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The authors have declared that no competing interests exist.

Conceived and designed the experiments: DEK RMM MJG. Performed the experiments: MJG. Analyzed the data: DEK MJG. Contributed reagents/materials/analysis tools: DEK RMM MJG. Wrote the paper: DEK RMM MJG.

The effect of mild depression on time estimation and production was investigated. Participants made both magnitude estimation and magnitude production judgments for five time intervals (specified in seconds) from 3 sec to 65 sec. The parameters of the best fitting psychophysical function (power law exponent, intercept, and threshold) were determined individually for each participant in every condition. There were no significant effects of mood (high BDI, low BDI) or judgment (estimation, production) on the mean exponent,

Subjective time passes slowly for people who are in a depressed state

Historically, there have been two main approaches to the psychology of direct time perception. The psychophysical judgment approach has used magnitude estimation and magnitude production tasks and has used estimated parameters of the psychophysical function relating psychological duration to clock time in order to explore timing accuracy. What will be termed here the bias approach looks at deviations of estimates from clock time, i.e. accuracy, as a function of participant groups and experimental conditions. As will be discussed shortly, deviation measures of accuracy bring particular analytic problems that have not been fully explicated in relation to between group effects, such as depression.

This study investigates the effect of mood state and judgment method on direct time judgments, involving durations from 2 s to 65 s, with 5 time categories, termed ‘timecats’ in each experimental condition Two methods of direct judgment are used: estimation and production, with the term ‘judgment’ used here to refer to either method. The term

The study as reported here had two main aims. The first was to establish whether a depressive realism effects is present for time estimation so one focus is on the effect of mood on time estimation. The second aim was to evaluate the relation between estimation and production judgments. Thus the second focus is on assessing classes of model, as one posited implication of internal clock or pacemaker models is that there will be a negative correlation between estimation and production. A final third aim was to compare results from the absolute judgment with results from the more complex form of relative judgment described above. In the end this final aim was not realized because nearly half the participants appeared unable to successfully perform the version of the relative task used here. The difficulties with the relative task in no way invalidate the highly reliable results from the absolute task. As a discussion of relative task performance and the relative merits of each method are beyond the scope of this paper and we do not discuss further (see

Psychophysical functions relate psychological sensation, Ψ, to physical intensity, P, where Ψ is expressed numerically on a ratio scale. That is, participants are instructed to assign numbers in such a way that if a physical stimulus, of magnitude P1, is perceived as twice as intense as a stimulus, P2, then the number Ψ1, assigned to P1 should be twice as large as the number, Ψ2, assigned to P2. Since the seminal work of Stevens

Marks and Stevens, showed as early as 1968, that

In order to use the ‘best’ psychophysical function in this study, we evaluated goodness of fit for ^{2} values were obtained separately for all functions for every participant. These adjusted r^{2} values were then converted to Z values to correct for ceiling effects, as r was close to 1 for most functions. Then an ANOVA was conducted with Z as response, mood (depressed, low BDI) as a between factor predictor, and judgment (estimation, production), number of parameters (2, 3) and format (log, power) as repeated measures predictors. The 3 parameter models that include the threshold parameter, ^{2} = .57 (η^{2} = .14 is a ‘large’ effect size by convention). The power models fit better than the log models overall, However, post hoc analyses, following up the interaction, shows that this superiority of power models is only present for the 2 parameter models, F (1,38) = 27.8, p<.0005, η^{2} = .42; and not significant for the 3 parameter models F (1,38) = 1.0, p = .333. In summary, the best fitting model is the 3-parameter power model, although it was not reliably superior to the 3-parameter log model. A similar re-analysis of previously reported roughness functions

Using

The second approach looks at bias, i.e. the average magnitude of over or under estimation, as the main dependent variable. Most investigations of non-time variables, such as mood, psychopathology, concurrent task, or drugs, use this approach

SET is often evaluated by a

Our interest is in mood, i.e. in whether there is a depressive realism effect on time estimation, where people who are mildly depressed are more accurate in time estimation than those who show little evidence of depression through their scores on depression questionnaires such as the Beck Depression Inventory, BDI,

This study remedies that problem. The effect of the explanatory variables, mood, judgment and time category are investigated using mixed model ANOVA on all three deviation from accuracy measures: raw = τ–t, ratio = τ/t, and ln = ln(τ /t). This enables not only evaluation of the effect of the explanatory variables, but also evaluation of the mean deviation from perfect accuracy in each combination of conditions. As with the psychophysical functions, the number of individuals showing each pattern of accuracy is also evaluated.

In summary, the major predictor variables are mood, judgment, and time category (timecat). Obviously we expect time judgments to increase with clock time. The psychophysical function question is the form of that increase, as expressed in the parameters,

Ethics approval was granted by the Psychology Ethics Committee under delegated authority from the Ethics Committee of the University of Hertfordshire, to Rachel Msetfi, Protocol Number: PSY/01/07/RM, extended to include Diana Kornbrot and Melvyn Grimwood, Jan 2011.

There were 46 students, who participated in this study as a course requirement. Participants were categorized post hoc on the basis of their Beck Depression Inventory scores [BDI: 40] as the: low BDI group, BDI <7, or high BDI group with BDI ≥7). The criterion of BDI ≥7 corresponds to a median split for these recruited participants. This is a lower value than the criterion of BDI ≥9 from the standardisation of the test,

All participants completed four counterbalanced conditions comprising two tasks (absolute, A, or relative, R) crossed with two judgment types (estimation, E, or production, P). For absolute estimation, participants judged the duration of presented intervals in seconds, with the following instructions.

“In this task you will be asked to listen to 5 tones of varying lengths. Before you listen to the tones you will be asked to remember a number. When the tone finishes you will be asked to estimate the length of the tone in seconds and remember the number.

Please ask if you have any questions. If you are comfortable to proceed to the experiment press any key.”

For absolute production, they generated intervals specified by the experimenter in seconds with the following instructions.

“In this task you will be asked to generate 5 tones of varying lengths by pressing the space bar to start and finish the tone. Before generating each tone you will be asked to remember a number.

Please ask if you have any questions. If you are comfortable to proceed to the experiment press the space bar.”

All participants judged five durations (timecat) per condition, varying from 2 s to 65 s on a logarithmic scale. Durations are shown in

Timecat | Production | Estimation | |||

1 | 2 | 3 | 4 | ||

1 | 5 | 2 | 3 | 4 | 5 |

2 | 10 | 11 | 10 | 12 | 13 |

3 | 18 | 24 | 20 | 16 | 22 |

4 | 34 | 36 | 28 | 39 | 30 |

5 | 65 | 52 | 64 | 55 | 58 |

The planned recruitment was 20 low BDI and 20 high BDI participants, with the intention of using all parameters separately as dependent variables. A negative correlation (−.2) between estimation and production was assumed (an estimate based on the known small negative correlation between estimation and production). The final design thus has one between subjects factor, mood, and one within subjects factor judgment. Power was 68% to detect a medium mood effect, f = .25 and 97% to detect a large effect, f = .40.4. Power for the judgment main effect and the mood by judgment interaction was 51% to detect a medium, f = .25, or 89% to detect a large effect, f = .4. Power was calculated using G*

Participants were seated in front of a PC in a quiet cubicle. They then read the general information sheet, signed the consent form, and received a verbal introduction. Each condition started with a screen presenting instructions. Participants initiated the first trial by pressing any key. In the estimation condition the interval to be estimated started and ended with a brief 200 Hz tone. In the production condition the interval started with a brief 200 Hz tone and was terminated by the participant pressing the space bar. There was a short break between conditions. After the fourth condition, participants completed the computerized version of the BDI. Participants were then debriefed and given a sheet including information on services for people feeling depressed.

Inferential tests were carried out at the 95% confidence level, lower and upper 95% confidence levels follow parameter estimates in parentheses. The 46 original participants comprised 24 low BDI and 22 high BDI participants. Psychophysical functions were obtained for each participant for each judgment combination using ^{2}_{adj} ≥.90 was used to assess success. Data from 4 out of 24 participants in the depressed group, and 3 out of 24 in the low BDI group, produced ^{2}_{adj} <0.90 for at least one condition, or showed disregard of the memory instructions. Data for these participants were excluded from all further analyses and are not discussed further. After this screening process 21 low BDI and 18 high BDI participants remained.

Psychophysical parameters

For the power exponent

There were 39 individual estimation functions and 39 individual production functions. If there is no tendency for

By contrast, for the intercept parameter ^{2} = .17, with no reliable main effects. ^{2} = .17; while for depressed participants mean ^{2} = .20.

Mood | Judgment | Mean | SD | LCL | UCL | Min | Max |

Normal | Estimation | 2.07 | 2.09 | 1.36 | 2.78 | .37 | 7.12 |

Production | 1.12 | .59 | .72 | 1.52 | .09 | 2.27 | |

Depressed | Estimation | .96 | .72 | .20 | 1.73 | .05 | 2.51 |

Production | 1.65 | 1.17 | 1.22 | 2.08 | .01 | 4.57 |

Mood | Judge | a<1, p<.05 | a<1, ns | a>1, ns | a>1, p<.05 |

Low BDI | Estimation | 1 | 8 | 10 | 2 |

Production | 2 | 5 | 12 | 2 | |

High BDI | Estimation | 4 | 6 | 7 | 1 |

Production | 1 | 5 | 12 | 0 |

There were no significant effects on the parameter

Legend: Upper panel,

Legend: Left panels, normal quantile plots; right panels box plots. Top panel,

The ANOVAs provide confidence intervals about means for each accuracy measure, but of course these measures are not directly comparable numerically. Consequently, all measures have been converted into a common metric of percentage over and underestimate, as shown in

Measure | Mood | Judgment | Mean | LCL | UCL | t | p |

Difference | Low BDI | Estimation | 13.3 | 1.2 | 25.3 | 2.23 | .038 |

Production | −14.3 | −27.9 | −.7 | 2.13 | .046 | ||

High BDI | Estimation | −4.0 | −17.0 | 9.0 | .62 | .540 | |

Production | 6.8 | −7.9 | 21.5 | .94 | .361 | ||

Ratio | Low BDI | Estimation | 16.0 | 3.4 | 28.7 | 2.58 | .018 |

Production | −13.0 | −25.2 | −.9 | 2.17 | .042 | ||

High BDI | Estimation | −3.1 | −16.7 | 10.5 | .46 | .649 | |

Production | 7.9 | −5.3 | 21.0 | 1.22 | .238 | ||

ln(Ratio) | Low BDI | Estimation | 10.8 | −1.0 | 24.1 | 1.84 | .081 |

Production | −15.5 | −23.9 | −6.2 | 3.27 | .004 | ||

High BDI | Estimation | −5.7 | −16.6 | 6.5 | .98 | .339 | |

Production | 3.0 | −8.0 | 15.3 | .52 | .607 |

The ANOVAs showed no main effects for mood (all F(1, 37) <1) or judgment (all F(1,37) <1.8). However, the depressive realism effect shows up for all three measures as significant mood by judgment interactions: for the ^{2} = .12; for the ^{2} = .14; for the ^{2} = .14.

At the individual level there was no significant asymmetry in the proportion of participants over or under estimating for estimation or production for the low BDI group, or for estimation in the high BDI group for any measure. By contrast, all measures had 17/21 participants underestimating for production, exact p = .0007.

Ln(ratio) and ratio were almost identical in terms of significant departures form accuracy, while difference showed many fewer significant departures. The results are reported for ln(ratio), since this is our preferred measure. For the low BDI group estimation gave 7/21 significant overestimates for, p = <.00005 and 2/21 underestimates, p = .0148; and for production it gave 8/21 significant underestimates, p<.00005 and 2/21 overestimates. For the high BDI group, estimation gave 4/18 underestimates, p = .0001 and 2/18 overestimates; while production gave 3/18 overestimates and 3/18 underestimates p = .0096. Thus the low BDI group shows more significant effects in the predicted direction 14/19, p<.0005; while the high BDI group also shows more significant departures than expected by chance, but with no discernible relation to estimation method.

The correlation between estimation accuracy and production accuracy was calculated for all three accuracy measures, separately for each mood group. All accuracy measures show a strong negative correlation between estimation and production, with all p values <.05 for the high BDI and all p values <.0005 for the low BDI. For the high BDI: r (

At the individual level, it is noteworthy that

Psychophysical functions and bias measures were used to assess timing accuracy and between groups differences related to depressed mood. As will be discussed below, data from both types of measure consistently indicated the presence of bias, such that people for whom there was evidence of mild depression (high BDI participants) made time judgments that were generally closer to accuracy than those made by people with low BDI. Below we discuss the results from each measure below, make several methodological recommendations for future work, and then discuss theoretical implications for timing models and depressive realism.

The key psychophysical parameter

However, the offset intercept parameter,

In summary, it appears that both mood and judgment method have at most a small effect on the way subjective time grows with physical time (study was powered to detect a medium effect), the exponent, ^{2} = .14 is ‘large’ by convention).

All three measures of bias show a depressive realism effect such that the high BDI group was more accurate than the low BDI group.

The current study was not designed to have sufficient power to detect differences in patterns of individual results. The findings are nevertheless interesting and suggest that differences in mean values may occur because more participants have values in one direction than another rather than because all participants have small effects in the same direction. Thus mean over estimates in estimation and under estimates in production for the low BDI group may occur because more of these participants have significant results following this pattern. The low BDI group had 9/21 significant departures from accuracy for estimation functions, seven of them over estimates; and 10/21 significant departures from accuracy for production, eight of them under estimates. The high BDI group also had more significant departures from accuracy (6/18) than is expected by chance but evenly split, three over, three under for estimation, and four under and two 2 over for production. Exploring patterns of accuracy amongst individual participants was shown to be useful in this study and deserves more attention.

Two main methodological recommendations follow from this work. Firstly, the best fitting psychophysical model should be used to estimate psychophysical parameters. As Allan (1983) pointed out, there is absolutely no excuse for lazily assuming two parameter logarithmic modes, although these may also need to be fitted to compare with earlier results. Good estimates of functional form require judgments of a minimum of 5 different physical values. Its our view, that one gets power per pound (bang per buck) by increasing the number of time intervals to be estimated than by having several replications of each estimate (but we have not yet tested this mathematically).

Secondly, estimates of accuracy, for time estimation at least, should use the

There has been much recent discussion of the shortcomings of psychological research, with social pressures for replication at the forefront of this debate

The negative correlations, between estimation and production parameters, are consistent with a timing mechanism involving the accumulation of ticks on an internal clock. Moreover, these correlations are salient for high BDI as well as low BDI participants in spite of the minimal effects on accuracy. A lack of correlation would have been a challenge to scalar timing. However, there are other explanations for such correlations that have either multiple clocks or no clocks at all, see

Some workers using the scalar timing framework postulate that variables that interact with physical time must have an effect on the internal clock itself, e.g.

Depressive realism has been demonstrated here to occur in time perception, in addition to the well-documented effects in other domains

So why are these participants, who score above average on a depression scale more accurate in their timing? The first point to note is that these mildly depressed people who are apparently fully functioning in a University environment are not similar to clinically depressed group, where performance has

The number of emotion or mood related variables that might bring about these effects and influence time perception is large and diverse

Depressive realism is a phenomenon that has been characterised as confined to a small number of specialised situations

We would like to acknowledge the contribution of Lorraine Allan, who sadly died in 2012, both to this Ms. discussions, to reviews of our earlier work and to our general thinking on both depressive realism and timing.