1 / 13

Inference and Confidence Intervals

Inference and Confidence Intervals. Outline. Inferring a population mean : Constructing confidence intervals Examining the difference between two means for the same p erson Confidence intervals for the difference between groups Confidence intervals for medians Summary.

paige
Télécharger la présentation

Inference and Confidence Intervals

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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Inference and Confidence Intervals

  2. Outline • Inferring a population mean: Constructing confidence intervals • Examining the difference between two means for the same person • Confidence intervals for the difference between groups • Confidence intervals for medians • Summary

  3. Constructing Confidence Intervals • Population μ (pronounced mu) • Estimate with sample mean ( ), the plug-in principle • But with sampling error. Estimating the region which will usually include the population mean. • t0.05is usually about 2, but you need to look it up the t table. • Need to know df. df = n - 1 for this test. Here 94 - 1 = 93.

  4. Example: Newton's (1998) Hostility Data • The mean on arrival for the 94 prisoners was 28.3 with a standard deviation of 8.0. • df = n-1 so 93, or about 90 for the t table

  5. t distribution with df = 93 and 2.5% in each tail

  6. What does having 95% CI of 28.3 ± 1.6 mean? We expect that about 95% of the time when a confidence interval is made that the population mean (μ) will be within the interval created. This allows us to be fairly confident that the confidence interval we calculate contains the population mean. It is not that there is a 95% probability that μ is within the interval. This is a tricky concept. Confidence intervals are a fundamental tool for the frequentist statistician. In the long run, you should be right (i.e., μ with the interval) about 95% of the time.

  7. Plotting the precision of the estimate (confidence intervals) and the spread of the distribution (standard deviations).Both are in units of the original variable (here in years).

  8. Examining the Difference between Two Means for the Same Person • Difference in means ± t0.05times standard error • Standard error of difference using estimate of the standard deviation of the difference. • Just calculate a variable for the difference, and perform the calculations as you did before.

  9. Brewed Awakeningshttp://mybrewedawakening.com/ • Table 5.1  Data from 10 participants comparing how much they like two different types of coffee. • FRESHi INSTANTi DIFFi DIFFi- (DIFFi- ) 2 • 5 3 2 1 1 • 4 3 1 0 0 • 6 5 1 0 0 • 3 4 -1 -2 4 • 4 4 0 -1 1 • 5 3 2 1 1 • 6 3 3 2 4 • 3 3 0 -1 1 • 5 3 2 1 1 • 4 4 0 -1 1 • Sum 45 35 10 0 14 • Mean 4.5 3.5 1.0 0 1.56* • * This 1.56 is not the actual mean. It is the variance of the variable DIFFi, the sum of squares divided by the number of cases minus one (14/9). We calculated it this way because it can be used in later calculations. • ________________________________________________________________________

More Related