1 / 16

Assignment: Read Chapter 21

Statistic for the day: Chance that a deep breath inhaled today will contain a molecule from Julius Caesar’s dying breath: 99%. Assignment: Read Chapter 21. These slides were created by Tom Hettmansperger and in some cases modified by David Hunter. Exam 3 results. The mean score was: 78.6

annalisan
Download Presentation

Assignment: Read Chapter 21

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. Statistic for the day:Chance that a deep breath inhaled today will contain a molecule from Julius Caesar’s dying breath: 99% Assignment: Read Chapter 21 These slides were created by Tom Hettmansperger and in some cases modified by David Hunter

  2. Exam 3 results The mean score was: 78.6 The median score was: 82.0 1 Student scored between 21% and 30% 2 Students scored between 31% and 40% 8 Students scored between 41% and 50% 13 Students scored between 51% and 60% 41 Students scored between 61% and 70% 50 Students scored between 71% and 80% 58 Students scored between 81% and 90% 61 Students scored between 91% and 100% (Total: 234 grades)

  3. Remember this slide? A General Strategy • Research Question or Hypothesis • Quantification • Measure something relevant • Count something relevant • Collect Data • Statistical Analysis • Conclusions and/or Action

  4. Suppose you feel that you have been cheated by the Pepsi dispensing machine in the dorm. • The machine promises 16 ounces. • Questions: • What is the true typical number of ounces? • Is the typical value less than stated on the machine? • Action: Dump the machine down the stairs The Pepsi Machine Before you take action: You should measure, collect data, analyze, make conclusion • 15, 15, 18, 17, 14, 13 Sample A • 14, 13, 12, 14, 15 , 14 Sample B

  5. Recast the Pepsi machine problem as a hypothesis test: • Research Advocate (the student) makes the hypothesis: • The machine is cheating: the mean amount dispensed • is less than the stated 16 oz. • The Skeptic (Pepsi machine guy?) makes the hypothesis: • Any variation from 16 oz is due to chance and not the machine cheating. • We want a decision rule to decide whether to believe • the machine is cheating or not.

  6. The Steps: • From the text: p374 • The basic steps for testing hypotheses: • Determine the null hypothesis and the alternative • hypothesis. • Collect and summarize the data and generate the • test statistic. • Determine how unlikely the test statistic is if • the null hypothesis is true. • 4. Make a decision.

  7. Determine the null hypothesis and the alternative • hypothesis. • The Research Advocate (the student) holds the research • hypothesis and this becomes the statistical alternative • hypothesis. • Namely, the machine is cheating. • The Skeptic (Pepsi machine guy) holds the null hypothesis. • Namely, the machine is ok.

  8. Collect and summarize the data and generate the • test statistic. • In the case of the Pepsi machine we have a data set: • 15, 15, 18, 17, 14, 13 Sample A • Summarize the data: mean = 15.3 oz, SD = 1.86 oz • and the sample size is 6. • Generate the test statistic: Measure the distance between • the sample mean of 15.3 oz and the machine promise of 16 oz. • SEM = SD/sqrt(sample size) = 1.86/sqrt(6) = .76 • TEST STATISTIC = (15.3 – 16)/.76 = -.92 • This tells us how many SEMs the sample mean is from 16 oz.

  9. Determine how unlikely the test statistic is if the null • hypothesis is true. So .18 represents how unlikely the test statistic is if the null hypothesis is true when Sample A is the data.

  10. Collect and summarize the data and generate the • test statistic. • In the case of the Pepsi machine we have a data set: • 14, 13, 12, 14, 15 , 14 Sample B • Summarize the data: mean = 13.7 oz, SD = 1.03 oz • and the sample size is 6. • Generate the test statistic: Measure the distance between • the sample mean of 13.7 oz and the machine promise of 16 oz. • SEM = SD/sqrt(sample size) = 1.03/sqrt(6) = .42 • TEST STATISTIC = (13.7 – 16)/.42 = -5.47 • This tells us how many SEMs the sample mean is from 16 oz.

  11. Determine how unlikely the test statistic is if the null • hypothesis is true. So 0 represents how unlikely the test statistic is if the null hypothesis is true and Sample B is the data.

  12. Make a decision. • Based on Sample A: • The test statistic is not very unlikey (.18). So the Skeptic • is correct. There is no evidence in Sample A that the • machine is dispensing less than 16 oz on the average. • Based on Sample B: • The test statistic is very unlikely ( about 0). So the • Research Advocate wins. There is strong evidence • in the data that the machine is cheating.

  13. Recall Step3: Determine how unlikely the test statistic is if the null hypothesis is true. The probability that we compute to see how unlikely the test statistic is is called the p-value. The p-value is the probability of committing a type 1 error. p-value = probability of rejecting the null hypothesis when the null hypothesis is true. p-value = probability of saying the Research Advocate is the winner when the Skeptic is correct.

  14. We decide who wins, the research advocate or the • skeptic, on the basis of the p-value • p-value = prob of type 1 error = prob Res. Adv. • is INCORRECTLY declared the winner. • If the p-value is small the Research Advocate wins. • If the p-value is not small the Skeptic wins (or more accurately, doesn’t lose). • What is small? • The scientific community has agreed to declare the • p-value small if it is less than or equal to .05. • This rule can be changed at any time by the researcher • and/or the consumer.

More Related