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.

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Confidence intervals
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
What a Confidence Interval Tells You

1. Range of values

2. Level of confidence

  • No hypothesis is directly tested


Confidence interval with z scores
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
How it Works

  • Start with your sample mean as the middle of the interval.

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


lower limit

upper limit

M



Example
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
APA Format Sentence

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


Confidence interval with t scores
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



Example1
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 sentence1
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
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



Example2
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 sentence2
APA Format Sentence

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


Changing the width of a confidence interval
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
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 error1
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


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