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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
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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 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)
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
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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
