1. Introductory Statistics for Laboratorians dealing with High Throughput Data sets Centers for Disease Control

2. Evaluation of a Laboratory Diagnostic Procedure for Mycoplasma pneumoniae We believe that serum levels of the immunoglobulin M antibody may have diagnostic significance for identification of Mycoplasma pneumoniae. First thing we need to know is if people who have the pneumonia show higher serum levels of the antibody.

3. Experimental Design We will select two groups of subjects – Experimental Group: Persons with clinically defined pneumonia – Control Group: Asymptomatic cases We will draw serum samples from each person and evaluate the serum level of immunoglobulin M antibody in each sample.

4. Step 1: State the Null and Alternative Hypotheses H 0 : The mean serum level for the experimental group will not be different from the mean serum level for the control group (no difference/ nothing is happening) H a : The mean serum level for the experimental group will be different from the mean serum level for the control group (there is a real difference/ something is happening)

5. Select Statistical Test and Specify the Region of Rejection We will use a t-test for two independent samples We will have 20 people in each group (degrees of freedom = 38) We will reject the null hypothesis if the probability of it being true is less that 5 chances in 100 (alpha =.05)

6. Conduct Experiment and Collect Data Serum Levels of IgM Data Table SubjectControl GroupExperimental Group 15997 25775 36978 43085 53460 66875 76487 82787 97778 106293 116063 124776 136149 148380 158251 166276 175765 185766 195666 205665 Mean 58.6775.60 SD 17.5014.28

7. Compute the Test Statistic Group Statistics GroupNMeanStd. DeviationStd. Error Mean IgM Serum Level Control Group 2058.415.069663.369679 Experimental Group 2073.612.946852.895005

8. Compute the Test Statistic Independent Samples Test for IgM Serum Level Levene's Test for Equality of Variancest-test for Equality of Means FSig.tdf Sig. (2- tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference LowerUpper Equal variances assumed 0.000770.978001-3.4215380.001503-15.24.442498-24.1934-6.20663 Equal variances not assumed -3.421537.156440.001529-15.24.442498-24.2001-6.19992

9. Accept or Reject H 0 : As seen in the previous table, the probability that these two means are samples from the same population (that the difference is zero) is p =.001503 That is less than our chosen alpha =.05 Reject the Null hypothesis. Conclude that the experimental group has significantly higher serum levels of IgM

10. Effectiveness of a Program to Increase Seatbelt Use Among High School Seniors We have developed a program for use with High School seniors to increase seatbelt use and wish to determine if the program is effective.

11. Experimental Design The school has a separate parking lot of seniors. There is only one entrance and the students must swipe their ID to enter or leave the lot. A security camera positioned at the entrance photographs every driver as they enter and exit. This system has been in place for a couple of years.

12. Students and their parents will sign a release granting permission to participate in the study. Two weeks later, unannounced, we will begin reviewing the security camera data and recording the drivers ID and if he/she was wearing a seatbelt. We will record for 2 weeks before the program is presented. (Pretest) All seniors will then complete the course and accompanying workbook. Then we will record for another two weeks. (Posttest)

13. Each student who regularly drives to school during the period (must drive at least 3 days a week during both pretest and posttest) will become subjects in the experiment. Subjects score will be the percent of time they were wearing a seatbelt when they exited the gate – Number of times wearing seatbelt/number of times exiting * 100 We will have a pretest score and a posttest score for each person.

14. Step 1: State the Null and Alternative Hypotheses H 0 : The mean percent seatbelt usage on the posttest will not be different from the mean percent seatbelt usage on the pretest. (The program did nothing, nothing happened). H a : The mean percent seatbelt usage on the posttest will be different from the mean percent seatbelt usage on the pretest. (The program changed the seatbelt usage, it did something.)

15. Select Statistical Test and Specify the Region of Rejection We will use a t-test for paired samples – Paired samples = repeated measures = matched samples = pretest posttest We will reject the null hypothesis if the probability that it could be true is less than 5 chances in 100, ie: Alpha =.05 In this case we don’t know in advance how many subjects we will get so we can’t specify the degrees of freedom until after we finish data collection. That’s OK as long as you specify alpha.

16. Conduct Experiment and Collect Data Percent Seatbelt Use Data Table SubjectPretestPosttest 1100 2110 3028 410082 5418 60100 70 84050 98100 105586 11100 12035 13710 143938 1554100 164366 172450 182348 192147 201448 Mean 37.2059.30 SD 33.9435.15

17. Compute the Test Statistic Paired Samples Statistics MeanNStd. DeviationStd. Error Mean Pretest 37.22033.93747.588634 Posttest 59.32035.153957.860662

18. Compute the Test Statistic Paired Samples Test Paired Differences 95% Confidence Interval of the Differencet- test Mean Std. Deviation Std. Error MeanLowerUppertdf Sig.(2- tailed) Pair 1 Pretest - Posttest -22.142.376639.475703-41.9329-2.26713-2.33228190.030838

19. Accept or Reject H 0 : As seen in the previous table, the probability that these two means are samples from the same population (that the difference is zero) is p =.030838 That is less than our chosen alpha =.05 Reject the Null hypothesis. Conclude that the Posttest mean is significantly higher than the Pretest mean. The program significantly increased seatbelt usage among our Highschool Seniors.