Chapter 11 estimation
This presentation is the property of its rightful owner.
Sponsored Links
1 / 32

Chapter 11: Estimation PowerPoint PPT Presentation


  • 37 Views
  • Uploaded on
  • Presentation posted in: General

Chapter 11: Estimation. Motivating Example. Research Question : What proportion of all currently-housed U.S. adults ever experienced homelessness? Research Study* Random sample of 1,507 currently-housed adults in the U.S. Proportion of the sample who ever experienced homeless was 0.14.

Download Presentation

Chapter 11: Estimation

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Chapter 11 estimation

Chapter 11: Estimation


Motivating example

Motivating Example

  • Research Question: What proportion of all currently-housed U.S. adults ever experienced homelessness?

  • Research Study*

    • Random sample of 1,507 currently-housed adults in the U.S.

    • Proportion of the sample who ever experienced homeless was 0.14

*Link, B. et al. (1994). “Lifetime and five-year prevalence of homelessness in the United States.” American Journal of Public Health, 84, 1907-1912.


Motivating example1

Motivating Example

  • Question 1: What is our best guess about the proportion of all currently-housed U.S. adults who ever experienced homelessness?

    • Answer: 0.14

    • Comment: This is called a point estimate

  • Question 2: How good is our guess?

    • Answer: We are fairly sure that the true proportion is between 0.13 and 0.15

    • Comment: This is called an interval estimate


Estimation

Estimation

  • Estimation: Using a sample statistic to estimate a population parameter

    • This is our ultimate goal in statistics!

  • Point Estimate: A sample statistic that is used to estimate the value of a population parameter

    • It is our “best guess” as to what’s going on in the population

  • Interval Estimate (Confidence Interval): A range of values within which the population parameter may fall

    • This gives us an idea about the accuracy of our point estimate


Confidence interval

Confidence Interval

  • Piece 1: Point estimate

    • We can use proportions or means

    • Calculated from the sample

    • You will be given this in class

  • Piece 2: Standard error of the point estimate

    • Calculated from the sample

    • You will have to calculate this

  • Piece 3: Confidence level

    • Defined based on a z-statistic from the normal distribution


Confidence level

Confidence Level

  • Definition: The likelihood that a given confidence interval will contain the population parameter

  • Example: 95% Confidence Level

    • We are 95% confident that a specific interval contains the population parameter


Confidence level1

Confidence Level

  • Z-Statistic: We use a z-statistic from the normal distribution to define the confidence level

    • This is true when N > 50

    • We are applying the central limit theorem!

  • Common Confidence Levels:


Confidence interval for a proportion

Point Estimate: Sample proportion (p)

This is an estimate of the population proportion (π)

Standard Error:

Z-Statistic: See Slide 7

Confidence Interval for a Proportion


Confidence interval for a proportion1

Confidence Interval: Mathematical Formulas

Lower Limit: p – (Z·SE)

Upper Limit: p + (Z·SE)

Confidence Interval: Pictorial Representation

Confidence Interval for a Proportion


Confidence interval for a proportion2

Example: From Slide 2

Sample Size: N = 1,507

Sample Proportion: p = 0.14

Standard Error:

Confidence Interval for a Proportion


Confidence interval for a proportion3

90% Confidence Interval:

Interpretation: We are 90% confident that the proportion of all currently-housed U.S. adults who ever experienced homelessness is between 0.13 and 0.15

Confidence Interval for a Proportion

I’m the Point Estimate

Lower Limit

Upper Limit


100 confidence interval for a proportion

Confidence Interval: 0 to 1

Reasoning: The only way we can be 100% confident is by considering every possible value from 0 to 1

100% Confidence Interval for a Proportion


Confidence interval for a proportion factors affecting width

Confidence Interval for a Proportion: Factors Affecting Width

  • Sample Size

    • Effect: As the sample size increases, the confidence interval gets smaller (more precise)

      • This is holding the proportion and confidence level constant

    • Why? The standard error (SE) decreases as the sample size increases

    • Examples: See diagram on the next slide


Confidence interval for a proportion factors affecting width1

Confidence Interval for a Proportion: Factors Affecting Width


Confidence interval for a proportion factors affecting width2

Confidence Interval for a Proportion: Factors Affecting Width

  • Level of Confidence

    • Effect: As the level of confidence increases, the confidence interval gets larger (less precise)

      • This is holding the proportion and sample size constant

    • Why? The Z-statistic increases as the level of confidence increases

    • Examples: See diagram on the next slide


Confidence interval for a proportion factors affecting width3

Confidence Interval for a Proportion: Factors Affecting Width


Margin of error moe

MoE: In the news, you will often see poll results and a “margin of error”

Calculation:

It includes the standard error assuming p = 0.50

It is based on a z-statistic of 1.96 (rounded up to 2)

Derivation: For the math-geek types

Margin of Error (MoE)


Margin of error moe1

Use: Construct a 95% confidence interval from the point estimate and the MoE

95% Confidence Interval: Mathematical Formulas

Lower Limit: p – MoE

Upper Limit: p + MoE

95% Confidence Interval: Pictorial Representation

Margin of Error (MoE)


Margin of error moe example dizziness from rozerem

Situation: In a clinical trial for Rozerem (a sleep aid), 6% of the 1,250 participants experienced dizziness

Margin of Error:

Margin of Error (MoE) Example:Dizziness From Rozerem


Margin of error moe example dizziness from rozerem1

95% Confidence Interval:

Interpretation: We are 95% confident that, among all people who take Rozerem, the proportion who will experience dizziness is between 0.03 and 0.09

Margin of Error (MoE) Example:Dizziness From Rozerem


Confidence interval for a mean

Point Estimate: Sample mean ( )

This is an estimate of the population mean (μ)

Standard Error:

Z-Statistic: See Slide 7

Confidence Interval for a Mean


Confidence interval for a mean1

Confidence Interval: Mathematical Formulas

Lower Limit: – (Z·SE)

Upper Limit: + (Z·SE)

Confidence Interval: Pictorial Representation

Confidence Interval for a Mean


Example of confidence interval for a mean tv watching

Research Question: On average, how many hours a day do all Texas children ages 2-18 spend watching TV?

Sample: From a sample of N = 749 children, the mean hours spent watching TV was with a standard deviation of S = 2.97

Example of Confidence Interval for a Mean: TV Watching


Example of confidence interval for a mean tv watching1

Goal: Calculate and interpret a 99% confidence interval

Standard Error:

Example of Confidence Interval for a Mean: TV Watching


Example of confidence interval for a mean tv watching2

99% Confidence Interval:

Interpretation: We are 99% confident that the average time spent watching TV among all Texas children ages 2-18 is between 3.26 and 3.82 hours

Example of Confidence Interval for a Mean: TV Watching

I’m the Point Estimate

Lower Limit

Upper Limit


100 confidence interval for a mean

Confidence Interval: -∞ to +∞

Reasoning: The only way we can be 100% confident is by considering every possible value from -∞ to +∞

100% Confidence Interval for a Mean


Confidence interval for a mean factors affecting width

Confidence Interval for a Mean: Factors Affecting Width

  • Sample Size

    • Effect: As the sample size increases, the confidence interval gets smaller (more precise)

      • This is holding the mean, standard deviation, and confidence level constant

    • Why? The standard error (SE) decreases as the sample size increases

    • Examples: See diagram on the next slide


Confidence interval for a mean factors affecting width1

Confidence Interval for a Mean: Factors Affecting Width


Confidence interval for a mean factors affecting width2

Confidence Interval for a Mean: Factors Affecting Width

  • Standard Deviation

    • Effect: As the standard deviation increases, the confidence interval gets larger (less precise)

      • This is holding the mean, sample size, and confidence level constant

    • Why? The standard error (SE) increases as the standard deviation increases

    • Examples: See diagram on the next slide


Confidence interval for a mean factors affecting width3

Confidence Interval for a Mean: Factors Affecting Width


Confidence interval for a mean factors affecting width4

Confidence Interval for a Mean: Factors Affecting Width

  • Level of Confidence

    • Effect: As the level of confidence increases, the confidence interval gets larger (less precise)

      • This is holding the mean, standard deviation, and sample size constant

    • Why? The Z-statistic increases as the level of confidence increases

    • Examples: See diagram on the next slide


Confidence interval for a mean factors affecting width5

Confidence Interval for a Mean: Factors Affecting Width


  • Login