Week 2: Confidence Intervals and Estimation

Question 1

What do we use as a point estimate?

Answer 1

We use the statistic from a sample as a point estimate for a population parameter

Question 2

Will point estimates match our population parameters?

Answer 2

Point estimates will not match population parameters exactly, but they are out best guess.

Question 3

What are interval estimates?

Answer 3

Estimates that give a range of plausible values for a population parameter.

Question 4

When are values most plausible?

Answer 4

Close to the point estimate = more plausible

Question 5

When are values less plausible?

Answer 5

Far from the point estimate = less plausible

Question 6

What is the margin of error?

Answer 6

One common form for an interval estimate is statistic ± margin of error

Question 7

What does the margin of error reflect?

Answer 7

The margin of error reflects the precision of the sample statistic as a point estimate for the parameter.

Question 8

Margin of Error question example… An ICM poll for the Guardian gave NO a lead of 51% to 49% (Scotland independence).
Polls in the news often have a margin of error of around 3%. In the absence of further information, assume a margin of error of 3%

Answer 8

51% ± 3% = [48%, 54%]

Question 9

How do we determine the margin of error?

Answer 9

We can use the standard deviation of the sampling distribution (the standard error) to determine the margin of error for a statistic

Question 10

What is the relationship between standard deviation of the sampling distribution and the margin of error?

Answer 10

The higher the standard deviation of the sampling distribution, the higher the margin of error.

Question 11

What is a confidence interval?

Answer 11

A confidence interval for a parameter is an interval computer form a sample data by method that will capture the parameter for a specified proportion of all samples.

Question 12

What is the confidence level?

Answer 12

The success rate (proportion of all samples whose intervals contain the parameter) is known as the confidence level

Question 13

What will a 95% confidence interval contain?

Answer 13

A 95% confidence interval will contain the true parameter for 95% of all samples

Question 14

What is the 95% confidence interval?

Answer 14

95% Confidence Interval: If the sampling distribution is relatively symmetric and bell-shaped, a 95% confidence interval can be estimated using statistic ± 2 x SE (statistic ± margin of error).

Question 15

What does 95% confidence interval mean in terms of getting it wrong?

Answer 15

95% CI means you are going to be wrong 5 out of 100 times. Or 1 in 20. Also, you won’t normally know when you are wrong, only how often you will be wrong

Question 16

Why do we use 95%? (five points)

Answer 16

• History
• Common standard in psychology
• Subjectively 1 in 20 seems “rare”
• 1 in 10 (90% CI) not very rare
• Consequences of being wrong 1 in 20 times are not usually severe

Question 17

When and how will a 68.3% confidence interval be estimated?

Answer 17

If the sampling distribution is relatively symmetric and bell-shaped, a 68.3% confidence interval can be estimated using statistic ± 1 x SE.

Question 18

Example of how we can interpret a confidence interval?

Answer 18

“We are 95% confident that the true proportion of all Scottish people that will vote against independence is between 47.9% and 54.1%”

Question 19

Example of reporting confidence intervals APA style?

Answer 19

Participants who heard one James Blunt song on repeat for 180 minutes reported a greater level of anxiety (M = 15.1, SD = 3.2) compared with those who heard one Mozart movement on repeat, 95% CI [11.1, 19.1].

Question 20

Two examples of MISINTERPRETATIONS of confidence intervals?

Answer 20

Misinterpretation 1: “A 95% confidence interval contains 95% of the data in the population”
Misinterpretation 2: “I am 95% sure that the mean of a sample will fall within a 95% confidence interval for the mean”

Question 21

Confidence interval diagram?

Answer 21

On slide 54 of week 2… VERY IMPORTANT