# Sampling Distributions Flashcards

1
Q

What are sampling distributions?

A

how sample statistics are themselves distributed when we repeatedly sample from a population

2
Q

What does the sampling distribution of the mean (SDM) describe?

A

how the sample mean is distributed

3
Q

What is a sampling error and how can it be reduced?

A

the error associated with examining statistics calculated by a sample rather than the whole population
- reduced by using a larger sample

4
Q

What is the magnitude of sampling error?

A

how far sample statistics depart from the population parameters

5
Q

What does the magnitude is sampling error depend on?

A
• sample size
• Bigger sample -> bigger sampling error less likely
• Smaller Sample -> bigger sampling error more likely
6
Q

Why is it more likely for there to be sample errors when sampling small samples?

A

because it is more likely that you will sample from the same side of the mean

7
Q

How do you obtain sample statistics?

A

By repeatedly sampling from a population

8
Q

How do you generate a sampling distribution?

A
1. Take a sample (size N) from a population
2. Calculate a sample statistic
3. Add the new statistic to a frequency plot (a histogram of the sample statistic)
4. Repeat these three steps
- you can use any sample statistic
9
Q

What valuable information does sampling distributions tells us?

A

What the mean values of the statistic is over all samples

• how variable the statistic is over all samples
• what shape the distribution is over all samples
10
Q

For a variable that is normal what is the sample distribution of the mean?

A
• also normal
• mean = u (same as parent population
• standard deviation (sigmaSDM) = sigma (s.d) parent population/ square root of sample size (square root N) (this is the standard error)
• standard error of SDM must be smaller than the standard deviation of the parent population
11
Q

What is the standard error of the mean (s.e.m) and how do you calculate it?

A

standard deviation of the sampling distribution of the mean (square root N)

• standard deviation of parent population/ square root of sample size
• sigma (parent pop)/ (square root N)
12
Q

Why can you work out the Z score from a sample distribution graph?

A

Because it is normal

13
Q

What is a sample distribution graph?

A

distribution of sample mean m for sample size N drawn at random from the parent population above

14
Q

What is the central limit theorem?

A
• Given a population with a mean u and s.d. sigma, the sampling distribution of the mean approaches a normal distribution with mean u and s.d. sigma/square root N as N, the sample size, increases
• This is true regardless of the underlying distribution
• So even if your population is not normal the distribution of means sample from it will be
15
Q

How do you work out Zm (z score for the SDM)?

A
• Zm = (m – u)/ sigma (s.d. parent pop)/ square root N

- = (sample mean - mean)/ standard error