1 / 12

Testing Differences Between Two Population Proportions in Statistical Analysis

This lecture covers the methodologies for testing the differences between two population proportions, akin to testing one proportion. It establishes hypotheses (H0: p1 - p2 = 0) and involves two large samples from distinct populations. Additionally, the lecture delves into comparing dependent samples through a matched pairs approach, using practical examples of students' performance before and after special training. Key statistical concepts including confidence intervals, hypothesis testing, and sample means are explored to illustrate the techniques used in real-world assessments.

tocho
Download Presentation

Testing Differences Between Two Population Proportions in Statistical Analysis

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. STA 291Summer 2010 Lecture 21 Dustin Lueker

  2. Testing Difference Between Two Population Proportions • Similar to testing one proportion • Hypotheses are set up like two sample mean test • H0:p1-p2=0 • Same as H0: p1=p2 • Test Statistic STA 291 Summer 2010 Lecture 21

  3. Testing the Difference Between Means from Different Populations • Hypothesis involves 2 parameters from 2 populations • Test statistic is different • Involves 2 large samples (both samples at least 30) • One from each population • H0: μ1-μ2=0 • Same as H0: μ1=μ2 • Test statistic STA 291 Summer 2010 Lecture 21

  4. Comparing Dependent Samples • Comparing dependent means • Example • Special exam preparation for STA 291 students • Choose n=10 pairs of students such that the students matched in any given pair are very similar given previous exam/quiz results • For each pair, one of the students is randomly selected for the special preparation (group 1) • The other student in the pair receives normal instruction (group 2) STA 291 Summer 2010 Lecture 21

  5. Example (cont.) • “Matches Pairs” plan • Each sample (group 1 and group 2) has the same number of observations • Each observation in one sample ‘pairs’ with an observation in the other sample • For the ith pair, let Di = Score of student receiving special preparation – score of student receiving normal instruction STA 291 Summer 2010 Lecture 21

  6. Comparing Dependent Samples • The sample mean of the difference scores is an estimator for the difference between the population means • We can now use exactly the same methods as for one sample • Replace Xi by Di STA 291 Summer 2010 Lecture 21

  7. Comparing Dependent Samples • Small sample confidence interval Note: • When n is large (greater than 30), we can use the z-scores instead of the t-scores STA 291 Summer 2010 Lecture 21

  8. Comparing Dependent Samples • Small sample test statistic for testing difference in the population means • For small n, use the t-distribution with df=n-1 • For large n, use the normal distribution instead (z value) STA 291 Summer 2010 Lecture 21

  9. Example • Ten college freshman take a math aptitude test both before and after undergoing an intensive training course • Then the scores for each student are paired, as in the following table STA 291 Summer 2010 Lecture 21

  10. Example STA 291 Summer 2010 Lecture 21

  11. Example • Compare the mean scores after and before the training course by • Finding the difference of the sample means • Find the mean of the difference scores • Compare • Calculate and interpret the p-value for testing whether the mean change equals 0 • Compare the mean scores before and after the training course by constructing and interpreting a 90% confidence interval for the population mean difference STA 291 Summer 2010 Lecture 21

  12. Reducing Variability • Variability in the difference scores may be less than the variability in the original scores • This happens when the scores in the two samples are strongly associated • Subjects who score high before the intensive training also tend to score high after the intensive training • Thus these high scores aren’t raising the variability for each individual sample STA 291 Summer 2010 Lecture 21

More Related