Hypothesis Testing - Matched Pairs t-test - ncssm

JILA Project NCSSM Stat Institute – July 2001JMP INTRO ® Lab ActivitiesLab Activity – Hypothesis Testing – Matched Pairs t-testData Set: THERM.jmpA health care center recently purchased a new eardrum probe thermometer, whichprovides an easier way to measure patients’ temperatures than the standard oral mercurythermometer. The nurses suspected, however, that the new device gave readings thatwere consistently higher than with the old method. To test this, readings were taken onsome patients twice, once with the eardrum probe and the other with the oralthermometer. The patients were chosen randomly from the population of patients whovisit the health care center.Open JMP INTRO, and from the JMP Starter menu, select Open Data Table. Open theTHERM.jmp file. Readings taken with the standard oral thermometer are recorded in theOral column, and readings taken with the new eardrum probe thermometer are recordedin the Tympanic column. Choose Analyze fi Distribution using both Oral andTympanic as the Y,Columns variables. To compare the two distributions more easily,you can select Uniform Scaling from the red triangle menu of Distributions in the popupwindow.Create a new column to represent the difference between the two temperaturemeasurements. Label the column Difference. To calculate the differences in JMPINTRO, select the Difference column by clicking on the column heading. Then, fromthe menu bar, choose Cols fi Formula. In the pop-up window, click on the variablename Tympanic, then -, then the variable name Oral. This enters the formula for thedifference. Click OK. Look at the distribution of the differences to see if the conditionsfor using the t test are reasonable by choosing Analyze fi Distribution for the newvariable Difference. Conduct a hypothesis test on the differences by selecting TestMean from the red triangle menu for Differences. Enter the correct hypothesized meanfor the hypothesis of interest.Using your results from JMP INTRO, carry out a complete hypothesis test using one ofthe commonly used significance levels. Include assumptions, hypotheses, samplestatistic values, test statistic and p-value, and conclusions in the context of the problem.Include a discussion of why a matched pairs design was appropriate for this problem.Include graphical displays for temperatures for both types of thermometers and for thedifference in temperatures. Include JMP INTRO output for the hypothesis test results,with the correct p-value circled. Explain how you chose the proper p-value for this test.Lab Activity – Hypothesis Testing – Matched Pairs t-Test 1

JILA Project NCSSM Stat Institute – July 2001• JMP-INTRO also features a “Matched Pairs” analysis. To use this analysis, ratherthan create a Difference column, go to Analyze fi Matched Pairs. Both Oraland Tympanic should be entered as Y,Paired Response variables. The resultingdisplay should provide the same results for the matched pairs test described in thestudent activity.Lab Activity – Hypothesis Testing – Matched Pairs t-Test 3

JILA Project NCSSM Stat Institute – July 2001JMP INTRO ® Lab ActivitiesAnswer KeyThe following are suggested answers for Hypothesis Testing – Matched Pairs t-test.Graphical Displays of Temperatures for Both Types of Thermometers:DistributionsOral96 97 98 99 100 101 102 103Tympanic96 97 98 99 100 101 102 103Graphical Display of the Differences in Temperatures:DistributionsDifferences0 .5 1 1.5 2 2.5Lab Activity – Hypothesis Testing – Matched Pairs t-Test 4

JILA Project NCSSM Stat Institute – July 2001Summary Statistics for the Difference in Temperatures:Quantiles100.0% maximum 2.300099.5% 2.300097.5% 2.300090.0% 2.180075.0% quartile 1.600050.0% median 0.900025.0% quartile 0.550010.0% 0.40002.5% 0.30000.5% 0.30000.0% minimum 0.3000MomentsMean 1.12Std Dev 0.6237408Std Err Mean 0.1394727upper 95% Mean 1.4119197lower 95% Mean 0.8280803N 20Hypothesis Test Results:Test Mean=valueHypothesized Value 0Actual Estimate 1.12df 19Std Dev 0.62374t TestTest Statistic 8.0302Prob > |t| t 0 The new eardrum thermometer producestemperature readings higher than the oralthermometer.x 1.12t = D= = 8.03s 0.62374n 20Lab Activity – Hypothesis Testing – Matched Pairs t-Test 5

JILA Project NCSSM Stat Institute – July 2001p < 0.0001Conclusion: At the α = 0.05 level, because p < 0.0001 < 0.05, we can reject the nullhypothesis. We have evidence that the new eardrum probe thermometer producestemperature readings that are higher than the standard oral mercury thermometeron average.Lab Activity – Hypothesis Testing – Matched Pairs t-Test 6