Lecture 6: Supplemental Material

Question 1

What will most studies do before data collection begins?

Answer 1

attempt to determine size of the sample needed to achieve certain degree of accuracy in estimation

Question 2

Two reasons why estimating minumum sample size commonly done with population proportions?

Answer 2

1. With population proportions, you do not need to make separate guesses about the population mean and standard deviation
2. With population proportions, it is easy to identify a conservative mean, and the bias does not vary much

Question 3

Why is estimating minimum sample size less commonly done with population means?

Answer 3

1. With population means, you need to make separate guesses about the population mean and standard deviation
2. We generally have a hard time making a good guess about a population standard deviation without measuring it

Question 4

Three things that must set to calculate the desired sample size

Answer 4

1. precision: decide on maximum error B around the proportion (i.e. how wide is the desired confidence interval)
2. Confidence: set probability with which the specified precision/this interval is achieved (ie.e what is the desired confidence coefficient)
3. Proportion: select a value of the population proportion pi (either using best available data or conservative estimate)

Question 5

why must we select a
value of the population proportion – π (most conservative is 0.5)

Answer 5

1. This is because the spread of the sampling
   distribution depends on the value of π

Question 6

Why is the most conservative guess of pi 0.5?

Answer 6

this value produces the largest standard error (most spread/variance); you’ll know you got the right sample size

Question 7

What is you guessed that pi is 0.5, but it turns out that it is was actually 0.8?

Answer 7

Either way, it would’ve said you needed a smaller sample size, less observations than you originally thought, your result will be even more precise

Question 8

What equation do you use to answer the question “for a given level of precision, how many observations do I need to ensure that election night +/- value that I want?”

Answer 8

n = π( 1− π)
( z/B)^2

Question 9

in the equation n = π( 1− π)
( z/B)^2, what does B denote?

Answer 9

the maximum error around the proporMon

Question 10

in the equation n = π( 1− π)
( z/B)^2, what does n denote?

Answer 10

denotes the sample size ensuring that, with fixed probability,
the error of esMmaMon of π by the sample proporMon is no
greater than B

Question 11

in the equation n = π( 1− π)
( z/B)^2, what does zw denote?

Answer 11

the corresponding z-score for a confidence interval
with a confidence coefficient equal to the fixed probability

Question 12

In the equation n = π( 1− π)
( z/B)^2, can you throw in a value for pi?

Answer 12

NO - that is the true population proportion (you don’t know that, and you can’t estimate it by throwing in sample value)

Question 13

Two solutions to not knowing pi in n the equation n = π( 1− π)
( z/B)^2

Answer 13

1. If another researcher collected data before, maybe could utilize that value as best guess.
2. Most of the time, researchers use a specific value (0.5) to figure out how many people they need to sample

Question 14

What equation do you use to calculate the necessary sample size for estimating means?

Answer 14

n = σ^2(z/B)^2

Question 15

What equation do you use to calculate the necessary sample size for estimating proportions?

Answer 15

n = π( 1− π)( z/B)^2,

Question 16

What must you specify when calculating sample size for estimating means? n = σ^2(z/B)^2

2 things

Answer 16

Desired confidence coefficient
population standard deviation

Question 17

What must you specify when calculating sample size for estimating means? n = σ^2(z/B)^2 , how might you specify the standard deviation?

Answer 17

*use standard deviation from past research, or related population data if possible

Question 18

when dealing with calculating sample size for estimating means: the __ the spread of the population
distribution, as measured by the __, the __ the
sample size needed to achieve a certain accuracy

Answer 18

greater
standard deviation
larger

Question 19

Two types of estimators?

Answer 19

Biased
Unbiased

Question 20

Unbiased estimator

Answer 20

the average sample statistic (from an indefinitely large number of samples) equals the population parameter in the long run/ (average of sampling distributions’ statistics will equal parameter)

Question 21

T/F: When you have an unbiased estimator, for some samples a statistic may underestimate the
parameter of interest and for others it may overesMmate
the parameter

Answer 21

True - but in the long run the estimates will “average” themselves out

Question 22

Biased estimator/statistic

Answer 22

In the long run, the statistic consistently over or underestimates the parameter it is estimating (the average of all possible statistics is not equal to the parameter)

Question 23

Why is range a biased estimator?

Answer 23

when find all possible sample ranges and take the average, doesn’t equal population range, since almost of all sample ranges might be like 4 or 7, only combos including outlier of 10 million have the true range captured

Question 24

Why is standard deviation a biased estimator?

Answer 24

end to underestimate, since most samples don’t contain the max and min value; the true population parameter will always be a bit larger, also using a different equation

Question 25

Does CLT still apply when you have biased estimators? and what's the caveat?

Answer 25

Yes - you'll still have data clustering, mode/median/mean will be equal, just won't be at the population parameter

Question 26

Examples (2) of biased estimators

Answer 26

Range Standard deviation

Question 27

Why do we care if estimator is biased or unbiased?

Answer 27

if biased, have implications for how to calculate interval; the logic of interval estimate requires that the value be in the middle, unbiased

Question 28

What makes a statistic POSITIVELY biased?

Answer 28

If it tends to overestimate the parameter

Question 29

What makes a statistic NEGATIVELY biased?

Answer 29

If it tends to underestimate the parameter

Question 30

T/F: An unbiased statistic is always an accurate statistic

Answer 30

FALSE - If a statistic is sometimes much too high and sometimes much too low, it can still be unbiased. It would be very imprecise, however.

Question 31

What is one possible saving situation for biased statistics?

Answer 31

A statistic can be slightly biased but still be efficient if it systemically results in a very small over or underestimate of a parameter

Question 32

T/F: If the population distribution is positively skewed (skewed to the right), then the expected value of the sampling distribution of the sample mean might not be equal to the population mean

Answer 32

FALSE - it still will be!

Question 33

T/F: If the population distribution is positively skewed (skewed to the right), then the expected value of the sampling distribution of the sample median might not be equal to the population mean

Answer 33

TRUE - value is consistently less than the true population mean, so it's a biased estimator of the population parameter when the population distribution is positively skewed

Question 34

What is efficiency/precision? (2 definitions)

Answer 34

Statistic more erfficient/precise if its standard error smaller relative to others: Idea that statistic obtained from any single sample from a population is close to the value of the parameter being estimated (not much error) how stable a statistic is from sample to sample

Question 35

The less subject to sampling fluctuation a statistic is, is it more or less efficient?

Answer 35

more efficient!

Question 36

Why is the efficiency of statistics often called the relative efficiency?

Answer 36

It's measured relative to the efficiency of other statistics

Question 37

What might cause us to say that statistic A is more efficient than statistic B?

Answer 37

If statistic A has a smaller standard error than statistic B

Question 38

T/F: If an estimator is biased, it is automatically inconsistent and inefficient

Answer 38

NO - something could be highly efficient and biased

Question 39

How do decide if one equation is more efficient/precise estimator?

Answer 39

Whichever one produces the smaller standard error

Question 40

Most important thing about efficiency/precision?

Answer 40

They are RELATIVE concepts - for two equations...which ones have smaller standard error?

Question 41

Area where efficiency/precision might be applied (and you can see it's relativity shine)

Answer 41

For a given parameter, might have multiple equations for how to get the interval (and some of those equations might have less error, give you tighter interval)

Question 42

T/F: The mean is always more efficient than the median

Answer 42

FALSE - relative efficiency of the two statistics may depend on distribution involved. For instance, the mean is more efficient than the median for normal distributions but not for some extremely skewed distributions

Question 43

What key factor does the relative efficiency of two statics depend on?

Answer 43

the distribution involved (normal or skewed)

Question 44

The more __ the statistic, the more __ the statistic is as an estimator of the parameter

Answer 44

efficient precise

Question 45

Three things to keep in mind when selecting a point estimate

Answer 45

Unbiased vs. biased Efficiency/precision consistency

Question 46

Consistency of an estimator

Answer 46

An estimator is consistent if the estimator tends to get closer to the parameter it is estimating as the sample size increases/error goes down

Question 47

Difference between consistent and unbiased estimators?

Answer 47

consistent estimators get better as the size of the sample increases, whereas unbiased estimators get better as you take the average of the statistic from a large number of samples

Question 48

What might cause you to label an estimator as inconsistent?

Answer 48

If, as you increased sample size, the error went up

Question 49

Why does consistency matter?

Answer 49

In general want biggest possible sample, but sometime it hurts

Question 50

What important concept does consistency (as sample size gets larger, a statistic gets closer and better at estimating the parameter) connect to?

Answer 50

LLN

Question 51

What does B entail

Answer 51

“Beta” term, aka the maximum error around the proportion

Question 52

If a confidence interval is NOT about where the parameter falls, what IS it about?

Answer 52

It's about having a good/reasonable guess of what the parameter is. Then its the classique interpretation of "we are x% confident our parameter falls within the (x,y) c.i." There is a trade off between precision and confidence level.

Question 53

What are the tradeoffs between precision and confidence levels (for intervals?) - careful, different type of precision

Answer 53

as precision increases, confidence level decreases

Question 54

How do you select the value of the population proportion pi when estimating B (2 options) - ## Footnote what do I mean here for estimatign b??

Answer 54

1. using best available data 2. conservative estimate

Question 55

Example of interpretation for estimating sample size of proportion, where n = 600.25?

Answer 55

n = 600.25, so we should select a minimum of 601 houses for our sample