Goal-setting for a healthier self: evidence from a weight loss challenge Séverine Toussaert (NYU) November 12, 2015
Goals as self-disciplining devices (1) 1. Goals are a key instrument of self-regulation. 2. n theory: -goals=referencepoint -falling below the goal) psychological loss 3. n the data: - higher goals) higher performance (Locke & Latham 2002) -largeevidenceforexternallyimposedgoals -evidencemorescarceforself-setgoals
Goals as self-disciplining devices (2) 1. For goals to work, they have to be SMART: Specific Measurable Achievable Realistic Time-bound 2. Often individuals set unrealistic goals for themselves: overconfidence bias lack of information 3. Can information provision help individuals: set more realistic goals? achieve higher performance outcomes?
This study: information and health goals 1. Study the effect of information provision on goal-setting and performance in the domain of health. 2. Field experiment w/ participants in a weight loss challenge: 8-week program with weekly weigh-ins Participants are NYU staff and faculty members Data from the 2015 challenge - 5th edition 3. Focus on health goals: weight loss and exercise Very popular goals The goal of 42% (16%) of contracts entered on stickk.com is to lose weight (exercise regularly).
Dataset (1) 1. Conducted a two-part online study: First survey administered in week 1 Follow-up survey administered at the end of week 4 2. Weekly weight loss recorded separately at a private gym: 9 weigh-ins organized (initial + 8 follow-up) weight measured on same day each week 3. Sample size: 257 participants in the challenge 176 enrolled in the study; 160 completed it. Final sample: 148 participants w/ available weight data.
Dataset (2) Sample characteristics: On average, 35 y.o. and 80% female. 45% are returning participants. Average starting weight: 169 lbs for females (US ref: 166 lbs) and 212 lbs for males (US ref: 196 lbs) BM: 28.5 for females and 30.2 for males. ref: 18.5-24.9 normal, 25.0-29.9 overweight, > 30 obese. 60% had a gym membership at the time of the challenge. Slightly over 50% exercise at least twice a week but 27% exercise less than once.
Road Map 1. Can goals be shaped by information? Are goal-setters responsive to information? s the effect domain-specific? 2. Can information help individuals achieve their goals? Overall impact on weight loss mpact on weight loss trajectory Goal achievement
Goal formation and information (1) Participants asked whether they wanted to set themselves a weight loss (exercise) goal for their internal motivation: weight loss: number of lbs to lose over the challenge (8 weeks) exercise: number of gym visits (first 4 weeks) purely intrinsic motivation; no incentives Two conditions: No nfo: Participants set their goals without guidance. nfo: Participants are told the choices and success rates of participants in the previous year.
Goal formation and information (2) On average, participants wanted to lose 14 pounds but managed to lose only 3 to 4 pounds over the eight week period. Overall, less than 3% of the participants who wanted to lose weight achieved their weight loss goal. On average, participants wanted to exercise at the gym about 13 times during the free month membership, but ended up exercising only about 6 times. Among those who indicated their interest in attending the gym, only 18% achieved their goal.
Effect of information on goal-setting
Table: Mean (std) of basic characteristics by nfo condition nformation No nformation p-value Panel A: Socio-demographic variables female 0.806 0.803 0.965 (0.047) (0.046) age 35.472 34.250 0.455 (1.169) (1.138) years of education 5.903 6.342 0.358 (0.342) (0.333) yearly income 65,763.89 62,960.53 0.398 (2,370.943) (2,307.707) Panel B: Challenge-related variables previous participant 0.417 0.500 0.313 (0.059) (0.057) # of weigh-ins attended 5.722 5.250 0.260 (0.299) (0.291) member of non-partner gym 0.514 0.513 0.993 (0.059) (0.058) intends to increase exercise 0.764 0.776 0.859 (0.050) (0.048) Panel C: Current weight status and goals initial weight 172.778 181.879 0.176 (4.801) (4.673) initial BM 28.069 29.637 0.095 (0.668) (0.650) satisfaction with current weight 2.319 2.579 0.253 (0.162) (0.158) ideal weight loss 27.413 29.771 0.552 (2.669) (2.899)
mpact of information on weight loss goals (1)
mpact of information on weight loss goals (2) Table: Distribution of weight loss goals by information condition weight loss goal w in lbs % of respondents (N) test diff =0 Goal number No nfo nfo p-value w < 10 22.4 (17) 40.3 (29) 0.019 w = 10 32.9 (25) 26.4 (19) 0.390 w > 10 44.7 (34) 33.3 (24) 0.158 Total 100.0 (76) 100.0 (72) 0.062 mean goal 13.1 10.8 0.041 Note: p-values from t-tests for each category and a 2 -test on all 3 categories.
mpact of information on weight loss goals (3)
mpact of information on weight loss goals (4) Table: Distribution of % weight loss goals by information condition weight loss goal pw as % of initial weight % of respondents (N) test diff =0 % goal No nfo nfo p-value pw apple 5 30.3 (23) 34.7 (25) 0.566 pw 2 (5, 8) 32.9 (25) 45.8 (33) 0.109 pw 8 36.8 (28) 19.4 (14) 0.019 Total 100.0 (76) 100.0 (72) 0.056 mean goal 7.02 6.03 0.031 Note: p-values from t-tests for each category and a 2 -test on all 3 categories.
mpact of information on exercise goals (1)
mpact of information on exercise goals (2) Table: Distribution of exercise goals by information condition exercise goal g (in gym visits) % of respondents (N) test diff =0 Goal number No nfo nfo p-value g < 10 51.3 (39) 52.8 (38) 0.860 g = 10 13.2 (10) 15.3 (11) 0.714 g > 10 35.5 (27) 31.9 (23) 0.648 Total 100.0 (76) 100.0 (72) 0.873 mean goal 8.9 9.1 0.829 Note: p-values from t-tests for each category and a 2 -test on all 3 categories.
Determinants of goal setting: regression analysis absolute weight loss w relative weight loss p w number of gym visits g (1) (2) (3) (4) (5) (6) nfo -1.61* -1.64* -1.01** -1.03** -0.19-0.31 (0.85) (0.86) (0.44) (0.44) (0.96) (1.00) initial weight w 0 0.08*** 0.06** 0.01-0.003-0.02 (0.02) (0.02) (0.01) (0.01) (0.03) satisfaction w/ current weight -0.64* -0.50-0.45** -0.36* 0.15 (0.35) (0.36) (0.18) (0.18) (0.42) ideal weight loss 0.03 0.05 0.01 0.02-0.02 (0.03) (0.04) (0.01) (0.02) (0.04) member of non-partner gym 1.39 0.97** -3.30*** -3.04*** (0.87) (0.44) (0.97) (1.00) intends to increase exercise 2.32** 1.41*** 1.99* 2.62** (1.04) (0.53) (1.16) (1.21) female -1.89-0.64-1.06 (1.51) (0.77) (1.75) age 0.05 0.04 0.02 (0.06) (0.03) (0.07) years of education 0.13 0.04 0.12 (0.16) (0.08) (0.19) yearly income -0.02-0.02-0.03 (0.03) (0.01) (0.03) returning participant 0.44 0.22-0.63 (0.85) (0.43) (0.98) Observations 148 148 148 148 148 148 R 2 0.44 0.48 0.16 0.23 0.11 0.15
Why a differential impact of information on weight loss and exercise? exercise goal: process-oriented goal weight loss: outcome-oriented goal Outcome-oriented goals are harder to evaluate: ) involve more uncertainty ) mapping between process and outcome is abstract Sensitivity of weight loss goals to information due to uncertainty about what is an achievable target.
Effect of information on weight loss outcomes
Weigh-in attendance data (1) 1. Despite some attrition, pretty good weight loss data: Graphs Almost 50% attended 7 or 8 weigh-ins. Less than 25% attended less than half of the weigh-ins (0-3). Halfway (final) weight recorded for 73% (57%) of participants. 2. No differential attrition across information conditions: Graphs Average # of weights recorded: 5.2 in No info and 5.7 in nfo (p-value = 0.28) 3. Assumptions on attrited sample: Data Zero weight loss imputed when final weight missing. Reasonable assumption: participants with fewer weights recorded tend to lose less weight at week 4 and 8. Average weekly weight loss computed when intermediate weight missing.
Weight loss outcomes Outcomes of interest: 1. cumulative weight loss 4w t 2 [ w, w] in lbs at week t 2 {4, 8} 2. % who lost, gained and maintained stable weight: weight loss: 4wt 1lbs weight stability: 4w t 2 ( 1, 1) lbs weight gain: 4w t apple 1lbs 3. % of goal reached: 4wt w 100
Weight loss statistics (1) Table: Mean (std) of weight loss measures week 4 week 8 outcome measures full sample restricted sample* full sample restricted sample weight loss w t in lbs 2.9 (3.5) 3.5 (3.6) 3.1 (4.2) 3.8 (4.1) % who lost weight 68.2 (46.7) 77.8 (41.8) 63.5 (48.3) 75.0 (43.6) % of goal reached 25.9 (36.6) 33.6 (36.9) 27.5 (45.0) 38.3 (51.8) N 148 108 148 84 *Restrictedsamplereferstothepeoplewhoseweightwasrecordedduringweekt. ** N = 145 for full sample and N = 105 (82) for restricted sample at week 4 (8).
Weight loss statistics (2) Figure: Distribution of weight loss at week 8 (full sample)
Weight loss by information condition (1)
Weight loss by information condition (2) weight loss w t (in lbs) % of goal reached 4wt w 100 t = 4 t = 8 t = 4 t = 8 (1) (2) (3) (4) (5) (6) (7) (8) nfo 1.03* 0.99* 0.67 0.76 13.31** 13.61** 13.28* 14.87** (0.56) (0.54) (0.68) (0.67) (6.08) (5.96) (7.55) (7.49) weight loss goal pw 0.31*** 0.35*** 0.37*** 0.42*** -1.10-0.69 0.47 0.05 (0.10) (0.10) (0.13) (0.12) (1.18) (1.14) (1.46) (1.43) initial weight w 0 0.02** 0.01 0.01 0.01 0.03 0.007-0.04-0.01 (0.01) (0.01) (0.01) (0.01) (0.08) (0.09) (0.10) (0.11) female -1.91** -1.75* -16.80** -12.65 (0.77) (0.96) (8.42) (10.59) age 0.03 0.01 0.41-0.02 (0.04) (0.05) (0.40) (0.51) years of education -0.25** -0.09-2.00* -0.97 (0.10) (0.13) (1.12) (1.41) yearly income 0.005 0.004-0.03 0.06 (0.017) (0.021) (0.19) (0.24) returning participant -0.26-0.86-5.53-12.09 (0.53) (0.66) (5.89) (7.40) exercise frequency 0.09*** 0.13*** 1.18*** 1.47*** (0.03) (0.04) (0.38) (0.48) Observations 148 148 148 148 145 145 145 145 R 2 0.12 0.25 0.08 0.18 0.04 0.16 0.03 0.12
Weight loss by information condition (3) Lost weight: P { w t 1} Gained weight: P{ w t apple 1} t = 4 t = 8 t = 4 t = 8 (1) (2) (3) (4) (5) (6) (7) (8) nfo 0.196*** 0.207*** 0.140* 0.164** -0.084** -0.073** -0.066* -0.066** (0.073) (0.073) (0.076) (0.078) (0.035) (0.030) (0.037) (0.034) weight loss goal pw 0.032** 0.036** 0.048** 0.057** -0.013** -0.012** -0.023*** -0.023*** (0.014) (0.014) (0.015) (0.015) (0.006) (0.005) (0.008) (0.007) initial weight w 0 0.001 0.0008 0.0001 0.0003-0.0005-0.0003-0.0001-0.0001 (0.001) (0.001) (0.001) (0.001) (0.0004) (0.0004) (0.0005) (0.0005) female -0.226*** -0.142 0.065*** 0.051 (0.081) (0.104) (0.025) (0.034) age 0.009* 0.003-0.003-0.001 (0.006) (0.006) (0.002) (0.002) years of education -0.031** -0.019 0.011** 0.008 (0.014) (0.015) (0.005) (0.006) yearly income -0.0008 0.0008 0.0003-0.0003 (0.003) (0.003) (0.001) (0.001) returning participant -0.115-0.148* 0.041 0.061* (0.075) (0.078) (0.028) (0.035) exercise frequency 0.012** 0.017*** -0.004** -0.007*** (0.005) (0.005) (0.002) (0.002) Observations 148 148 148 148 148 148 148 148 Mean dependent variable 0.682 0.682 0.635 0.635 0.095 0.095 0.115 0.115 Nb: Ordered probit models of the propensity to lose (=1), maintain (=0) or gain (= -1) weight. Coefficients are marginal effects evaluated at the mean of the covariates.
Weight loss by information condition: summary 1. Overall, participants in nfo do better than in No nfo: Controlling for p w,weightlossatweek4is1lbshigherinnfo. Controlling for p w, participants in nfo reach a higher % of their goal both at week 4 & 8. They are also more (less) likely to lose (gain) at least 1lbs. 2. However the benefits of information vanish over time: No effect of nfo on total weight loss at week 8. Weaker effect on probability to lose/gain weight at week 8. 3. nterestingly, there is heterogeneity in the effect of information depending on the goal level: Low (p w apple 5%), Medium (p w 2 (5%, 8%)), High (p w 8%)
Heterogeneity (1)
Heterogeneity (2)
Heterogeneity (3) weight loss w t (in lbs) % of goal reached 4wt w 100 t = 4 t = 8 t = 4 t = 8 (1) (2) (3) (4) (5) (6) (7) (8) nfo 1.63* 1.67* 2.50** 2.55** 33.29*** 34.35*** 46.30*** 48.78*** (0.98) (0.95) (1.18) (1.17) (10.76) (10.38) (13.14) (12.84) medium goal pw,m 2.25** 2.10** 3.47*** 3.23*** 20.44* 17.84* 34.18*** 31.24** (0.97) (0.93) (1.17) (1.15) (10.38) (10.01) (12.68) (12.38) high goal pw,h 2.51*** 2.68*** 4.00*** 4.02*** 7.69 8.14 20.61* 21.50* (0.95) (0.93) (1.14) (1.15) (10.12) (9.98) (12.36) (12.34) pw,m nfo -1.17-1.45-2.76* -2.95* -31.48** -35.36** -50.54*** -55.13*** (1.33) (1.30) (1.60) (1.61) (14.40) (14.09) (17.59) (17.44) pw,h nfo -1.02-0.85-3.34* -2.89-28.32* -24.93-48.89** -45.55** (1.47) (1.45) (1.77) (1.78) (15.90) (15.61) (19.42) (19.31) initial weight w 0 0.018** 0.014* 0.015* 0.015 0.056 0.029-0.0001 0.032 (0.007) (0.008) (0.009) (0.010) (0.077) (0.089) (0.094) (0.110) additional controls No Yes No Yes No Yes No Yes Observations 148 148 148 148 145 145 145 145 R 2 0.13 0.24 0.12 0.20 0.08 0.10 0.20 0.19 Nb: p w,m (p w,h )isanindicatorvariable=1iftheparticipant sgoalp w lies between 5% and 8% (above 8%) of his initial weight w 0.
nterpretation (1) 1. Participants who set low goals in nfo are different from those in No nfo: nfo: lower goal set as a result of more realistic beliefs about chances of success No nfo: goal perceived as a limited tool of self-regulation (for instance because of low self-control) 2. Among those who set higher goals, overconfidence may have overridden the positive effect of information: Overconfident individuals may consider that statistics about the average participant do not apply to them. Therefore they will discard the information and behave like people in the No nfo treatment.
nterpretation (2)
Theoretical analysis Analysis based on Koch and Nafziger (2015) Key insight: Goals act as a reference point and deviations from the reference point are painful. Two key ingredients: 1. Reference-dependent utility with goals acting as the reference point. 2. Present-biased preferences generating intertemporal conflict. ) Goals = internal commitment mechanism to provide effort to lose weight
Model (1): Decisions Three-period model: t 2 {0, 1, 2} t = 0 : the agent sets effort goal e 2 [0, E]. No payoffs. t = 1 : the agent chooses effort level e with cost c(e). t = 2 : the agent loses weight w(e) with prob p 2 (0, 1) and 0 o.w. Assumptions: c 0 (e) > 0, c 00 (e) 0, w 0 (e) > 0, w 00 (e) < 0, w(0) =c(0) =0 w 0 (0) c 0 (0) > 0andlim e!e w 0 (e) c 0 (e) < 0
Model (2): Reference-dependent utility The instantaneous utility at t of effort e given goal e is given by u t (e e )=m t (e)+µ(m t (e) m t (e )) where m t (.) is the material payoff received at t and µ(.) reference-dependent utility (Köszegi & Rabin 2006): ( if > 0 µ( )= if apple 0 is the where 0=weightattachedtoreference-dependentcomponent and > 1=degreeoflossaversionoftheagent
Model (3): Reference-dependent utility (cont d) At t = 1, effort level e and goal e yield reference utility: ( µ(c(e) c(e [c(e ) c(e)] if c(e) < c(e ) )) = [c(e ) c(e)] if c(e) c(e ) At t = 2, goal e induces a reference lottery for the benefits L(e ):=(p w(e ); (1 p) 0) and the agent evaluates the outcome of the lottery L(e) :=(p w(e); (1 p) 0) against each possible realization of the reference lottery.
Model (4): Reference-dependent utility (cont d) Therefore µ(l(e) L(e )) = p 2 µ(w(e) w(e )) + p(1 p) (0 w(e )) + p(1 p) (w(e) 0)+ (1 p) 2 0 where µ(w(e) w(e )) = ( [w(e) w(e )] if w(e) > w(e ) [w(e) w(e )] if w(e) apple w(e )
Model (5): Present bias in effort The agent has a present bias 2 (0, 1) (Cf Laibson 1997) The expected utility of self t is: U t (e e )=u t (e e )+ 2X =t+1 u (e e ) Since m 0 = 0, m 1 (e) = c(e) and m 2 (e) =pw(e), self 0 weighs all payoff-relevant periods equally. However, self 1 discounts expected benefits by. As a result, e 1 < e 0 where e t = argmax e U t (e e )
Model (6): nformation When setting a goal e at t = 0, the agent overestimates his likelihood of success: p 2 (p, 1) At t = 1, before choosing e, the agent perfectly learns about the mapping between effort and weight loss p = p. nformation at t = 0aboutpastsuccessratescanshift downward the agent s perceived probability of success: p < p apple p N Downward shift only occurs if information about others past performance is considered as an informative signal for oneself.
Model (7): Predictions Problem solved by backward induction, starting with the optimal effort choice e of self 1 given goal e. t can be shown that the optimal goal e is a weakly increasing function of p and. Since p N p, the model predicts that: 1. Participants in No nfo set (weakly) more ambitious goals. 2. To counteract the effect of p N, those who set low goals in No nfo must have a lower (assuming is fixed). 3. Since participants in No nfo have more overoptimistic beliefs ( p p), they deviate from the goal more often than in nfo.
Conclusion Goal-setting = key instrument of self-regulation. However, effective instrument only if there is minimum knowledge about what is an appropriate target. nformation about others past performance may improve goal-setting and performance. The positive effect might be mitigated by an individual s overconfidence about his likelihood of success.
Additional data and robustness analysis
Weigh-in attendance data (2) Go back
Weigh-in attendance data (3) Go back
Weigh-in attendance data (4) Table: Relationship between weight loss and attendance Go back 4-week weight loss w 4 8-week weight loss w 8 (1) (2) (3) (4) # weights recorded t=4 1.15** (0.47) first 4 weights recorded 1.58** (0.72) # weights recorded t=8 0.63 (0.42) 7or8weightsrecorded 2.01* (1.10) constant -0.60 2.44*** -0.70 2.22** (1.69) (0.59) (3.07) (0.98) Observations 108 108 84 84 R 2 0.05 0.04 0.03 0.04 Note: #weightsrecorded t=j refers to the number of weights recorded up to week j; weight loss is measured in lbs, with w t < 0 measuring weight gain.
Regressions on restricted sample (1) weight loss w t (in lbs) % of goal reached 4wt w 100 t = 4 t = 8 t = 4 t = 8 (1) (2) (3) (4) (5) (6) (7) (8) nfo 1.27* 0.95 0.97 0.14 15.84** 13.38** 16.81 7.78 (0.67) (0.67) (0.90) (0.93) (7.00) (7.07) (11.40) (11.77) weight loss goal pw 0.37*** 0.37*** 0.32* 0.30* -2.58* -2.51* -2.60-3.45 (0.13) (0.12) (0.18) (0.17) (1.38) (1.35) (2.41) (2.32) initial weight w 0 0.008-0.001 0.003 0.02-0.07-0.15-0.13 0.04 (0.008) (0.01) (0.01) (0.01) (0.09) (0.11) (0.13) (0.16) female -2.75*** -0.30-27.45*** -4.08 (0.96) (1.27) (10.04) (16.12) age 0.07-0.02 0.63-0.67 (0.05) (0.06) (0.54) (0.80) years of education -0.23* -0.22-1.60-1.98 (0.13) (0.18) (1.37) (2.23) yearly income -0.10 0.03-0.16 0.29 (0.02) (0.03) (0.23) (0.37) returning participant -0.06-2.70*** -3.70-35.55*** (0.66) (0.95) (7.03) (12.34) exercise frequency 0.05 0.16*** 0.66 2.16*** (0.04) (0.05) (0.43) (0.75) Observations 108 108 84 84 105 105 82 82 R 2 0.12 0.22 0.05 0.21 0.10 0.20 0.06 0.22
Regressions on restricted sample (2) Lost weight: P{ w t 1} Gained weight: P{ w t apple 1} t = 4 t = 8 t = 4 t = 8 (1) (2) (3) (4) (5) (6) (7) (8) nfo 0.211*** 0.175** 0.055-0.076-0.098** -0.067** -0.027 0.027 (0.074) (0.071) (0.092) (0.093) (0.040) (0.033) (0.047) (0.034) weight loss goal pw 0.032** 0.024* 0.064*** 0.056*** -0.014** -0.009-0.032*** -0.020** (0.014) (0.013) (0.020) (0.019) (0.007) (0.006) (0.011) (0.009) initial weight w 0-0.0003-0.001-0.0008 0.0001 0.0001 0.0003 0.0003-0.00004 (0.001) (0.001) (0.001) (0.001) (0.0004) (0.0004) (0.0005) (0.0004) female -0.211*** -0.098 0.068** 0.032 (0.060) (0.105) (0.028) (0.033) age 0.008-0.002-0.003 0.0007 (0.007) (0.007) (0.002) (0.002) years of education -0.016-0.026 0.006 0.009 (0.014) (0.021) (0.006) (0.008) yearly income 0.0002 0.004-0.0001-0.001 (0.003) (0.003) (0.001) (0.001) returning participant -0.084-0.321*** 0.032 0.132** (0.075) (0.105) (0.030) (0.061) exercise frequency 0.002 0.016*** -0.001-0.006** (0.004) (0.006) (0.002) (0.003) Observations 108 108 84 84 108 108 84 84 Mean dependent variable 0.778 0.778 0.750 0.750 0.083 0.083 0.107 0.107 Nb: Ordered probit models of the propensity to lose (=1), maintain (=0) or gain (= -1) weight. Coefficients are marginal effects evaluated at the mean of the covariates.
Regressions on restricted sample (3) weight loss w t (in lbs) % of goal reached 4wt w 100 t = 4 t = 8 t = 4 t = 8 (1) (2) (3) (4) (5) (6) (7) (8) nfo 2.21* 1.67 3.72** 2.18 51.54*** 44.94*** 71.17*** 51.01** (1.22) (1.21) (1.54) (1.64) (12.71) (12.50) (19.56) (20.43) medium goal pw,m 2.17* 1.85 4.83*** 3.52** 14.08 9.72 44.50** 24.66 (1.14) (1.11) (1.53) (1.58) (11.25) (11.02) (18.88) (19.53) high goal pw,h 2.72** 2.40** 4.00** 2.79* 2.59-2.85 18.90 0.92 (1.16) (1.17) (1.58) (1.65) (11.50) (11.55) (19.46) (20.38) pw,m nfo -2.04-2.01-4.85** -3.93* -52.46*** -51.80*** -84.92*** -73.02*** (1.60) (1.59) (2.05) (2.11) (16.29) (16.18) (25.65) (26.14) pw,h nfo -0.77-0.09-3.57-1.88-41.62** -30.91-68.43** -45.07 (1.83) (1.86) (2.36) (2.53) (18.49) (18.74) (29.43) (31.30) initial weight w 0 0.012 0.000 0.009 0.016-0.062-0.162-0.069 0.026 (0.01) (0.01) (0.01) (0.01) (0.08) (0.10) (0.13) (0.16) additional controls No Yes No Yes No Yes No Yes Observations 108 108 84 84 105 105 82 82 R 2 0.12 0.22 0.14 0.25 0.18 0.29 0.19 0.30 Nb: pw,m (p w,h )isanindicatorvariable=1iftheparticipant sgoalp w lies between 5% and 8% (above 8%) of his initial weight w 0.