Reading 11: Sampling and Estimation

Question 1

Simple Random Sampling

Answer 1

Method of selecting a sample where each variable has the same likelihood of being included e.g. drawing names out of a hat

Question 2

Sampling Error

Answer 2

Sampling Error = sample mean - population mean

Question 3

Sampling Distribution

Answer 3

Distribution of all values that a sample statistic can take on when computed from samples of identical size randomly drawn from the same population

Question 4

Stratified Random Sampling uses a…

Answer 4

classification system to separate the population into smaller groups based on one or more distinguishing characteristics

Question 5

Time-Series Data

Answer 5

Observations taken over a period of time at specific and equally spaced intervals

Question 6

Cross Sectional Data

Answer 6

Sample of observations taken at a single point in time

Question 7

Longitudinal Data

Answer 7

Observations over time of multiple characteristics of the same entity (think country)

Question 8

Panel Data

Answer 8

Observations over time of the same characteristics over multiple entities

Question 9

Central Limit Theorem (Definition)

Answer 9

The larger the same size, (>30) the closer the sample gets to normal distribution. The means of the population and sample will be equal

Question 10

Central Limit Theorem (Variance Formula)

Answer 10

SD^2 / n

n = sample size

Question 11

Standard error of the sample mean (definition)

Answer 11

Standard deviation around the population mean

Question 12

Standard error of the sample mean (If population Sd known) (formula)

Answer 12

Standard Error = SD of population / Square Root of n

n = size of sample

Question 13

Standard error of the sample mean (if population Sd unknown) (formula)

Answer 13

S / Square Root of N
Where:
S = SD of the sample

Question 14

Desirable Properties of an Estimator

Answer 14

1. Unbiasedness
2. Efficiency
3. Consistency

Question 15

Unbaisedness

Answer 15

EV of estimator = EV of parameter

Question 16

Efficiency

Answer 16

Lower sampling error than any other unbiased estimator

Question 17

Consistency

Answer 17

Variance of sampling error will decrease with sample size e.g. it will become more accurate

Question 18

Point Estimate

Answer 18

Single sample values used to estimate population parameters (mean)

Question 19

Confidence Interval

Answer 19

Range of values in which the population parameter is expected to lie

Question 20

Confidence interval (Formula)

Answer 20

Point Estimate + / - (reliability factor x standard error)

Question 21

Student’s t distribution

Answer 21

Distribution to use when constructing confidence intervals based on:

1. Small sample sizes (n < 30)
2. unknown variance
3. normal distribution

Question 22

t - distribution (properties)

Answer 22

1. Symmetrical
2. Defined by degrees of freedom (n- 1) (df)
3. Fatter tails

Question 23

Degrees of Freedom (df) (Affect on distribution)

Answer 23

More df results in a greater percentage of observations near the center of the distribution

Confidence Intervals will be narrower

Question 24

Confidence Interval Formula (Known Variance)

Answer 24

Point Estimate + (reliability factor x standard error)

Question 25

Confidence Interval Formula (Unknown Variance)

Answer 25

Point Estimate + (t-reliability factor x standard error of sample mean)

Question 26

Confidence Interval Formula (large sample unknown variable)

Answer 26

Point Estimate + (Z Statistic x standard error)

Question 27

Limitations of large sample size

Answer 27

1. Observations from different population/distribution

2. Cost (Must be weighed against increase in precision)

Question 28

Data-Mining Limitation

Answer 28

Repeated use of same database to search for patterns

Question 29

Data-Mining Bias

Answer 29

Overstating the statistical significance of a pattern because a the data was derived through data mining

Question 30

Sample Selection Bias

Answer 30

Systematic exclusion of some data which renders the sample non-random

Question 31

Survivorship Bias

Answer 31

Excluding badly performing funds

Question 32

Look-ahead bias

Answer 32

Testing relationship when the data was not available at the test date

Question 33

Time-period bias

Answer 33

Data gather is either too short or too long