures of a sample distribution?

Answer 7

Sample skewness measures asymmetry of a distribution, sample kurtosis measures ‘tailedness’ or ‘peakness’ or how much of the variability is due to large deviations from the mean

Question 8

What measures of relationship between variables are there?

Answer 8

Sample covariance which is positive if high x values are associated with high y values and 0 if there is no linear relationship, correlation coefficient

Question 9

What is the formula for the population variance?

Answer 9

σ_n² = 1/n * Σ_i=1ⁿ(x_i-x̄)²

Question 10

What is the formula for the sample variance?

Answer 10

s_n-1² = 1/(n-1) * Σ_i=1ⁿ(x_i-x̄)²

Question 11

What is the formula for sample skewness?

Answer 11

(1/n * Σ_i=1ⁿ(x_i-x̄)³) / s_n³

Question 12

What is the formula for sample kurtosis?

Answer 12

(1/n * Σ_i=1ⁿ(x_i-x̄)⁴) / s_n⁴

Question 13

What is one common reason why correlation does not equal causation?

Answer 13

There can be a third variable causally correlated with both variables, often time

Question 14

What is a sample survey?

Answer 14

A fraction of the total population observed to make statistical inferences about the population from which they are drawn (instead of using a census)

Question 15

Why are samples are needed?

Answer 15

To estimate parameters for the probability distribution used in the analysis of events

Question 16

What is the effect of an unrepresentative or non-random sample?

Answer 16

Estimates based on it aren’t useful
Can’t make population generalisations

Question 17

What is random sampling and why is it not always done?

Answer 17

Create a list of all the possible units that could be sampled and then use a random number generator to select from the list
This isn’t always feasible (not always able to list every unit)

Question 18

When is stratified sampling used?

Answer 18

When the population consists of identifiable sub-groups

Question 19

How can sampling uncertainty be reduced?

Answer 19

Taking averages from random samples, use larger samples

Question 20

What is the tradeoff to sampling?

Answer 20

Larger samples improve sampling uncertainty and precision but are more expensive

Question 21

What are some issues with the data used for microeconomic analysis?

Answer 21

Confidentiality, non-response can be systematic which introduces bias, attrition can affect cohort studies with survivorship bias

Question 22

What makes a sample random?

Answer 22

It is a collection of IID random variables

Question 23

What is an observation?

Answer 23

A known value that each collected random variable assumes

Question 24

What is a statistic?

Answer 24

A function of the sample which is a random variable and so has a sampling distribution

Question 25

What is the distribution of the sample mean of observations of IID normal random variables?

Answer 25

X̄ ~ N(μ, σ²/n)
Uses property that sum of normal distributions is a normal distribution