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Psych 100A - Psychological Statistics > Chapter 6: Sampling Error & Sampling Distributions > Flashcards

Chapter 6: Sampling Error & Sampling Distributions Flashcards

1
Q

What is random sampling error?

A

The difference between the population mean
and our sample estimate

She might also say “The difference between the true
population parameter and an estimate from a sample.”

The population and sample means usually differ

The sample mean could be higher or lower than
the true/population mean of all possible
participants

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2
Q

How do you calculate sampling error?

A

Sample mean (X̄) - Population mean (μ) = Sampling error, which can be either positive or negative

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3
Q

True or false: Estimates (sample mean) vary across samples?

A

True!

Let’s say you have 3 different researchers and each of those researchers recruited 1,071 participants and collected their answers to a specific question. Each researcher is going to have samples that are comprised
of different scores. That means they’ll also have estimates that aren’t the same…

1st Researcher: X̄ = 3.8
2nd Researcher: X̄ = 2
3rd Researcher: X̄ = 3.15

Each sample is a subset of the population, so
each sample has different members producing different answers.

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4
Q

True or false: Sampling errors vary across samples?

A

True!

Just like how estimates (sample mean) vary across samples so do sampling errors:

1st Researcher: 3.8 (X̄) - 3 (μ) = .8 sampling error
2nd Researcher: 2 (X̄) - 3 (μ) = -1 sampling error
3rd Researcher: 3.15 (X̄) - 3 (μ) = .15 sampling error

Any given sample will produce a mean that is
higher or lower than the true population mean

Each sample we could potentially work with will
produce a different amount of sampling error

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5
Q

___________ vary accross samples.
Just like _________ vary across people.

A: Spread, Opinions
B: Estimates, Scores
C: Scores, Estimates

A

B: Estimates, Scores

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6
Q

True or false: The true mean in the
full population of potential study participants is
known?

A

False!

The true mean in the full population of potential study participants is UNKNOWN!

It’s rare that we have access to the entire population, so the population mean is therefore unknown!

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7
Q

True or false: Each sample we could potentially work with gives a different estimate of the unknown
population mean?

A

True!

Each sample will produce its own unique sample mean/estimate (X̄)

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8
Q

True or false: Any given sample mean could be higher or lower than the unknown population mean (i.e.,
sampling errors can be positive or negative)?

A

True!

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9
Q

Given a sample mean, what do we know about the population mean?

A. It can be higher or lower than this sample
mean

B. It must be higher than this sample mean

C. It must be lower than this sample mean

A

A. It can be higher or lower than this sample
mean

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10
Q

True or false:

Parameter = Population (mean, median, kurtosis, skewness, etc.)

Estimate = Sample (mean, median, kurtosis, skewness, etc.)

A

True!

The parameter is any value/data connected to the population AND an estimate is any value/data connected to a sample

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11
Q

True or false: Since a sample mean can change from sample to sample in a single study a population mean can also change from sample to sample in a single study.

A

False!

The population mean in a single study does NOT change from sample to sample. You are simply comparing multiple samples (filled with different people, answers, and values) to ONE population mean (whichever population you’re studying and comparing the samples to).

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12
Q

What are the two methods for calculating sampling error?

A
  1. Monte Carlo computer simulation
  2. Statistical theory
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13
Q

What is the Monte Carlo computer simulation method?

A

It is one of two methods used to calculate sampling error.

It generates artificial sample data from a hypothetical
population.

This method uses hypothetical data and assumes everything (population mean, standard deviation, etc.).

She might also call it the “Hypothetical Population Distribution.”

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14
Q

What is the statistical theory method?

A

It is one of two methods used to calculate sampling error.

It uses a key theorem to derive an equation that estimates sampling error based on the sample data.

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15
Q

What is “Sampling Distribution Of The Means?”

A

The distribution of means (estimates) from many different samples.

Think of this as “repeated sampling.”

We can get a clearer picture of sampling error if
we look at MANY samples, not just two.

Much of what we do for the rest of the quarter
relies on a hypothetical process of drawing a
LARGE (think 10,000 samples for instance) number of samples from a population.

This concept is ABSTRACT because we usually only
have one sample, not many samples.

So if you have 10,000 samples, you’ll have 10,000 sample means and 10,000 sampling errors (BUT remember, you’ll only have ONE population mean).

In a histogram/density plot, you’ll see a distribution of SAMPLE MEANS not a distribution of scores.

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16
Q

Describe the shape of a sampling distribution:

A

The distribution of means (estimates) from many
different samples is symmetric and
approximates a normal curve

The distribution centers around the unknown
population mean (the center is the population mean).

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17
Q

What are the 3 different types of distributions we’re dealing with in this class so far?

A
  1. The distribution of the population
  2. The distribution of a sample
  3. The sampling distribution
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18
Q

Describe a population distribution:

A

It is all of the scores in the population and it’s centered around the population mean (μ).

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19
Q

Describe a sample distribution:

A

It is all of the scores in a sample and it’s centered around the sample mean (X̄).

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20
Q

Describe a sampling distribution:

A

It is a collection of many sample means and it’s centered around the population mean (μ).

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21
Q

The sampling distribution is a distribution of __________.

The population distribution is a distribution of __________.

The sample distribution is a distribution of __________.

A. Sample means; individual scores in the population; sample means in a sample

B. Sample means; individual scores in the population; individual scores in a sample

C. Individual scores in the population; sample means; individual scores in a sample

A

B. Sample means; individual scores in the population; individual scores in a sample

22
Q

What does standard deviation measure?

A

Standard deviation is the average distance between individual scores and the sample/population mean (center of the score distribution); the average amount of deviation scores.

She might also say: Standard deviation measures the spread/similarity of a distribution.

For population, it’s represented as, σ (sigma)
For sample, it’s represented as, s

23
Q

What is standard error?

A

Standard error is the average difference between many sample means and the population mean (center of the sampling distribution); the average amount of sampling errors

She might also say:
* We can use the standard deviation to quantify
spread in the sampling distribution

  • The standard error is the standard deviation of
    the sample means from many random samples
  • The standard error is the average or typical
    amount of sampling error in an estimate (average amount of sampling error)
  • The standard error projects the average amount of
    error from many different random samples

We only use this terminology for sampling distributions (many, many samples)

It’s a type of standard deviation but only for sampling distributions (many, many samples)

In Jamovi’s descriptives section, for a sampling distribution, the standard deviation represents the standard error of the sample mean

24
Q

True or false:

If the standard deviation of the sample means
from 10,000 random samples was about .03, when we select N = 1,071 participants from the population, the sample mean should differ from the unknown population mean by about .03 on average

A

True!

25
Q
  • PUT SLIDE 55 ON YOUR CHEAT SHEET *
A
  • PUT SLIDE 55 ON YOUR CHEAT SHEET *
26
Q

Suppose there are 100 participants in the sample.
There are 100 _____. Select all that apply

A. Sample means
B. Standard errors
C. Deviation scores
D. Sampling errors
E. Sample standard deviations

A

C. Deviation scores

27
Q

Suppose there are 100 participants in each sample. There are 200 samples. There are 200 _____. Select all that apply

A. Sample means
B. Standard errors
C. Deviation scores
D. Sampling errors
E. Sample standard deviations

A

A. Sample means
D. Sampling errors
E. Sample standard deviations

28
Q

Suppose there are 100 participants in each sample. There are 200 samples. There is one _____. Select all that apply

A. Sample mean
B. Standard error
C. Deviation score
D. Sampling error
E. Population mean

A

B. Standard error
E. Population mean

29
Q

Why would we use statistical theory instead of Monte Carlo computer simulation?

A

Estimating sampling error with simulation requires
that we specify the true mean and standard
deviation from the population

However, we don’t know the population mean and
we don’t have multiple datasets in practice!

Instead, we can use statistical theory and simple
equations to estimate sampling error based on a
single sample of data

30
Q

What is the central limit theorem?

A
  1. Estimates from many different samples approximates a normal distribution (this ALWAYS holds true for sampling distributions)
  2. The average of estimates equals the unknown population parameter
  3. The average amount of sampling error in the
    estimates (the standard error) is equal to:
    The standard error (AKA standard deviation of a sampling distribution (σX̄) = σ ÷ √N

This ^ formula assumes we know the population variability

31
Q

Estimate standard error - What we don’t know and what we do know:

A

The standard error formula from the central limit theorem assumes we know the population variability

In practice, we compute the standard error by substituting the sample standard deviation

SX̄ = the estimated standard error

We DO know this: SX̄ = S ÷ √N

We DON’T know this: σX̄ = σ ÷ √N

FOR EXAMPLE: Let’s say the sample standard deviation (s) is 1.11 and the number of people in the study (N) is 1071, the estimated standard error (SX̄) = 1.1 ÷ √1071 = 0.034. This means that the expected/average difference between the sample mean and the true population mean (amount by which the estimate is “off”) is estimated to be .034

  • You can only have one true standard error
32
Q

True or false: Even when the distribution of the population is not normal, the sampling distribution still
approximates a normal distribution.

A

True!

33
Q

What are the two factors influencing standard error?

A
  1. Sample size (N)
  2. Population standard deviation (σ)
34
Q

What will happen to the standard error if we decrease
the sample size from 1071 to 100?

A. Increase
B. Decrease
C. Keep the same

A

A. Increase

  • If you have a larger sample size you’ll have a smaller standard error. If you have a smaller sample size you’ll have a larger standard error.
  • If you see a histogram/density plot that’s long and flat it means there is more variability, most likely a smaller sample size (let’s say 100) and a larger standard error (let’s say .1)

BUT, if you see a histogram/density plot that’s short and pointy it means there is less variability, most likely a larger sample size (let’s say 1,071) and a smaller standard error (let’s say .03)

35
Q

If there are 10 participants in my study and there
are 100 participants in Ben’s study, we can say
that my sample mean and Ben’s sample mean
come from the same sampling distribution?

A. Yes
B. No

A

B. No

  • If they’re in the same sampling distribution they MUST have the same number of participants in each sample (if Han has N = 1,071 participants then so must Ben, Jordan, and Ega)
36
Q

What happens to the standard error if the
population variance/standard deviation
changes?

A

If the population variance/standard deviation goes up then the standard error will also go up. If the population variance/standard deviation goes down then the standard error will also go down.

37
Q

Which population will produce sample means
that are closer to the true population mean
(i.e., which will have a smaller standard error)?

A. SD=0.5
B. SD=1

A

A. SD=0.5

38
Q

True or false:

Samples with different population means, different population standard deviations, and different sample sizes come from the same sampling distribution.

A

False! They do not come from the same sampling distribution.

39
Q

Is deviation score for (select all that apply):

A: Sample distribution
B: Population distribution
C: Sampling distribution

A

A: Sample distribution
B: Population distribution

  • And you calculate it by subtracting the sample mean (X̄) or population mean (μ) from an individual score (x).

x - X̄ = deviation score
x - μ = deviation score

  • PUT THIS ON YOUR CHEAT SHEET!!!
40
Q

Is sample standard deviation for (select all that apply):

A: Sample distribution
B: Population distribution
C: Sampling distribution

A

A: Sample distribution

  • You can calculate a deviation score for each of the
    participants in your study (x - X̄). Once you’ve done that you can calculate the average of all the deviation scores (the average distance between the individuals’
    scores and the sample mean). This is your sample
    standard deviation (s).
  • PUT THIS ON YOUR CHEAT SHEET!!!
41
Q

Is population standard deviation for (select all that apply):

A: Sample distribution
B: Population distribution
C: Sampling distribution

A

B: Population distribution

  • If you have access to the entire population and happen to know the population mean (μ), you can calculate a deviation score for each of the
    participants in your study (x - μ). Once you’ve done that you can calculate the average of all the deviation scores (the average distance between the individuals’
    scores and the population mean). This is your population standard deviation (σ).
  • PUT THIS ON YOUR CHEAT SHEET!!!
42
Q

Is sampling error for (select all that apply):

A: Sample distribution
B: Population distribution
C: Sampling distribution

A

C: Sampling distribution

  • Once you have your sample mean (X̄) you can compare it to the population mean (μ), this is the sampling error.

This is the formula: Sampling error = X̄ - μ

Each researcher can have a different sampling error for their individual studies since each of their studies produces different sample means.

  • Remember that when we’re comparing multiple samples we ONLY focus on comparing sample means (X̄) - we no longer focus on individual scores (x)!!!

Remember that a sample mean is only an approximation of the population mean

  • PUT THIS ON YOUR CHEAT SHEET!!!
43
Q

Is standard error for (select all that apply):

A: Sample distribution
B: Population distribution
C: Sampling distribution

A

C: Sampling distribution

  • Standard error: The standard deviation of a sampling distribution is equal to the average amount of sampling errors
  • Think of this as the standard deviation of a sampling distribution (which compares MANY samples to the population mean).
  • So, if you were looking at a histogram/density plot for a sample distribution/population distribution you would be looking at the individual scores compared to the sample/population mean (deviation scores), and all of those deviation scores averaged out would equal the sample standard deviation/population standard deviation.

It’s exactly the same for a sampling distribution except now you’re comparing all the sample means to the population mean (sampling errors), and all of those sampling errors averaged out would equal the standard error (standard deviation of the sampling distribution).

  • It is the expected difference between the sample
    mean and the true population mean.
  • PUT THIS ON YOUR CHEAT SHEET!!!
44
Q

1000 researchers including me are interested in a new
depression treatment. Each of us recruited 100 participants and calculated the sample mean in each
study. In my study, the sample mean is 60 and Participant A’s depression score is 80. What is the difference between Participant A’s score and the sample mean (i.e., 80-60)?

A. Deviation score
B. Sample standard deviation
C. Population standard deviation
D. Sampling error
E. Standard error

A

A. Deviation score

45
Q

1000 researchers including me are interested in a new
depression treatment. Each of us recruited 100 participants and calculated the sample mean in each study. In my study, the sample mean is 60. I calculate the average distance between individual depression scores and the sample mean. What should I call this statistic?

A. Deviation score
B. Sample standard deviation
C. Population standard deviation
D. Sampling error
E. Standard error

A

B. Sample standard deviation

46
Q

If I have access to all individuals’ depression scores in the population, and I calculate the average distance between individual scores and the population mean, what should I call this statistic?

A. Deviation score
B. Sample standard deviation
C. Population standard deviation
D. Sampling error
E. Standard error

A

C. Population standard deviation

47
Q

1000 researchers including me are interested in a new depression treatment. Each of us recruited 100 participants and calculated the sample mean in each study. In my study, the sample mean is 60. I know the population mean is 65. What is the difference between my sample mean and the population mean (i.e., 60-65)?

A. Deviation score
B. Sample standard deviation
C. Population standard deviation
D. Sampling error
E. Standard error

A

D. Sampling error

48
Q

1000 researchers including me are interested in a new depression treatment. Each of us recruited 100
participants and calculated the sample mean in each
study. Then there are 1000 sample means. It indicates
that there are 1000___________. Select all that apply

A. Deviation scores
B. Sample standard deviations
C. Population standard deviations
D. Sampling errors

A

D. Sampling errors

49
Q

1000 researchers including me are interested in a new
depression treatment. Each of us recruited 100 participants and calculated the sample mean in each
study. Then there are 1000 sample means and sampling errors. What is the average amount of sampling errors?

A. Deviation score
B. Sample standard deviation
C. Population standard deviation
D. Sampling error
E. Standard error

A

E. Standard error

50
Q

1000 researchers including me are interested in a new
depression treatment. Each of us recruited 100 participants and calculated the sample mean. Then there are 1000 sample means. What is the average difference between these sample means and the true population mean?

A. Deviation score
B. Sample standard deviation
C. Population standard deviation
D. Sampling error
E. Standard error

A

E. Standard error

51
Q

1000 researchers including me are interested in a new depression treatment. Each of us recruited 100 participants and calculated the sample mean in each study. In my study, the sample standard deviation is 4. Based on my sample standard deviation and the
sample size, I calculated 4 ÷ √100. What is this?

A. Deviation score
B. Sample standard deviation
C. Population standard deviation
D. Sampling error
E. Estimated standard error

A

E. Standard error

Psych 100A - Psychological Statistics (26 decks)

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