1 / 27

Statistical Testing for Comparing Two Populations

Perform a significance test to compare two populations/groups and determine if there is a statistically significant difference between them. Estimate confidence intervals and margin of error for mean differences.

sonyal
Download Presentation

Statistical Testing for Comparing Two Populations

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. Ch. 10 Comparing Two Populations or Groups Ch. 10-2 Comparing Two Means

  2. less decay more decay Maybe, but it could be that we got this difference of means purely by chance. We need to perform a significance test.

  3. statistically significant? -value Assuming there’s no difference in decay, there is a ____________ probability of obtaining a value of or more purely by chance. This provides _____________ evidence, so we __________ conclude that the length of time in the ground does affect the breaking strength of the polyester specimen.

  4. N OR dist dist N OR dist dist

  5. N dist OR dist

  6. N dist OR dist

  7. true mean lap time for old tires (in seconds) true mean lap time for new tires (in seconds) We want to estimate the true difference at a confidence level.

  8. Two-sample interval for “SRS of 38 laps” and “SRS of 40 laps” Random: and , so by CLT the sampling distribution of is approximately normal. Normal: Independent: Two things to check: The two samples need to be independent of each other. Individual observations in each sample have to be independent. When sampling without replacement for both samples, must check 10% condition for both. We must assume the old lap times are independent from new lap times. We must also assume that Mr. Hussey has driven more than laps with the old tires and laps with the new tires.

  9. Estimate Margin of Error Standard Error Calculating degrees of freedom for two sample means: Option 1: Use calculator (2-SampTInt). Actual formula is: Option 2: (conservative approach) Use the smaller of and .

  10. Estimate Margin of Error smaller Option 1 Option 2 With calculator: STAT  TESTS  2-SampTInt (0) or use -table Inpt: Data Stats x1: Sx1: n1: x2: Sx2: n2: C-Level: Pooled: No Yes ALWAYS do no pooled for procedures

  11. We are confident that the interval from to captures the true difference in means of mean lap times between the old and new tires. This suggests that the mean lap time with the old tires is between and seconds longer than the mean lap time with the new tires. Yes, because is NOT captured in the interval.

  12. two-sample No, this is not a matched pairs design. Use 1 Var-Stats on each list to find and . true mean ACT score for students who take “smart pill” true mean ACT score for students who take placebo We want to estimate the true difference at a confidence level.

  13. Two-sample interval for “10 student chosen at random are given the ‘smart pill’” and “8 students chosen at random are given a placebo” Random: Both population distributions are normal so the sampling distribution of is approximately normal. Normal: Independent: Two things to check: The two groups need to be independent of each other. Individual observations in each group have to be independent. When sampling without replacement for both samples, must check 10% condition for both. Due to random assignment, these two groups can be viewed as independent. No 10% condition since there was no sampling. Individual observations in each group should also be independent: knowing one subject’s ACT score gives no information about another subject’s ACT score.

  14. Estimate Margin of Error smaller Option 1 Option 2 We can use the “data” option now since our data is in lists. or use -table With calculator: STAT  TESTS  2-SampTInt (0) Inpt: Data Stats List1: List2: Freq1: Freq2: C-Level: Pooled: No Yes ALWAYS do no pooled for procedures

  15. We are confident that the interval from to captures the true difference in means for ACT scores between kids given a smart pill and kids given a placebo. This suggests that the “smart pill” may improve scores by up points or the placebo may improve scores by up points. Answer key will use conservative approach for degrees of freedom.

  16. one sided State: true mean ACT score for students who take “smart pill” true mean ACT score for students who take placebo OR OR

  17. Plan: Two sample test for “10 student chosen at random are given the ‘smart pill’” and “8 students chosen at random are given a placebo” Random: Both population distributions are normal so the sampling distribution of is approximately normal. Normal: Independent: Two things to check: The two groups need to be independent of each other. Individual observations in each group have to be independent. When sampling without replacement for both samples, must check 10% condition for both. Due to random assignment, these two groups can be viewed as independent. No 10% condition since there was no sampling. Individual observations in each group should also be independent: knowing one subject’s ACT score gives no information about another subject’s ACT score.

  18. Do: Sampling Distribution of conservative approach: N smaller cdf -value

  19. Conclude: Assuming is true , there is a probability of obtaining a value of or more purely by chance. This provides weak evidence against and is not statistically significant at level . Therefore, we fail to reject and cannot conclude that the smart pill increases ACT scores. With calculator: STAT  TESTS  2-SampTTest (4) -value Inpt: Data Stats List1: List2: Freq1: Freq2: : Pooled: No Yes ALWAYS do no pooled for procedures

  20. experiment Yes Not a random sample, so conclusion only holds for the people in the experiment What population can we target?

  21. matched pairs Yes, since it’s a matched pairs design. Very important to know when you use a matched pairs test for or a two sample test for If groups were formed using a completely randomized design: two-sample test for If subjects were paired, then split at random into two treatments or if each subject receives both treatments: matched pairs test for

  22. We will do (smart – placebo) so that + values represent pill worked Differences Use 1 Var-Stats State: true mean difference (smart pill – placebo) in test scores Plan: Matched pairs T test for Random: Treatments were randomized Population distribution is normal so the sampling distribution of is approximately normal. Normal: Independent: There are more than students at ECRCHS.

  23. Do: Sampling Distribution of N area = tcdf -value

  24. Conclude: Assuming is true , there is a probability of obtaining a value of or higher purely by chance. This provides strong evidence against and is statistically significant at level . Therefore, we reject and canconclude that the smart pills work. experiment Yes All ECRCHS students

  25. Two sample test for Matched pairs test for more less Equal

More Related