CONFIDENCE INTERVALS - PowerPoint PPT Presentation

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CONFIDENCE INTERVALS. point estimate : estimate exact value precise likely to be wrong interval estimate : range of values less precise less likely to be wrong. What a Confidence Interval Tells You. 1. Range of values 2. Level of confidence No hypothesis is directly tested.

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CONFIDENCE INTERVALS

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CONFIDENCE INTERVALS

• point estimate: estimate exact value

• precise

• likely to be wrong

• interval estimate: range of values

• less precise

• less likely to be wrong

What a Confidence Interval Tells You

1. Range of values

2. Level of confidence

• No hypothesis is directly tested

Confidence Interval with z- scores

• Purpose: provide a range of values containing the population mean

• Design: any design where a mean is calculated

• Assumptions: same as for z-test

How it Works

• Establish upper and lower limits depending on how confident you want to be.

lower limit

upper limit

M

Example

A sample of 25 students took an aptitude test with a population standard deviation of 40. The mean of the 25 students was 500. Compute the 95% confidence interval for the mean.

STEP 1: Compute the standard error.

STEP 2: Find the z score for your confidence level.

For 95% confidence, use z = 1.96

For 99% confidence, use z = 2.58

z = 1.96

STEP 3: Compute the lower and upper limits.

APA Format Sentence

The 95% confidence interval for the mean aptitude test score was 484.32 - 515.68.

Confidence Interval with t- scores

• Purpose: provide a range of values containing the population mean

• Design: any design where a mean is calculated

• Assumptions: same as for single sample t-test

Example

64 research participants were timed on a motor task. Their mean time was 20 sec, with s = 4.00. Compute the 99% confidence interval for the mean.

STEP 1: Compute the standard error.

• STEP 2: Find the t score for your confidence level. Look up two-tailed t in table, using df = N-1, and 1- level of confidence for a.

• df = 64-1=63

• a = 1-.99=.01

• two-tailed t = 2.660

STEP 3: Compute the lower and upper limits.

APA Format Sentence

The 99% confidence interval for the mean time to complete the task was 20 sec +/- 1.33.

Confidence Interval for a Proportion

• Purpose: provide a range of values containing the population proportion

• Design: any design where a proportion or percent is calculated

• Assumptions:

• representative sample

• independent observations

Example

A sample of 500 registered voters rated how well the President is doing his job. The proportion who gave him a “good” rating was .52, or 52%. Compute the 95% confidence interval for the proportion.

STEP 1: Compute the standard error.

• STEP 2: Find the z score for your confidence level.

• For 95% confidence, use z = 1.96

• For 99% confidence, use z = 2.58

• z = 1.96

STEP 3: Compute the lower and upper limits.

APA Format Sentence

The 95% confidence interval for the proportion of “good” ratings was .52 +/- .04.

Changing the Width of a Confidence Interval

• A wider interval is less precise and therefore less informative.

• The interval will be narrower with

• a larger sample

• lower variability

• a lower level of confidence

Margin of Error

• The media often report poll results and include margin of error. This is the +/- part, usually in fine print.

• Add and subtract the margin of error to get the confidence interval

Margin of Error

• Can be used as an indirect test of significance

• Construct confidence interval around sample statistic using margin of error

• If interval includes Ho value, difference is not significant