Two-Way ANOVA Analysis of Complex Motor Tasks in a Sleep Deprivation Study

The study investigates the impact of sleep deprivation and stimulant types on motor task performance in a driving simulation game. Factors such as sleep deprivation methods (control, jet lag, interrupted, total deprivation) and stimulant types (placebo, caffeine, reward) are analyzed through a two-way ANOVA. Results show varying effects on motor task scores based on these factors.

• ANOVA Analysis
• Sleep Deprivation
• Driving Simulation
• Motor Task Performance

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1. TWO-WAY ANOVA COHEN CHAPTER 13 TEXTBOOK EXAMPLE

2. 3 X 4 TWO-WAY ANOVA, COMPLEX MOTOR TASKS DV (dependent variable) score on a video game that simulates driving a large truck at night IV (categorical independent variables) Sleep deprivation (subjects spend four days in a sleep lab) (1) Control: allowed to follow their own sleep schedule (2) Jet Lag: keep usual amount, but not allow any during 11pm-7am (3) Interrupted: usual amount, but no more that 2 hours at a time, separated by 1+ hours awake (4) Total Deprivation: total lack of any sleep Stimulant (1) placebo: sugar pill, but told it is caffeine (2) caffeine: caffeine pill, told it is caffeine (3) reward: mild electric shocks for mistakes & money for good performance Subjects 5 per sleep x stimulant combination 5 x (4 x 3) = 5 x 12 = 60

3. DATA Placebo 24 20 29 20 28 22 18 16 25 27 Caffeine 26 22 20 30 27 25 31 24 27 21 Reward 28 23 24 30 33 26 20 32 23 30 Control Jet Lag 16 20 11 19 14 14 17 12 18 10 23 28 26 17 19 23 16 26 18 24 16 13 12 18 19 15 11 19 11 17 Interrupted Total Lack

5. MARGINAL MEANS Placebo 24 20 29 20 28 22 18 16 25 27 16 20 11 19 14 14 17 12 18 Placebo 24 20 29 20 28 22 18 16 25 27 16 20 11 19 14 14 17 12 18 10 10 Placebo Caffeine 26 22 20 30 27 25 31 24 27 21 23 28 26 17 19 23 16 26 18 24 24 Caffeine 26 22 20 30 27 25 31 24 27 21 23 28 26 17 19 23 16 26 18 Caffeine Reward 28 23 24 30 33 26 20 32 23 30 16 13 12 18 19 15 11 19 11 17 17 Reward 28 23 24 30 33 26 20 32 23 30 16 13 12 18 19 15 11 19 11 Reward Control Control Control M = 25.6 N = 15 25.6 24.2 25.0 27.6 Jet Lag Jet Lag Jet Lag M = 24.47 N = 15 24.47 21.6 25.6 26.2 Interrupted Interrupted Interrupted M = 18.07 N = 15 18.07 16.0 22.6 15.6 Total Lack Total Lack Total Lack M = 16.73 N = 15 16.73 14.2 21.4 14.6 M = 19.0 N = 20 19.0 M = 23.65 N = 20 23.65 M = 21.0 N = 20 21.0 21.217 M = 21.217 N = 60

6. PLOT OF MEANS Placebo Caffeine Reward Norm 24.2 25.0 27.6 25.6 Main Effect of Sleep Lag 21.6 25.6 26.2 24.47 Int 16.0 22.6 15.6 18.07 Interaction between Sleep & Stimulant None 14.2 21.4 14.6 16.73 Main Effect of Stimulant 19.0 23.65 21.0 21.217

7. DEGREES OF FREEDOM c = number of columns Total r = number of rows 60 1 = 59 n = subjects per cell Denominator of F ratios Total = rnc 1 Within Cells 60 - 12 = 48 Between Cells 12 1 = 11 Between cells = rc - 1 Columns 3 1 = 2 Rows Rows = r - 1 4 1 = 3 Columns = c - 1 Interaction 3 x 2 = 6 Numerators of F ratios Interaction = (r 1)(c 1) Within cells = rnc - rc

8. 2-WAY ANOVA IF THE INTERACTION IS SIGNIFICANT SS Df 11 MS F p Between-Cells SLEEP Row Groups STIM Column Groups INTER (Row x Col) Within-Cells (Residual) Total 1309.38 896.98 3 298.99 18.241 <.001 217.63 2 108.82 6.639 .003 MAIN EFFECTS SHOULD NOT BE INTERPRETED IN ISOLATION 197.77 786.80 2096.18 6 48 59 32.46 16.39 1.980 .087

9. INTERACTION CONTRASTS Does CAFFEINE have the same effect in NO SLEEP as NORMAL SLEEP? If the interaction is significant pick TWO PAIRS to compare (extreme) ? = 2?2: ?????= ? 1 ? 1 = 1 Caffeine s Effect in None Caffeine s Effect in Normal ??= 1, -1, -1, 1 ?11 ?12 ?21 ?22 ? = 2= 4 ?? ?11 ?12 ?21 + ?22 Placebo Caffeine Reward Placebo Caffeine Reward Placebo Caffeine ? = ? ?11 + ? ?12 ? ?21 + ? ?22 + Norm Norm Norm 24.2 24.2 24.2 25.0 25.0 25.0 27.6 27.6 25.6 25.6 ? = ? ? = 24.2 25.0 14.2 + 21.4 = ?.? ? ?2 ?? + ? + ? +? Lag Lag ????? ??? 21.6 21.6 25.6 25.6 26.2 26.2 24.47 24.47 25.0 24.2 ?????= ????= 2 Int Int 16.0 16.0 22.6 22.6 15.6 15.6 18.07 18.07 14.2 21.4 5 6.42 1 + 1 + 1 + 1=5 40.96 =204.8 ?????= = ??.? None None None 4 4 14.2 14.2 14.2 21.4 21.4 21.4 14.6 14.6 16.73 16.73 51.2 ??.??= ?.?? ????= ??? ????= ????? ? ?????,??? 19.0 19.0 23.65 23.65 21.0 21.0 21.217 21.217 ????????= ? ? ?,?? = 6 ?.056,40 = 6 2.34 = ??.??

10. INTERACTION CONTRASTS Does CAFFEINE have the same effect in NO SLEEP as NORMAL SLEEP? Placebo Caffeine Reward ?????????= ?.?? Norm Are the lines PARALLEL? 24.2 25.0 27.6 25.6 Vs ????????= ??.?? 0.8 Lag 21.6 25.6 26.2 24.47 Int 16.0 22.6 15.6 18.07 7.2 None Just compare the 2 pairs of points (ignore the rest) 14.2 21.4 14.6 16.73 19.0 23.65 21.0 21.217 This provides no evidence that CAFFEINE has a different effect in NORMAL SLEEP vs TOTAL DEPRIVATION.