Test 2: Chapter 7

How do you represent standard error in graphs?

The bracket extends 1 standard error above and below the sample mean. M +/- SE You can use bar graphs, or line graphs.

What is a distribution of sample means?

The collection of sample means for all the possible random samples of a particular size (n) that can be obtained from a population.

How does sampling error relate to a distribution of sample means?

The distribution of sample means typically does not represent it's population perfectly accurately. It is the discrepancy between the sample mean and the population mean.

What distribution do you use when you have a probability question about a sample mean?

The distribution of sample means.

What is the law of large numbers?

The larger the sample size (n), the more probable it is that the sample mean will be close to the population mean.

What is the expected value of M?

The mean of the distribution of sample means is equal to the mean of the population of scores, μ, and is called the expected value of M.

According to central limit theorem, what n will make a distribution of sample means look almost totally normal?

n=30

We can use a distribution of sample means to predict ____.

sample characteristics

If you view a sample as a "measurement" of a population, then a ___ is a measurement of a population mean.

sample mean

A distribution of statistics is often referred to as a _____.

sampling distribution

Name the 2 main uses of a distribution of sample means.

1) Determining the probability of obtaining an M of a particular value, when selecting a sample with a specified n from a population 2) Using the z-scores to determine the probability of randomly selecting a sample mean of a given value.

What 3 different distributions do we deal with in this chapter? What qualities do they have?

1) Original population of scores 2) Sample selected from the population 3) Distribution of sample means They're interrelated.

The distribution is almost perfectly normal if either of the 2 conditions is satisfied:

1) The population is normal 2) The # of scores is relatively large, around 30+.

The standard error of the mean measures the difference between 1) and 2).

1) difference between sample means from one sample to another 2) measures the distance between the sample mean and the overall mean for a distribution of sample means (μ)

Traits of a distribution of sample means: 1) Sample means should ___. 2) Pile of sample means should resemble a ___. 3) The larger the ___, the closer the sample means should be to the ___. It will also have a lower ___.

1) pile up around the population mean. Not perfect, but representative of the population 2) normal-shaped distribution 3) sample size, population mean, variance

Define sampling distribution.

A distribution of statistics obtained by selecting all the possible samples of a specific size from the population.

What is central limit theorem?

A mathematical theory that allows us to estimate the complete distribution of sample means for any sample of a given size, n, drawn from a population. - Shape, expected value of M, and standard error of M For any population, the distribution of sample size n will have a mean of μ and a standard deviation of σ/√n. It will approach a normal distribution as n approaches infinity.

What distributions does a central limit theorem apply to?

It describes a distribution of sample means for any population, no matter its shape, mean, or standard deviation!

According to central limit theorem, when will a distribution of sample means approach a normal distribution?

It will approach a normal distribution as n approaches infinity.

What is μM?

It's also used instead of μ for a distribution of sample means. Often μ is used because they're usually the same.

How do you report standard error in a journal? Do you say the standard deviation?

SE or SEM is used for standard error You report the standard error for a sample mean, rather than standard deviation.

The natural discrepancy, or amount of error, between a sample statistic and its corresponding population parameter.

Sampling error

The magnitude of the standard error is determined by 2 factors: 1) ___ and 2) ___.

Size of the sample (larger samples mean less standard error) Standard deviation of the population

Standard error decreases in relation to the ____ of the sample size.

Square root. It's why n=30 substantially reduces error.

What is a good indication that lets researchers know how accurately their sample data represent the population they're studying?

Standard error

What measures how well a sample mean represents the entire distribution?

Standard error of M

What is the standard error of M?

The standard deviation of sample means, σM, is called the standard error of M. The standard error provides a measure of how much distance is expected on average between a sample mean (M) and the population mean (μ)

What is the standard deviation for the distribution of sample means?

The standard error of M

How does standard error relate to a distribution of sample means?

The standard error provides a way to measure the "average" (standard) distance between a sample mean and the population mean.

What formula allows us to find the exact location of a sample mean within a distribution of sample means?

The z-score formula.

What do infants know about probability?

They are able to know the expected outcome vs. an unexpected outcome. E.g. reach into a bag of mostly white balls and getting a pink one.

What is the primary use of the distribution of sample means?

To find the probability associated with a specific sample.

What is the largest standard error?

When n = 1. Standard error = σ Because the sample is a single score, the distribution of sample scores is identical to the original distribution of scores.

When would you use the central limit theorem?

When you have a large population, so that you don't have to manually select hundreds of samples.

When do you need to be using the standard error?

Whenever you work with a sample mean.

Will the distribution of sample means be normal, regardless of original population?

Yes

Can you use standard error, even when you don't know the population mean?

Yes!

To find the probability of a sample mean, you must know ___.

all possible sample means

The difference between samples and populations always have a ____ of uncertainty and error in all inferential processes

degree

Two samples are likely to be ____ from one another

different

Researchers, using standard error, can determine if they need to increase the ___ to increase the reliability.

sample size

The standard error defines the relationship between ___, and the accuracy w/ which ___ represents μ.

sample size M

a distribution of sample means is an example of a ___.

sampling distribution. It is also equivalent to a sampling distribution of M.

Standard error is a way of defining and measuring ___.

sampling error

A large standard error of M means the sample means are ____.

scattered

Central limit theorem describes the distribution of sample means by identifying 3 basic characteristics: ___, ___ and ___.

shape, central tendency (expected value of M), and variability (standard error of M)

___ can be viewed as a measure of the reliability of a sample mean.

standard error

Standard deviation is the ___ of the standard error. Larger sample results in smaller standard error.

starting point

The sample mean is an example of an ___, and on average the sample statistic produces a value exactly equal to the ___.

unbiased statistic population parameter, μ

Large standard error = ____

unreliable measure of the population

If all samples have similar results, you can be confident that...

your results are a fair representation of the population.

What is the formula for standard error?

σ/√n This formula is also mentioned in the central limit theorem. You can incorporate variance into this equation, too, with √σ^2 / n