Estimation-Based Interference

Question 1

What is statistical inference?

Answer 1

We use information from a sample to make inference about the population

Descriptive statistics relate to the sample

Inferential statistics relate to the population

We infer properties of the population by using sample statistics to derive estimates of population parameters and test hypotheses

When making inference from a sample we need to account for uncertainty in our sample estimates

Question 2

What is the central limit theorem?

Answer 2

If we were to take repeat samples and calculate the mean each time…

Those sample means will be Normally distributed around the true population mean

…even if the population itself is not Normally distributed

Question 3

What is standard error?

Answer 3

The standard error is a type of standard deviation
(It is the standard deviation of the sampling distribution)
(Both are measures of spread)

Question 4

What does standard error indicate?

Answer 4

The standard error indicates how different a sample mean is likely to be from the population mean

It tells us the precision of estimation

The smaller the standard error of the mean, the more precise our estimate of the mean

Question 5

How do you calculate standard error?

Answer 5

We estimate the standard error using our sample size (n) and standard deviation (SD)

Standard error of the mean = SD/√n

Question 6

What is standard error affected by?

Answer 6

This means our precision is affected by these two things: how variable our data are (the SD) and how large our sample is (n)

The other thing being held constant…
The bigger the SD, the bigger the standard error
The bigger the sample size, the smaller the standard error

Question 7

What is confidence interval?

Answer 7

Use sample mean, standard error of the mean and properties of the Normal distribution to calculate a range of values we can be confident includes the true mean

Question 8

What factors affect confidence interval width?

Answer 8

Factors affecting confidence interval width:
Variability in the sample (SD)
Sample size (n)
The desired level of confidence
- typically we use 95% but it could be 90%, 99%, etc.

As with SE:
Greater variability = wider interval
Greater sample size = narrower interval
And in addition, greater confidence level = wider interval