65 WORKSHOP DATA SETS DAVID f. HAND Data set is a very simple three group continuous variable set. Data set involves a categorical ordinal scale with missing values. Data set 3 is a more complicated continuous variable set with two values recorded at each time. Data set 4 is a still more complicated continuous variable data set with missing values and three variables measured at each time. It has a structure of conditions over time. Interest is in relationships between the variables. Faculty of Mathematics The Open University Milton Keynes MK76AA England Editor's Note: As mentioned often during the Workshop, the most informative approach, and one which is strongly recommended when the data are first analysed, is to produce separate graphs of the responses against time for each subject. To aid the reader considering the various approaches, we have done this here for Data sets and 3 using the Macintosh software StatViewii. The data can also be obtained by sending an email message to srw308@csc.anu.edu.au.
66 DATASET These data arose during a study of the effect of a vitamin E diet supplement on the growth of guinea pigs. The body weight (grams) was measured at the end ofweeks, 3, 4, 5, 6, and 7. All animals were given a growth inhibiting substance during week and the vitamin E therapy was started at the beginning of week 5. The animals were divided into three groups: group received no vitamin E, group a low dose, and group 3 a high dose. The data below give first the animal number, then its group, and then its six weight measures. 455 460 50 504 436 466 467 565 60 596 54 587 3 445 530 580 597 58 69 4 485 54 594 583 6 6 5 480 500 550 58 56 576 6 54 560 565 54 55 597 7 440 480 536 484 567 569 8 495 570 569 585 576 677 9 50 590 60 637 67 70 0 503 555 59 605 649 675 3 496 560 6 6 63 670 3 498 540 589 557 568 609 3 3 478 50 568 555 576 605 4 3 545 565 580 60 633 649 5 3 47 498 540 54 53 583 Editor's Note: These data are also considered in Crowder MJ & Hand DJ (990), Analysis of Repeated Measures. Chapman & Hall: London.
67 700 Group : No vitamin E 650 600 550 500 X D A3 <>4 +5 450 0 3 4 5 6 7 8 700 Group : Low dose vitamin E 650 600 550 500 X6 D7 A8 <>9 +0 450 0 3 4 5 6 7 8 700 Group 3: High dose vitamin E 650 600 550 500 D A3 <>4 +5 450 0 3 4 5 6 7 8 Week
68 DATASET These data arose during a clinical trial of a treatment for sprains. The first value for each patient is the patient number, the second is the group ( = treatment, = control) and the next four are tenderness scores on a scale 0 =none, =slight, =moderate, 3 =severe. A BLANK represents a missing value. Primary interest centred on differences between the two groups. 7 3000 0 8 0 3 00 9 0 4 0 0 00 5 00 0 6 0 7 0 0 8 00 3 9 00 4 0 0 0 5 00 3 6 3 3 7 0 3 30 8 4 333 9 5 33 30 6 3
69 DATASET3 These data are part of the data collected during a larger study. I am grateful to Dr Gudrun Sartory and Dr Irene Daum of the Institute of Psychiatry for permission to use the data. The aim of the study was to explore the effects of predictability and control on the anxiety experienced by phobics. In the data extracted below, 4 snake and spider phobics were exposed to 6 repeated presentations of a slide depicting the object of their phobia. Subjects are divided into two groups, indicated by the first column (after the subject number). In levell a tone sounded to indicate that the slide was about to switch off, while in level the tone did not presage the disappearance of the image. At each of the six presentations two measures were taken: first the onset level of skin conductance and second the peak level of skin conductance obtained for this presentation of the slide. The values below are presented in the order onset, peak for presentation ; onset, peak for presentation, etc. Questions of interest are such things as: Is there acclimatisation over exposures? Are there differences between groups and if so what are the differences? And so on.
70 3 4 5 6 7 8 9 0 3.6 5.4.33.7.33.6.6.9.7.5.4.0 6.6 6.6 6.0 6.0 5.8 5.8 5.5.4.44.4 4.4. 33.7 47.8 34.8 34.8 33.4 35.8 40.3 40.3 34.0 34.0 36. 36. 4.0 4.0 4.35.0 3.0 3.7.8.7.8.8.5 3. 6.3 6.5 6.5 6.6 6. 6.4 6.5 6.5 6.3 6.3 6. 6. 6. 8.0 7.4 7.4 7.8 9.4 8.7 8.7 9.5 9.5 3. 3. 7.5 7.5 8.7 8.7 8.9 8.9 8.4 8.4 8.3 8.3 7. 7. 4.0 4.3 4.5 4.5 3.9 3.9 4.0 4.0.9.9.4.4 0.0.6 0.8.30.0. 9.3 9.3 8.6 8.6 8. 8.4 6. 7.0 6.5 6.8 5.9 5.9 5.4 5.4 4.7 4.7 4.4 4.4 9.60.3 9. 9. 9. 9. 8.8 8.8 8.4 8.4 8. 8..7 3. 3.6 3.9 5.3 6.5 6.0 6.9 5.4 5.7 4.9 4.9 Group 35 30 5 0 I 5 X Obs i o obs Obs 3 <> obs 4 + obs 5 o obs 6 obs 7 obs 8 A obs 9 obs 0 Gobs i cobs 0 5 (NB For easier visual comparisons between the two Groups, Observation 3's high values have been truncated.)
7 3 4 5 6 7 8 9 0 3 4.7 0.6 6.5.54.5 4.5 5.5.6.8 0.4 4.4 4.4 3. 3.3.4 3.4 3.7 3.7 33.33. 33.4 33.4 33.6 33.6 0.0.0 0.4 0.4 0.4 0.4 0.6 0.6.0.6 0.8 0.8 4. 4. 4. 4. 4.0 4.0 3.8 3.8 3.6 3.6 3.5 3.5 6.0 7.8 5.5 6.6 4.9 5. 4.6 4.6 4. 4. 3.4 3.4 9.5 0. 9. 9.9 9.0 9.0 8.5 8.5 8.3 8.9 8. 8.6...9.9.8.8.7.7.6.6.6.6.9.9.4 4.6.9 3.7. 4.0.8 3.8.0 4.3 5.0 8.0 6.4 8.3 5.5 5.5 5.5 5.7 6.0 6.0 5.3 5.3 7.6 9. 8.7.0 9.3. 9.4.9 9.8.60.. 4.3 9.6 5.0 5.0.9.9 0.7 0.7 9.3 9.8 8.5 8.5 6.9 7.6 7.9 8.4 7.3 7.3 7. 7.4 7.4 7.4 7. 7. Group 35 30 5 0 5 obs 3 o obs 4 8 obs 5 o obs 6 + obs 7 o obs 8 obs 9 o obs 0 obs i obs Gobs 3 : obs 4 0 5
7 DATASET4 I am grateful to Dr Christopher Bass of King's College Hospital, London for permission to use these data. They describe patients who suffer from panic attacks and control subjects. The first variable is the subject number. The second has values, meaning that this is a patient who suffers panic attacks, and, meaning that this is a control subject. The next variables are scores on an anxiety scale measured at the following times in minutes: 4, 6, 8, 0, 4, 6, 7, 8, 9, 3. The next are scores (on the next line in the listing) on a carbon dioxide expiration scale measured at the same times. The final (on the third line on the the same times. are pulse rates measured at Times 4,, 4, 9, and 3 are rest times. Times 6, 8, and 0 are times at which the subject is spoken to about the topic which they are anxious about. Times 6, 7, and 8 are times at which the subject is asked to hyperventilate. * 's signify missing values.
73 The researchers were interested in a number of hypotheses, including: (i) Do panic patients have lower C0 at rest than controls, and a greater fall during panic attacks? (ii) Do falls in C0 during phobic talk correlate inversely with levels of anxiety? (iii) Are ratings of anxiety during overbreathing correlated with speed of recovery of C0 level after overbreathing? 4 58 6 4 4 56 6 7 4 33 30 6 7 8 8 5 4 9 08 08 8 6 08 4 4 0 08 00 5 6 6 5 3 3 7 8 8 8 4 40 39 40 40 39 40 3 3 0 5 3 94 04 06 04 9 * * * * 08 84 3 5 5 5 5 5 5 6 6 7 6 4 30 3 5 5 30 30 8 5 3 8 4 96 96 96 84 96 960 0808 96 84 4 3 3 3 7 8 7 7 9 9 8 8 8 9 9 7 5 9 90 90 90 90 84 84 96 96 90 84 84 5 4 5 7 8 4 3 4 35 3 3 30 3 34 9 7 6 7 33 78 78 84 78 78 78 78 78 84 84 78 6 3 5 6 7 5 3 7 7 7 4 38 34 8 7 33 7 8 4 3 8408408 90 84 9608 96 80 78 7 5 6 6 5 7 8 5. 36 38 36 35 35 35 8 7 5 30 86 94 88 8 84 80 04 04 04 96 74 8 4 6 6 4 4 6 7 4 3 3 30 3 3 3 9 3 0 0 3 70 74 7 7 70 68 86 84 8 68 70 9 5 0
74 37 36 35 36 37 37 9 7 6 3 9 80 80 80 78 78 7 96 96 90 80 76 0 4 8 8 8 3 4 7 7 8 8 5 9 9 9 4 4 7 78 78 78 78 7 78 90 90 90 84 7 4 4 6 7 4 7 7 7 7 7 3 3 3 9 9 30 8 7 4 90 90 96 96 96 90 90 90 90 84 78 8 8 8 8 7 6 4 3 4 30 9 9 9 30 34 7 6 5 3 9 4 4 3 30 8 4 40 5 48 30 0 3 3 4 8 8 7 4 6 8 8 7 8 6 5 3 3 3 4 9 7 6 9 0 80 8 86 8 80 86 9 90 84 80 80 4 3 4 5 6 3 8 9 8 6 6 7 8 5 4 8 0 98 0 0 0 08 0 3 34 40 4 78 5 3 6 8 8 6 8 * * * * * 35 37 34 34 33 8 * * * * * 96 98 04 04 98 * * * *,. 6 4 7 8 8 3 7 8 * 7 3 34 33 3 3 34 34 9 5 * 3 30 76 74 70 6 64 94 9 * 7 6 7 4 6 6 6 4 6 8 8 * 7 7 3 3 30 30 8 6 9 8 * 9 9 86 86 86 8 78 780 * 94 8 5 5 8 6 3 6 8 * 5 3 34 34 3 33 33 34 3 0 * 5 3 96 08 8 6 00 00 4 30,, 0 90 9 4 6 6 6 4 3 4 6 6 5 3 30 8 7 3 3 6 5 5 9 7 86 88 90 88 8 900 98 9 84 8 0 3 4 4 7 8 * 4 36 36 37 36 35 35 0 8 * 7 36 80 86 86 8 78 784 * 86 80 7 7 6 7 6 5 7 * * 6 6 3 3 3 3 3 3 5 * * 8 30 04 00 98 98 98 96 * * * 98 96
75 6 6 8 8 5 3 6 6 6 4 30 3 3 33 30 30 5 3 8 40808408000808 3 6 7 7 6 3 3 4 5 6 4 40 39 37 36 39 39 8 4 4 7 9 04 0 0 9 84 46 66 66 3 0 4 4 6 7 5 5 7 3 34 34 34 33 34 33 9 8 5 3 88 00 0 96 90 84 96 96 0 84 84 5 3 3 4 0 3 3 3 0 37 38 37 37 38 36 0 6 3 3 84 86 84 88 74 7 08 08 08 84 74 6 0 0 0 0 0 0 0 0 0 34 34 34 33 33 33 9 8 7 7 34 84 78 88 84 84 84 90 90 90 84 8 7 4 8 8 3 4 37 36 36 36 37 37 0 7 5 4 30 80 00 98 96 9 84 0 6 3 90 80 8 0 3 6 6 0 0 0 0 0 37 37 37 36 36 36 0 8 5 3 64 68 66 66 66 66 7 7 74 66 6 9 0 0 0 0 0 0 4 4 0 0 35 34 35 35 35 35 5 0 8 35 98 04 06 06 94 94 0 8 94 90 30 3 6 7 3 6 8 8 3 0 40 38 37 39 40 4 8 3 0 8 36 9 04 08 08 9 90 34 60 7 4 90 3 4 8 3 0 6 8 8 6 34 34 5 0 3 8 5 4 3 7 0 74 80 84 88 70 6836 9 68 3 0 0 3 3 3 3 3 3 9 8 9 3 84 84 84 8 8 8 8 84 84 8 80 33 0 0 3 0 0 3 4 5 0 0 35 33 33 34 34 35 9 8 7 6 3 70 78 76 78 74 7 80 80 80 74 70 34 3 3 4 40 40 40 40 40 40 8 6 4 7 38
76 64 66 64 6 64 64 98 84 80 64 66 35 0 0 0 0 36 36 36 35 35 35 8 5 3 0 8 90 98 98 98 90 84 08 4 98 84 36 4 5 * 3 3 3 30 7 8 3 5 3 * 3 7 90 94 88 86 8 78046 * 8 8 37 4 6 7 0 0 5 6 7 5 0 39 38 37 36 37 40 6 4 0 8 78 84 80 80 70 68 08 0 4 84 68 38 4 4 5 3 5 5 6 3 3 37 35 35 35 35 34 0 5 3 5 3 90 96 9 94 94 9 0 30 86 8 39 4 6 7 3 5 5 4 40 40 40 40 40 40 7 5 3 3 33 78 86 80 80 76 80 00 06 06 78 86 40 4 8 8 6 6 4 38 38 38 38 39 40 3 9 8 6 38 98 96 98 94 98 94080 98 98 4 3 3 3 3 3 3 4 * * 4 6 7 6 6 5 5 5 * * 3 4 34 30 6 4 4 8 * * * 8 40