Week 2: Confidence Intervals and Estimation Flashcards

1
Q

What do we use as a point estimate?

A

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

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2
Q

Will point estimates match our population parameters?

A

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

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3
Q

What are interval estimates?

A

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

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4
Q

When are values most plausible?

A

Close to the point estimate = more plausible

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5
Q

When are values less plausible?

A

Far from the point estimate = less plausible

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6
Q

What is the margin of error?

A

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

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7
Q

What does the margin of error reflect?

A

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

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8
Q

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%

A

51% ± 3% = [48%, 54%]

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9
Q

How do we determine the margin of error?

A

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

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10
Q

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

A

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

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11
Q

What is a confidence interval?

A

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.

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12
Q

What is the confidence level?

A

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

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13
Q

What will a 95% confidence interval contain?

A

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

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14
Q

What is the 95% confidence interval?

A

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).

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15
Q

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

A

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

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16
Q

Why do we use 95%? (five points)

A
  • 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
17
Q

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

A

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

18
Q

Example of how we can interpret a confidence interval?

A

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

19
Q

Example of reporting confidence intervals APA style?

A

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].

20
Q

Two examples of MISINTERPRETATIONS of confidence intervals?

A

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”

21
Q

Confidence interval diagram?

A

On slide 54 of week 2… VERY IMPORTANT