Meditation Routine Effectiveness

Summary

This experiment investigates meditation routine effectiveness. Box-Behnken design to maximize stress reduction and focus improvement by tuning session duration, time of day, and technique.

The design varies 3 factors: duration min (min), ranging from 5 to 30, time of day (hour), ranging from 6 to 22, and guided pct (%), ranging from 0 to 100. The goal is to optimize 2 responses: stress reduction (pts) (maximize) and focus score (pts) (maximize). Fixed conditions held constant across all runs include frequency = daily, environment = quiet_room.

A Box-Behnken design was chosen because it efficiently fits quadratic models with 3 continuous factors while avoiding extreme corner combinations — requiring only 15 runs instead of the 8 needed for a full factorial at two levels.

Quadratic response surface models were fitted to capture potential curvature and factor interactions. The RSM contour plots below visualize how pairs of factors jointly affect each response.

Key Findings

For stress reduction, the most influential factors were time of day (38.3%), guided pct (35.8%), duration min (25.9%). The best observed value was 6.8 (at duration min = 17.5, time of day = 14, guided pct = 50).

For focus score, the most influential factors were time of day (39.8%), guided pct (37.2%), duration min (23.0%). The best observed value was 6.3 (at duration min = 17.5, time of day = 14, guided pct = 50).

Recommended Next Steps

Run confirmation experiments at the predicted optimal settings to validate the model.
Consider whether any fixed factors should be varied in a future study.

Experimental Setup

Factors

Factor	Low	High	Unit
`duration_min`	5	30	min
`time_of_day`	6	22	hour
`guided_pct`	0	100	%

Fixed: frequency = daily, environment = quiet_room

Responses

Response	Direction	Unit
`stress_reduction`	↑ maximize	pts
`focus_score`	↑ maximize	pts

Configuration

use_cases/110_meditation_routine/config.json

{
  "metadata": {
    "name": "Meditation Routine Effectiveness",
    "description": "Box-Behnken design to maximize stress reduction and focus improvement by tuning session duration, time of day, and technique"
  },
  "factors": [
    {
      "name": "duration_min",
      "levels": [
        "5",
        "30"
      ],
      "type": "continuous",
      "unit": "min"
    },
    {
      "name": "time_of_day",
      "levels": [
        "6",
        "22"
      ],
      "type": "continuous",
      "unit": "hour"
    },
    {
      "name": "guided_pct",
      "levels": [
        "0",
        "100"
      ],
      "type": "continuous",
      "unit": "%"
    }
  ],
  "fixed_factors": {
    "frequency": "daily",
    "environment": "quiet_room"
  },
  "responses": [
    {
      "name": "stress_reduction",
      "optimize": "maximize",
      "unit": "pts"
    },
    {
      "name": "focus_score",
      "optimize": "maximize",
      "unit": "pts"
    }
  ],
  "settings": {
    "operation": "box_behnken",
    "test_script": "use_cases/110_meditation_routine/sim.sh"
  }
}

Experimental Matrix

The Box-Behnken Design produces 15 runs. Each row is one experiment with specific factor settings.

Run	`duration_min`	`time_of_day`	`guided_pct`
1	17.5	6	0
2	17.5	14	50
3	30	14	100
4	30	14	0
5	17.5	14	50
6	17.5	14	50
7	5	14	100
8	30	6	50
9	17.5	6	100
10	30	22	50
11	5	14	0
12	17.5	22	100
13	5	6	50
14	5	22	50
15	17.5	22	0

Step-by-Step Workflow

1

Preview the design

Terminal

$ doe info --config use_cases/110_meditation_routine/config.json

2

Generate the runner script

Terminal

$ doe generate --config use_cases/110_meditation_routine/config.json \
    --output use_cases/110_meditation_routine/results/run.sh --seed 42

3

Execute the experiments

Terminal

$ bash use_cases/110_meditation_routine/results/run.sh

4

Analyze results

Terminal

$ doe analyze --config use_cases/110_meditation_routine/config.json

5

Get optimization recommendations

Terminal

$ doe optimize --config use_cases/110_meditation_routine/config.json

6

Multi-objective optimization

With 2 competing responses, use --multi to find the best compromise via Derringer–Suich desirability.

Terminal

$ doe optimize --config use_cases/110_meditation_routine/config.json --multi

7

Generate the HTML report

Terminal

$ doe report --config use_cases/110_meditation_routine/config.json \
    --output use_cases/110_meditation_routine/results/report.html

Features Exercised

Feature	Value
Design type	`box_behnken`
Factor types	`continuous` (all 3)
Arg style	`double-dash`
Responses	2 (stress_reduction ↑, focus_score ↑)
Total runs	15

Analysis Results

Generated from actual experiment runs using the DOE Helper Tool.

Response: stress_reduction

Top factors: time_of_day (38.3%), guided_pct (35.8%), duration_min (25.9%).

ANOVA

Source	DF	SS	MS	F	p-value
Source	DF	SS	MS	F	p-value
duration_min	2	2.5608	1.2804	9.849	0.0070
time_of_day	2	5.4075	2.7038	20.798	0.0007
guided_pct	2	5.2833	2.6416	20.320	0.0007
Lack	of	Fit	6	8.7178	1.4530
Pure	Error	2	0.2600
Error	8	8.9778	0.1300
Total	14	22.2293	1.5878

Pareto Chart

Main Effects Plot

Normal Probability Plot of Effects

Normal probability plot for stress_reduction

Half-Normal Plot of Effects

Model Diagnostics

Response: focus_score

Top factors: time_of_day (39.8%), guided_pct (37.2%), duration_min (23.0%).

ANOVA

Source	DF	SS	MS	F	p-value
Source	DF	SS	MS	F	p-value
duration_min	2	1.2879	0.6440	0.986	0.4143
time_of_day	2	4.0022	2.0011	3.063	0.1029
guided_pct	2	3.6697	1.8349	2.808	0.1191
Lack	of	Fit	6	7.3775	1.2296
Pure	Error	2	1.3067
Error	8	8.6841	0.6533
Total	14	17.6440	1.2603

Pareto Chart

Main Effects Plot

Normal Probability Plot of Effects

Half-Normal Plot of Effects

Model Diagnostics

Response Surface Plots

3D surfaces fitted with quadratic RSM. Red dots are observed data points.

focus score duration min vs guided pct

focus score duration min vs time of day

focus score time of day vs guided pct

stress reduction duration min vs guided pct

stress reduction duration min vs time of day

stress reduction time of day vs guided pct

Multi-Objective Optimization

When responses compete, Derringer–Suich desirability finds the best compromise. Each response is scaled to a 0–1 desirability, then combined via a weighted geometric mean.

Overall Desirability

D = 0.9545

Per-Response Desirability

Response	Weight	Desirability	Predicted	Dir
`stress_reduction`	1.5	0.9545	6.80 0.9545 6.80 pts	↑
`focus_score`	1.5	0.9545	6.30 0.9545 6.30 pts	↑

Recommended Settings

Factor	Value
`duration_min`	17.5 min
`time_of_day`	6 hour
`guided_pct`	100 %

Source: from observed run #8

Trade-off Summary

Sacrifice = how much worse than single-objective best.

Response	Predicted	Best Observed	Sacrifice
`focus_score`	6.30	6.30	+0.00

Top 3 Runs by Desirability

Run	D	Factor Settings
#10	0.8681	duration_min=17.5, time_of_day=22, guided_pct=100
#3	0.8621	duration_min=5, time_of_day=14, guided_pct=100

Model Quality

Response	R²	Type
`focus_score`	0.3396	linear

Full Multi-Objective Output

doe optimize --multi
============================================================
MULTI-OBJECTIVE OPTIMIZATION
Method: Derringer-Suich Desirability Function
============================================================

Overall desirability: D = 0.9545

Response                  Weight Desirability    Predicted  Direction
---------------------------------------------------------------------
stress_reduction             1.5       0.9545        6.80 pts   ↑
focus_score                  1.5       0.9545        6.30 pts   ↑

Recommended settings:
  duration_min = 17.5 min
  time_of_day = 6 hour
  guided_pct = 100 %
  (from observed run #8)

Trade-off summary:
  stress_reduction: 6.80 (best observed: 6.80, sacrifice: +0.00)
  focus_score: 6.30 (best observed: 6.30, sacrifice: +0.00)

Model quality:
  stress_reduction: R² = 0.6846 (quadratic)
  focus_score: R² = 0.3396 (linear)

Top 3 observed runs by overall desirability:
  1. Run #8 (D=0.9545): duration_min=17.5, time_of_day=6, guided_pct=100
  2. Run #10 (D=0.8681): duration_min=17.5, time_of_day=22, guided_pct=100
  3. Run #3 (D=0.8621): duration_min=5, time_of_day=14, guided_pct=100

Full Analysis Output

doe analyze
=== Main Effects: stress_reduction ===
Factor                   Effect    Std Error   % Contribution
--------------------------------------------------------------
time_of_day              1.4536       0.3254            38.3%
guided_pct               1.3607       0.3254            35.8%
duration_min             0.9857       0.3254            25.9%

=== ANOVA Table: stress_reduction ===
Source                      DF           SS           MS          F    p-value
-----------------------------------------------------------------------------
duration_min                 2       2.5608       1.2804      9.849     0.0070
time_of_day                  2       5.4075       2.7038     20.798     0.0007
guided_pct                   2       5.2833       2.6416     20.320     0.0007
Lack of Fit                  6       8.7178       1.4530     11.177     0.0844
Pure Error                   2       0.2600       0.1300
Error                        8       8.9778       0.1300
Total                       14      22.2293       1.5878

=== Summary Statistics: stress_reduction ===

duration_min:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  17.5                7     4.8143     1.4276     3.0000     6.7000
  30                  4     5.8000     0.3916     5.4000     6.3000
  5                   4     5.0000     1.5253     3.1000     6.8000

time_of_day:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  14                  7     4.5714     1.1996     3.0000     6.3000
  22                  4     6.0250     0.6652     5.2000     6.8000
  6                   4     5.2000     1.5122     3.1000     6.7000

guided_pct:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  0                   4     5.8750     0.7411     5.2000     6.7000
  100                 4     5.4500     0.5745     4.8000     6.2000
  50                  7     4.5143     1.5443     3.0000     6.8000

=== Main Effects: focus_score ===
Factor                   Effect    Std Error   % Contribution
--------------------------------------------------------------
time_of_day              1.2536       0.2899            39.8%
guided_pct               1.1714       0.2899            37.2%
duration_min             0.7250       0.2899            23.0%

=== ANOVA Table: focus_score ===
Source                      DF           SS           MS          F    p-value
-----------------------------------------------------------------------------
duration_min                 2       1.2879       0.6440      0.986     0.4143
time_of_day                  2       4.0022       2.0011      3.063     0.1029
guided_pct                   2       3.6697       1.8349      2.808     0.1191
Lack of Fit                  6       7.3775       1.2296      1.882     0.3869
Pure Error                   2       1.3067       0.6533
Error                        8       8.6841       0.6533
Total                       14      17.6440       1.2603

=== Summary Statistics: focus_score ===

duration_min:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  17.5                7     4.7857     1.2020     2.8000     6.3000
  30                  4     5.4000     0.7024     4.7000     6.1000
  5                   4     4.6750     1.4385     2.9000     6.3000

time_of_day:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  14                  7     4.4714     1.0420     2.8000     6.1000
  22                  4     5.7250     0.6946     4.9000     6.3000
  6                   4     4.9000     1.3760     2.9000     5.9000

guided_pct:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  0                   4     5.6000     0.9018     4.3000     6.3000
  100                 4     5.1000     0.2944     4.7000     5.4000
  50                  7     4.4286     1.3708     2.8000     6.3000

Optimization Recommendations

doe optimize
=== Optimization: stress_reduction ===
Direction: maximize

Best observed run: #8
  duration_min = 17.5
  time_of_day = 14
  guided_pct = 50
  Value: 6.8

RSM Model (linear, R² = 0.3529, Adj R² = 0.1764):
  Coefficients:
    intercept                      +5.1267
    duration_min                   -0.2500
    time_of_day                    +0.9500
    guided_pct                     -0.1250

RSM Model (quadratic, R² = 0.7557, Adj R² = 0.3160):
  Coefficients:
    intercept                      +5.6000
    duration_min                   -0.2500
    time_of_day                    +0.9500
    guided_pct                     -0.1250
    duration_min*time_of_day       +0.0250
    duration_min*guided_pct        +0.5750
    time_of_day*guided_pct         +1.1250
    duration_min^2                 -0.6125
    time_of_day^2                  -0.5125
    guided_pct^2                   +0.2375

  Curvature analysis:
    duration_min                   coef=-0.6125  concave (has a maximum)
    time_of_day                    coef=-0.5125  concave (has a maximum)
    guided_pct                     coef=+0.2375  convex (has a minimum)

  Notable interactions:
    time_of_day*guided_pct         coef=+1.1250  (synergistic)
    duration_min*guided_pct        coef=+0.5750  (synergistic)

  Predicted optimum (from quadratic model, at observed points):
    duration_min = 17.5
    time_of_day = 22
    guided_pct = 100
    Predicted value: 7.2750

  Surface optimum (via L-BFGS-B, quadratic model):
    duration_min = 21.0714
    time_of_day = 22
    guided_pct = 100
    Predicted value: 7.3250

  Model quality: Good fit — general trends are captured, some noise remains.

Factor importance:
  1. time_of_day  (effect: 1.9, contribution: 59.6%)
  2. duration_min  (effect: 0.8, contribution: 26.5%)
  3. guided_pct  (effect: 0.4, contribution: 13.9%)

=== Optimization: focus_score ===
Direction: maximize

Best observed run: #4
  duration_min = 17.5
  time_of_day = 14
  guided_pct = 50
  Value: 6.3

RSM Model (linear, R² = 0.2988, Adj R² = 0.1076):
  Coefficients:
    intercept                      +4.9200
    duration_min                   -0.4000
    time_of_day                    +0.6875
    guided_pct                     -0.1625

RSM Model (quadratic, R² = 0.8314, Adj R² = 0.5280):
  Coefficients:
    intercept                      +5.9333
    duration_min                   -0.4000
    time_of_day                    +0.6875
    guided_pct                     -0.1625
    duration_min*time_of_day       +0.0750
    duration_min*guided_pct        +0.0250
    time_of_day*guided_pct         +0.5500
    duration_min^2                 -0.9667
    time_of_day^2                  -1.1417
    guided_pct^2                   +0.2083

  Curvature analysis:
    time_of_day                    coef=-1.1417  concave (has a maximum)
    duration_min                   coef=-0.9667  concave (has a maximum)
    guided_pct                     coef=+0.2083  convex (has a minimum)

  Notable interactions:
    time_of_day*guided_pct         coef=+0.5500  (synergistic)

  Predicted optimum (from quadratic model, at observed points):
    duration_min = 17.5
    time_of_day = 22
    guided_pct = 100
    Predicted value: 6.0750

  Surface optimum (via L-BFGS-B, quadratic model):
    duration_min = 14.7779
    time_of_day = 14.4245
    guided_pct = 0
    Predicted value: 6.3541

  Model quality: Good fit — general trends are captured, some noise remains.

Factor importance:
  1. time_of_day  (effect: 1.8, contribution: 49.4%)
  2. duration_min  (effect: 1.3, contribution: 36.1%)
  3. guided_pct  (effect: 0.5, contribution: 14.5%)