Study 2: every table and figure
Each analysis from the dissertation, rebuilt from the released data, with a figure beside every table. Hover over any mark for the details.
Deep dive: every table and figure
The rest of this page rebuilds each analysis from the public data. Hover over any mark for the details, and open the guide below if a term is unfamiliar.
Plain-language guide to the terms
- Trust
- How willing someone is to follow the advice. In these studies, people rated this from 0 (not at all) to 10 (completely).
- Quantitative reasoning
- Deciding with numbers, data and statistics, like reading a lab result.
- Intuition
- Deciding with experience and judgment, like a doctor sensing that something is off when the tests look fine.
- Effect size (Cohen's d)
- How big a difference is, on a scale that can be compared across studies. This site uses the Funder and Ozer (2019) labels for psychology: about 0.20 is small, 0.41 is medium, 0.63 is large, and 0.87 or more is very large.
- 95% interval
- The range of values the true average probably falls in. A narrow range means a precise estimate; a range that includes zero means the difference may not be real.
- p value
- How surprising the result would be if there were no real difference. A p below .05 is the usual bar for calling a result reliable, and "p < .001" means chance is a very unlikely explanation.
- Mixed model
- A way to analyze data when each person gives many ratings, so that people who rate everything high or low do not distort the results.
- Mediation
- A test of whether one thing explains part of the link between two others. Here: does seeing a doctor as more competent explain part of why people trust the doctor more?
- Preregistered
- The plan for the study and its analysis was written and posted publicly before anyone looked at the data.
How to read this page. Differences are always doctor minus AI, so a positive number means more trust in, or a higher rating of, the doctor. Ratings are shown on the scales people saw: 0 to 10, except competence and warmth (0 to 4). The public file groups age into four bands, so the models that used age in years use the band number (1 = 18 to 44, 4 = 70 and over) and the age results differ a little from the dissertation; the “Does the gap differ between people?” section shows both.
Who took part
106 adults, recruited through CloudResearch's Prime Panels, finished the study. Each answered the same questions about a doctor and about an AI, so every comparison below is within a person.
What to look for. The share in each group. Older adults and women make up the largest groups, so the results speak most directly to them.
| Group | People | Share |
|---|---|---|
| Age group: 18-44 | 19 | 17.9% |
| Age group: 45-59 | 13 | 12.3% |
| Age group: 60-69 | 31 | 29.2% |
| Age group: 70+ | 43 | 40.6% |
| Gender: Woman | 64 | 60.4% |
| Gender: Man | 39 | 36.8% |
| Race: White | 86 | 81.1% |
| Race: Another or multiple | 18 | 17.0% |
| Education: No college degree | 56 | 52.8% |
| Education: College degree or more | 50 | 47.2% |
| How religious: Not at all to slightly | 36 | 34.0% |
| How religious: Moderately | 23 | 21.7% |
| How religious: More than moderately | 47 | 44.3% |
| Experience with AI: None or a little | 86 | 81.1% |
| Experience with AI: Moderate or more | 20 | 18.9% |
Shares are of all 106 people. Left blank in the file: gender (3), race (2). Race is shown as White or another or multiple because no other group reached 30 people. Age is in bands; exact age is not released.
Table 1 as a figure
Each bar is the share of the 106 people in that group. Longer means more of the sample. Hover a bar for the head count.
Twelve medical decisions
The twelve decisions cross four kinds of health problem (bodily injury, mental health, acute sickness, chronic sickness) with three stages of care (preventing, diagnosing and prescribing). For each, people slid from 0 (needs only intuition) to 100 (needs only quantitative reasoning).
What to look for. Every mean sits above 50, so all twelve decisions were seen as leaning somewhat toward quantitative reasoning. The preventative decisions sit lowest.
| Decision | n | Mean | SD | Median | Min | Max | Skew | Kurtosis | SE |
|---|---|---|---|---|---|---|---|---|---|
| Diagnose diabetes | 105 | 68.82 | 26.61 | 73.15 | 1.53 | 100.00 | −0.78 | −0.05 | 2.60 |
| Prescribe insulin | 105 | 66.39 | 25.30 | 68.99 | 0.78 | 100.00 | −0.57 | −0.18 | 2.47 |
| Diagnose a broken bone | 105 | 65.23 | 30.21 | 71.34 | 0.00 | 100.00 | −0.69 | −0.50 | 2.95 |
| Diagnose strep throat | 105 | 62.97 | 30.65 | 68.03 | 0.00 | 100.00 | −0.58 | −0.74 | 2.99 |
| Prescribe pain medication | 105 | 60.80 | 25.78 | 55.98 | 1.36 | 100.00 | −0.23 | −0.49 | 2.52 |
| Prescribe antibiotics | 105 | 60.55 | 29.83 | 65.61 | 0.91 | 100.00 | −0.58 | −0.66 | 2.91 |
| Prescribe antidepressants | 105 | 60.10 | 25.19 | 56.89 | 0.00 | 100.00 | −0.34 | −0.22 | 2.46 |
| Diagnose depression | 105 | 58.93 | 28.70 | 57.78 | 0.00 | 100.00 | −0.35 | −0.75 | 2.80 |
| Recommend a strict diet | 105 | 57.64 | 28.67 | 55.40 | 0.78 | 100.00 | −0.41 | −0.68 | 2.80 |
| Recommend vitamin C and zinc | 105 | 57.14 | 30.61 | 53.58 | 0.00 | 100.00 | −0.30 | −1.03 | 2.99 |
| Recommend meditation | 105 | 55.52 | 28.19 | 51.63 | 0.00 | 100.00 | −0.15 | −0.79 | 2.75 |
| Recommend stretching | 105 | 54.10 | 25.38 | 50.98 | 0.00 | 100.00 | −0.16 | −0.34 | 2.48 |
Sorted from most to least quantitative reasoning needed. Skew and kurtosis are the estimates psych::describe reports.
Figure 1. Every decision, every person
Each row is one decision. Every dot is one person's answer on a 0 to 100 slider, from needs only intuition (0) to needs only quantitative reasoning (100), and the curve shows where answers pile up.
Outline: how answers are spread (smoothed). Dots: one person each. Diamond and bar: the average and its bootstrapped 95% interval.
View as a table
| Measure | n | Mean | 95% interval |
|---|---|---|---|
| Diagnose diabetes | 105 | 68.8 | 63.7 to 73.7 |
| Prescribe insulin | 105 | 66.4 | 61.6 to 71.0 |
| Diagnose a broken bone | 105 | 65.2 | 59.1 to 70.8 |
| Diagnose strep throat | 105 | 63.0 | 57.0 to 68.6 |
| Prescribe pain medication | 105 | 60.8 | 55.9 to 65.7 |
| Prescribe antibiotics | 105 | 60.5 | 54.6 to 66.1 |
| Prescribe antidepressants | 105 | 60.1 | 55.1 to 65.0 |
| Diagnose depression | 105 | 58.9 | 53.2 to 64.2 |
| Recommend a strict diet | 105 | 57.6 | 52.1 to 62.9 |
| Recommend vitamin C and zinc | 105 | 57.1 | 51.5 to 62.9 |
| Recommend meditation | 105 | 55.5 | 50.0 to 60.9 |
| Recommend stretching | 105 | 54.1 | 49.1 to 58.8 |
What to look for. The same ratings averaged into the groups used later. Compare the means across rows; the gaps between groups are what the later tests build on.
| Group | n | Mean | SD | Median | Min | Max | Skew | Kurtosis | SE |
|---|---|---|---|---|---|---|---|---|---|
| Diagnostic (4 decisions) | 105 | 63.99 | 24.90 | 66.13 | 4.45 | 100.00 | −0.66 | −0.14 | 2.43 |
| Prescriptive (4 decisions) | 105 | 61.96 | 22.69 | 61.23 | 4.39 | 100.00 | −0.37 | −0.10 | 2.21 |
| Preventative (4 decisions) | 105 | 56.10 | 24.25 | 53.06 | 1.53 | 100.00 | −0.25 | −0.38 | 2.37 |
| Physical health (9 decisions) | 105 | 61.52 | 21.71 | 61.01 | 4.68 | 100.00 | −0.33 | −0.18 | 2.12 |
| Mental health (3 decisions) | 105 | 58.18 | 23.09 | 56.48 | 0.00 | 100.00 | −0.19 | −0.11 | 2.25 |
| Bodily injury (3 decisions) | 105 | 60.04 | 21.93 | 58.35 | 3.46 | 100.00 | −0.30 | −0.15 | 2.14 |
| Acute sickness (3 decisions) | 105 | 60.22 | 26.54 | 61.25 | 1.51 | 100.00 | −0.41 | −0.60 | 2.59 |
| Chronic sickness (3 decisions) | 105 | 64.28 | 22.10 | 64.16 | 4.72 | 100.00 | −0.41 | −0.08 | 2.16 |
Each group is the average of its decisions. A person missing any decision in a group is missing for that group. Physical health is every decision except the mental health ones.
Figure 2. By kind of health problem
The same slider ratings, grouped by kind of health problem. Each dot is one person; the curve shows where answers cluster.
Outline: how answers are spread (smoothed). Dots: one person each. Diamond and bar: the average and its bootstrapped 95% interval.
View as a table
| Measure | n | Mean | 95% interval |
|---|---|---|---|
| Chronic sickness | 105 | 64.3 | 59.9 to 68.6 |
| Physical health | 105 | 61.5 | 57.2 to 65.7 |
| Acute sickness | 105 | 60.2 | 55.3 to 65.0 |
| Bodily injury | 105 | 60.0 | 55.8 to 64.3 |
| Mental health | 105 | 58.2 | 53.8 to 62.5 |
Figure 3. By stage of care
The same slider ratings, grouped by stage of care: preventing, diagnosing or prescribing.
Outline: how answers are spread (smoothed). Dots: one person each. Diamond and bar: the average and its bootstrapped 95% interval.
View as a table
| Measure | n | Mean | 95% interval |
|---|---|---|---|
| Diagnostic | 105 | 64.0 | 59.3 to 68.8 |
| Prescriptive | 105 | 62.0 | 57.8 to 66.1 |
| Preventative | 105 | 56.1 | 51.5 to 60.8 |
What to look for. Alpha near or above .80 means the decisions in a group can safely be averaged. Lower values mean the group is a looser bundle.
| Group | Decisions | Alpha | Mean inter-item r |
|---|---|---|---|
| Diagnostic | 4 | .88 | .65 |
| Prescriptive | 4 | .88 | .65 |
| Preventative | 4 | .88 | .65 |
| Physical health | 9 | .91 | .54 |
| Mental health | 3 | .80 | .57 |
| Bodily injury | 3 | .73 | .48 |
| Acute sickness | 3 | .84 | .65 |
| Chronic sickness | 3 | .76 | .52 |
Table 4 as a figure
Each dot is the alpha for one group of decisions: how alike people answered the decisions inside it. The dashed lines mark .70, .80 and .90; above .70 is usually taken as acceptable and above .80 as good.
Doctor versus AI
On average people would trust a doctor about 4.0 points more than an AI on the 0 to 10 scale (d = 1.34). 97 of 103 people trusted the doctor more across the twelve decisions, 4 trusted both the same, and 2 trusted the AI more. The preregistered tests (H1) ask this for each decision.
Figure 4. Each person's average trust, doctor and AI
Each dot is one person's average trust across the twelve decisions, once for the doctor and once for the AI, on a 0 to 10 scale. Higher means more trust.
Outline: how answers are spread (smoothed). Dots: one person each. Diamond and bar: the average and its bootstrapped 95% interval.
View as a table
| Measure | n | Mean | 95% interval |
|---|---|---|---|
| Doctor, average of twelve decisions | 104 | 8.0 | 7.6 to 8.4 |
| AI, average of twelve decisions | 105 | 4.2 | 3.6 to 4.7 |
What to look for. The gap column. Every decision shows more trust in the doctor, and the effect size (d) shows how large that is.
| Comparison | Doctor, AI: mean (SD) | Difference [95% CI] | t (df) | p | d [95% CI] | Doctor higher / same / lower |
|---|---|---|---|---|---|---|
| Recommend stretching | 8.08 (2.29), 4.80 (3.44) | 3.28 [2.66, 3.89] | 10.61 (104) | < .001 | 1.04 [0.80, 1.27] | 78 / 25 / 2 |
| Diagnose a broken bone | 8.48 (2.17), 4.05 (3.52) | 4.43 [3.74, 5.12] | 12.73 (104) | < .001 | 1.24 [0.99, 1.50] | 83 / 19 / 3 |
| Prescribe pain medication | 7.94 (2.50), 3.87 (3.30) | 4.08 [3.40, 4.75] | 12.05 (105) | < .001 | 1.17 [0.92, 1.42] | 81 / 21 / 4 |
| Recommend meditation | 7.60 (2.56), 4.49 (3.32) | 3.11 [2.43, 3.80] | 9.05 (105) | < .001 | 0.88 [0.65, 1.10] | 72 / 25 / 9 |
| Diagnose depression | 7.60 (2.49), 3.47 (3.02) | 4.13 [3.44, 4.82] | 11.85 (104) | < .001 | 1.16 [0.91, 1.40] | 84 / 17 / 4 |
| Prescribe antidepressants | 7.76 (2.63), 3.36 (3.02) | 4.40 [3.73, 5.07] | 13.11 (104) | < .001 | 1.28 [1.02, 1.54] | 87 / 15 / 3 |
| Recommend vitamin C and zinc | 7.75 (2.67), 4.67 (3.50) | 3.08 [2.42, 3.75] | 9.16 (105) | < .001 | 0.89 [0.66, 1.11] | 73 / 26 / 7 |
| Diagnose strep throat | 8.39 (2.23), 3.85 (3.32) | 4.54 [3.87, 5.22] | 13.32 (104) | < .001 | 1.30 [1.04, 1.56] | 85 / 17 / 3 |
| Prescribe antibiotics | 8.35 (2.38), 4.25 (3.25) | 4.10 [3.47, 4.74] | 12.76 (105) | < .001 | 1.24 [0.98, 1.49] | 84 / 21 / 1 |
| Recommend a strict diet | 7.88 (2.37), 4.63 (3.46) | 3.25 [2.59, 3.90] | 9.84 (105) | < .001 | 0.96 [0.72, 1.18] | 74 / 25 / 7 |
| Diagnose diabetes | 8.30 (2.10), 3.99 (3.29) | 4.30 [3.63, 4.98] | 12.72 (104) | < .001 | 1.24 [0.98, 1.49] | 84 / 17 / 4 |
| Prescribe insulin | 8.21 (2.06), 3.83 (3.43) | 4.38 [3.69, 5.07] | 12.61 (105) | < .001 | 1.22 [0.97, 1.48] | 81 / 20 / 5 |
Paired t tests, two-sided. The 95% interval for d inverts the noncentral t distribution. The gap is large for every decision and smallest for the four preventative ones.
Figure 5. Trust in a doctor and in an AI, decision by decision
Each row is a decision. The two dots show the average trust in the doctor and in the AI, with a bar for the 95% interval. The farther apart the dots, the bigger the gap.
View as a table
| Decision | Trust: average [95% interval] |
|---|---|
| Doctor | 8.1 [7.6, 8.5] |
| AI | 4.8 [4.2, 5.5] |
| Doctor | 8.4 [8.0, 8.8] |
| AI | 4.0 [3.4, 4.7] |
| Doctor | 7.9 [7.5, 8.4] |
| AI | 3.9 [3.2, 4.5] |
| Doctor | 7.6 [7.1, 8.1] |
| AI | 4.5 [3.9, 5.1] |
| Doctor | 7.6 [7.1, 8.1] |
| AI | 3.5 [2.9, 4.1] |
| Doctor | 7.8 [7.3, 8.3] |
| AI | 3.4 [2.8, 4.0] |
| Doctor | 7.8 [7.2, 8.3] |
| AI | 4.7 [4.0, 5.3] |
| Doctor | 8.4 [8.0, 8.8] |
| AI | 3.9 [3.3, 4.5] |
| Doctor | 8.3 [7.9, 8.8] |
| AI | 4.3 [3.6, 4.9] |
| Doctor | 7.9 [7.4, 8.3] |
| AI | 4.6 [4.0, 5.3] |
| Doctor | 8.3 [7.9, 8.7] |
| AI | 4.0 [3.4, 4.7] |
| Doctor | 8.2 [7.8, 8.6] |
| AI | 3.8 [3.2, 4.5] |
Figure 6. The gap and its size, decision by decision
Each dot is the gap for one decision: average trust in the doctor minus average trust in the AI. The right panel puts the gap in standard deviations (Cohen's d). The dashed lines mark a small, medium and large effect on the Funder and Ozer scale.
View as a table
| Decision | Trust gap (doctor − AI): value [95% interval] | Effect size (d): value [95% interval] |
|---|---|---|
| Recommend stretching | 3.3 [2.7, 3.9] | 1.0 [0.8, 1.3] |
| Diagnose a broken bone | 4.4 [3.7, 5.1] | 1.2 [1.0, 1.5] |
| Prescribe pain medication | 4.1 [3.4, 4.8] | 1.2 [0.9, 1.4] |
| Recommend meditation | 3.1 [2.4, 3.8] | 0.9 [0.7, 1.1] |
| Diagnose depression | 4.1 [3.4, 4.8] | 1.2 [0.9, 1.4] |
| Prescribe antidepressants | 4.4 [3.7, 5.1] | 1.3 [1.0, 1.5] |
| Recommend vitamin C and zinc | 3.1 [2.4, 3.8] | 0.9 [0.7, 1.1] |
| Diagnose strep throat | 4.5 [3.9, 5.2] | 1.3 [1.0, 1.6] |
| Prescribe antibiotics | 4.1 [3.5, 4.7] | 1.2 [1.0, 1.5] |
| Recommend a strict diet | 3.3 [2.6, 3.9] | 1.0 [0.7, 1.2] |
| Diagnose diabetes | 4.3 [3.6, 5.0] | 1.2 [1.0, 1.5] |
| Prescribe insulin | 4.4 [3.7, 5.1] | 1.2 [1.0, 1.5] |
What to look for. The same gap, now for whole groups of decisions. Compare the d column across rows to see which groups show a bigger or smaller gap.
| Group | Doctor, AI: mean (SD) | Difference [95% CI] | t (df) | p | d [95% CI] | Doctor higher / same / lower |
|---|---|---|---|---|---|---|
| All twelve decisions | 8.09 (1.99), 4.10 (2.96) | 3.99 [3.41, 4.57] | 13.61 (102) | < .001 | 1.34 [1.07, 1.61] | 97 / 4 / 2 |
| Diagnostic | 8.23 (1.90), 3.85 (3.03) | 4.38 [3.78, 4.98] | 14.40 (103) | < .001 | 1.41 [1.14, 1.68] | 95 / 5 / 4 |
| Prescriptive | 8.09 (2.15), 3.82 (3.01) | 4.27 [3.67, 4.86] | 14.17 (104) | < .001 | 1.38 [1.11, 1.65] | 94 / 8 / 3 |
| Preventative | 7.82 (2.31), 4.62 (3.16) | 3.20 [2.60, 3.81] | 10.53 (104) | < .001 | 1.03 [0.79, 1.26] | 86 / 14 / 5 |
| Physical health | 8.20 (1.95), 4.22 (3.05) | 3.98 [3.40, 4.57] | 13.55 (103) | < .001 | 1.33 [1.06, 1.59] | 98 / 4 / 2 |
| Mental health | 7.65 (2.32), 3.74 (2.86) | 3.91 [3.30, 4.53] | 12.67 (103) | < .001 | 1.24 [0.98, 1.50] | 89 / 10 / 5 |
| Bodily injury | 8.21 (2.02), 4.23 (3.14) | 3.97 [3.38, 4.56] | 13.32 (103) | < .001 | 1.31 [1.04, 1.57] | 91 / 11 / 2 |
| Acute sickness | 8.16 (2.23), 4.23 (3.14) | 3.93 [3.33, 4.54] | 12.85 (104) | < .001 | 1.25 [1.00, 1.51] | 88 / 15 / 2 |
| Chronic sickness | 8.12 (2.00), 4.12 (3.13) | 4.00 [3.40, 4.60] | 13.20 (104) | < .001 | 1.29 [1.03, 1.55] | 91 / 12 / 2 |
Trust is the average of the decisions in the group.
Table 6 as a figure
Each dot is how much more people trusted a doctor than an AI, in standard deviations (Cohen's d), with a 95% interval. The dashed lines mark a small, medium and large effect on the Funder and Ozer scale. Every dot sits far to the right of all three.
How the doctor and the AI were seen
People also rated the doctor and the AI on eleven qualities. The doctor was rated higher on every one. The gaps are largest for warmth, understanding feelings, competence and intuition, and smallest for transparency, anticipating needs and quantitative reasoning.
What to look for. The difference column and d. Positive means the doctor was rated higher; larger d means a bigger difference.
| Quality (scale) | Doctor, AI: mean (SD) | Difference [95% CI] | t (df) | p | d [95% CI] | Doctor higher / same / lower |
|---|---|---|---|---|---|---|
| Quantitative reasoning (0 to 10) | 8.01 (2.42), 5.31 (3.40) | 2.70 [1.99, 3.41] | 7.53 (105) | < .001 | 0.73 [0.52, 0.94] | 66 / 25 / 15 |
| Intuition (0 to 10) | 8.15 (2.22), 4.35 (3.34) | 3.80 [3.08, 4.53] | 10.42 (105) | < .001 | 1.01 [0.78, 1.25] | 77 / 20 / 9 |
| Competence (0 to 4) | 2.96 (1.01), 1.49 (1.21) | 1.47 [1.20, 1.74] | 10.81 (105) | < .001 | 1.05 [0.81, 1.29] | 74 / 27 / 5 |
| Warmth (0 to 4) | 2.98 (1.10), 0.98 (1.22) | 2.00 [1.69, 2.31] | 12.71 (100) | < .001 | 1.26 [1.00, 1.53] | 80 / 18 / 3 |
| Accurate recommendations in general (0 to 10) | 7.97 (2.23), 4.97 (3.24) | 3.00 [2.34, 3.66] | 8.96 (105) | < .001 | 0.87 [0.64, 1.09] | 73 / 20 / 13 |
| Can anticipate my health needs (0 to 10) | 7.36 (2.64), 4.79 (3.41) | 2.57 [1.87, 3.27] | 7.27 (105) | < .001 | 0.71 [0.49, 0.92] | 66 / 23 / 17 |
| Understands my feelings (0 to 10) | 7.62 (2.62), 3.61 (3.34) | 4.01 [3.30, 4.72] | 11.14 (105) | < .001 | 1.08 [0.84, 1.32] | 84 / 12 / 10 |
| Can account for my health needs (0 to 10) | 7.67 (2.47), 4.63 (3.30) | 3.04 [2.33, 3.75] | 8.46 (105) | < .001 | 0.82 [0.60, 1.04] | 73 / 18 / 15 |
| Process feels familiar (0 to 10) | 7.66 (2.48), 4.56 (3.31) | 3.10 [2.39, 3.82] | 8.61 (105) | < .001 | 0.84 [0.61, 1.06] | 72 / 24 / 10 |
| Process is transparent (0 to 10) | 7.29 (2.56), 4.57 (3.37) | 2.73 [1.98, 3.47] | 7.25 (105) | < .001 | 0.70 [0.49, 0.92] | 69 / 18 / 19 |
| I understand the process (0 to 10) | 7.50 (2.53), 4.40 (3.31) | 3.10 [2.36, 3.85] | 8.27 (105) | < .001 | 0.80 [0.58, 1.02] | 66 / 29 / 11 |
Competence and warmth are on a 0 to 4 scale, the rest on 0 to 10, so differences are not comparable across scales; effect sizes (d) are. The seven mind-perception items are the last seven rows.
Figure 7. Quantitative reasoning
Each dot is one person's rating of this quality, for the doctor and for the AI. Where the two clouds sit apart, people saw the two recommenders differently.
Outline: how answers are spread (smoothed). Dots: one person each. Diamond and bar: the average and its bootstrapped 95% interval.
View as a table
| Measure | n | Mean | 95% interval |
|---|---|---|---|
| Doctor | 106 | 8.0 | 7.5 to 8.4 |
| AI | 106 | 5.3 | 4.7 to 6.0 |
Figure 8. Intuition
Each dot is one person's rating of this quality, for the doctor and for the AI. Where the two clouds sit apart, people saw the two recommenders differently.
Outline: how answers are spread (smoothed). Dots: one person each. Diamond and bar: the average and its bootstrapped 95% interval.
View as a table
| Measure | n | Mean | 95% interval |
|---|---|---|---|
| Doctor | 106 | 8.2 | 7.7 to 8.6 |
| AI | 106 | 4.3 | 3.7 to 5.0 |
Figure 9. Competence
Each dot is one person's rating of this quality, for the doctor and for the AI. Where the two clouds sit apart, people saw the two recommenders differently.
Outline: how answers are spread (smoothed). Dots: one person each. Diamond and bar: the average and its bootstrapped 95% interval.
View as a table
| Measure | n | Mean | 95% interval |
|---|---|---|---|
| Doctor | 106 | 3.0 | 2.8 to 3.2 |
| AI | 106 | 1.5 | 1.3 to 1.7 |
Figure 10. Warmth
Each dot is one person's rating of this quality, for the doctor and for the AI. Where the two clouds sit apart, people saw the two recommenders differently.
Outline: how answers are spread (smoothed). Dots: one person each. Diamond and bar: the average and its bootstrapped 95% interval.
View as a table
| Measure | n | Mean | 95% interval |
|---|---|---|---|
| Doctor | 102 | 3.0 | 2.8 to 3.2 |
| AI | 105 | 0.9 | 0.7 to 1.2 |
Does the gap depend on the decision?
The second preregistered hypothesis (H2) asked whether the doctor's edge changes with how much quantitative reasoning a decision needs. On its own, that need shifts the gap a little: for every extra 10 points the doctor's edge shrinks by 0.08 points (Table 8). The dissertation tests H2 with intuition, quantitative reasoning, warmth, competence, age and gender in the model, and there the interaction disappears (b = -0.002, p = .38; Table 11). I read that as no evidence that the need for quantitative reasoning moderates the gap. Comparing the twelve decisions with each other (Figure 11) shows a different pattern, because the four preventative decisions are rated as needing less quantitative reasoning and also show the smallest gaps; that comparison is descriptive and does not test H2.
What to look for. The 'Doctor' row is the gap; the 'need' row is whether trust moves with how much quantitative reasoning a decision needs; the last row is whether the gap changes with that need.
| Predictor | b [95% CI] | Standardized β | z | p | VIF |
|---|---|---|---|---|---|
| Intercept | 3.635 [3.101, 4.168] | 13.35 | < .001 | ||
| Doctor (versus AI) | 4.415 [4.034, 4.797] | 0.63 | 22.67 | < .001 | 5.63 |
| Quantitative reasoning the decision needs | 0.008 [0.002, 0.014] | 0.06 | 2.46 | .014 | 1.28 |
| Doctor × need for quantitative reasoning | −0.008 [−0.013, −0.002] | −2.65 | .008 | 5.92 |
Does the gap depend on how much quantitative reasoning a decision needs (H2). 2,514 ratings from 105 people. Person variance 4.18, slope variance 0.00016, residual 4.23. Share of variance between people (ICC) .50. R² .32 from the predictors alone, .66 with the person effects. AIC 11134.2. Random intercept for each person, plus a random slope for how much quantitative reasoning the decision needs in every model but the first; restricted maximum likelihood; Wald z tests. R squared is Nakagawa's marginal and conditional version, and the person share is the person variance over person plus residual variance. Standardized betas are b times the SD of the predictor over the SD of trust. AIC refits by maximum likelihood. Age enters as the age group number (1 = 18 to 44, 4 = 70 and over) because the public file does not hold age in years. The notebook's other attempts are not reproduced: one used a person's own average as its outcome and predictor and the notebook records that it was singular.
Table 8 as a figure
Each dot is one predictor's standardized effect on trust (β) with a 95% interval; the dashed lines mark a small, medium and large effect. An interval that crosses zero means the data cannot rule out no effect. Interactions have no standardized β, so they appear only in the table.
Figure 11. The gap and the need for quantitative reasoning, by decision
Each dot is one decision. Left to right is how much quantitative reasoning people said it needs; bottom to top is how much more they trusted the doctor than the AI. A flat cloud means the gap does not depend on the need.
Twelve dots, one per decision. The line is the best fit across the twelve (r = 0.80).
What goes with trust
The third hypothesis (H3) asked whether trust follows how people see the recommender. Quantitative reasoning, intuition, competence and warmth are all positively correlated for the doctor and for the AI. Because every person rated both, I also separate the part of each correlation that comes from who the person is (between people) from the part that comes from whether the recommender is the doctor or the AI (within people).
What to look for. Every correlation is positive, so people who rate a recommender high on one quality tend to rate it high on the others.
| Recommender | Pair | r | p | n |
|---|---|---|---|---|
| Doctor | Quantitative reasoning and Intuition | .790 | < .001 | 106 |
| Doctor | Quantitative reasoning and Competence | .524 | < .001 | 106 |
| Doctor | Quantitative reasoning and Warmth | .568 | < .001 | 102 |
| Doctor | Intuition and Competence | .691 | < .001 | 106 |
| Doctor | Intuition and Warmth | .625 | < .001 | 102 |
| Doctor | Competence and Warmth | .686 | < .001 | 102 |
| AI | Quantitative reasoning and Intuition | .637 | < .001 | 106 |
| AI | Quantitative reasoning and Competence | .694 | < .001 | 106 |
| AI | Quantitative reasoning and Warmth | .490 | < .001 | 105 |
| AI | Intuition and Competence | .547 | < .001 | 106 |
| AI | Intuition and Warmth | .610 | < .001 | 105 |
| AI | Competence and Warmth | .658 | < .001 | 105 |
Pearson correlations among the people who answered both items.
Table 9 as a figure
Each square is the correlation between two qualities. Darker blue means the two move together more strongly. The left grid is ratings of the doctor, the right is ratings of the AI.
What to look for. Compare the two columns. A strong between-people value means the pattern is about who the person is; a strong within-people value means it is about the recommender.
| Pair | Between people, r (p) | Within people, r (p) |
|---|---|---|
| Competence and Quantitative reasoning | .637 (< .001) | .771 (< .001) |
| Competence and Warmth | .609 (< .001) | .838 (< .001) |
| Competence and Intuition | .637 (< .001) | .777 (< .001) |
| Competence and Mind perception | .776 (< .001) | .889 (< .001) |
| Competence and Mind perception, three items | .773 (< .001) | .864 (< .001) |
| Quantitative reasoning and Warmth | .510 (< .001) | .671 (< .001) |
| Quantitative reasoning and Intuition | .783 (< .001) | .734 (< .001) |
| Quantitative reasoning and Mind perception | .811 (< .001) | .857 (< .001) |
| Quantitative reasoning and Mind perception, three items | .772 (< .001) | .842 (< .001) |
| Warmth and Intuition | .584 (< .001) | .781 (< .001) |
| Warmth and Mind perception | .640 (< .001) | .821 (< .001) |
| Warmth and Mind perception, three items | .646 (< .001) | .811 (< .001) |
| Intuition and Mind perception | .839 (< .001) | .827 (< .001) |
| Intuition and Mind perception, three items | .818 (< .001) | .831 (< .001) |
| Mind perception and Mind perception, three items | .983 (< .001) | .979 (< .001) |
Within-person correlations ask whether, for one person, the target rated higher on one quality (the doctor or the AI) is also rated higher on another. Between-person correlations use each person's average over the doctor and the AI. Within-person p values treat each person as one doctor-minus-AI difference, so they use 104 degrees of freedom, not the thousands of rows the notebook's long file holds.
Table 10 as a figure
The same idea for the between-person correlations: people who rate the doctor and AI high on one quality tend to rate them high on the others. Darker blue is a stronger link.
Reliability of the mind-perception items: Mind perception, seven items, alpha .97; Alternative, three items (anticipate, account for, understand feelings), alpha .94.
Mixed models of trust
These add the qualities to the model above. Every version keeps the doctor-versus-AI gap large, and competence and quantitative reasoning carry the most weight. Adding the qualities cuts the unexplained gap in trust by more than half, from 3.91 to 1.68 points.
What to look for. Read the standardized β column for which qualities carry the most weight, and compare the doctor row with Table 8 to see how much the gap shrinks.
| Predictor | b [95% CI] | Standardized β | z | p | VIF |
|---|---|---|---|---|---|
| Intercept | 0.504 [−0.318, 1.326] | 1.20 | .229 | ||
| Doctor (versus AI) | 1.680 [1.265, 2.094] | 0.24 | 7.94 | < .001 | 8.69 |
| Quantitative reasoning the decision needs | 0.003 [−0.003, 0.009] | 0.03 | 1.13 | .258 | 1.22 |
| Doctor × need for quantitative reasoning | −0.002 [−0.008, 0.003] | −0.88 | .376 | 6.32 | |
| Intuition | 0.140 [0.090, 0.189] | 0.14 | 5.55 | < .001 | 3.51 |
| Quantitative reasoning | 0.272 [0.223, 0.321] | 0.25 | 10.88 | < .001 | 2.66 |
| Warmth | 0.137 [0.015, 0.258] | 0.06 | 2.20 | .028 | 5.06 |
| Competence | 0.576 [0.430, 0.722] | 0.22 | 7.72 | < .001 | 4.64 |
| Age group (1 to 4) | 0.129 [−0.113, 0.372] | 0.04 | 1.05 | .295 | 1.08 |
| Man (versus woman) | −0.029 [−0.590, 0.532] | −0.00 | −0.10 | .920 | 1.09 |
2,454 ratings from 105 people. Person variance 1.89, slope variance 0.00031, residual 3.09. Share of variance between people (ICC) .38. R² .58 from the predictors alone, .74 with the person effects. AIC 10079.
Table 11 as a figure. Each dot is one predictor's standardized effect on trust (β) with a 95% interval. The dashed lines mark a small, medium and large effect. Intervals that cross zero are not distinguishable from no effect.
What to look for. Read the standardized β column for which qualities carry the most weight, and compare the doctor row with Table 8 to see how much the gap shrinks.
| Predictor | b [95% CI] | Standardized β | z | p | VIF |
|---|---|---|---|---|---|
| Intercept | 0.530 [−0.252, 1.311] | 1.33 | .184 | ||
| Doctor (versus AI) | 1.557 [1.197, 1.918] | 0.22 | 8.46 | < .001 | 7.44 |
| Quantitative reasoning the decision needs | 0.001 [−0.004, 0.007] | 0.01 | 0.50 | .618 | 1.23 |
| Doctor × need for quantitative reasoning | 0.002 [−0.003, 0.007] | 0.77 | .440 | 6.03 | |
| Intuition | 0.048 [0.002, 0.094] | 0.05 | 2.05 | .041 | 3.64 |
| Quantitative reasoning | 0.095 [0.041, 0.149] | 0.09 | 3.42 | < .001 | 3.80 |
| Mind perception | 0.588 [0.519, 0.657] | 0.51 | 16.72 | < .001 | 5.80 |
| Age group (1 to 4) | 0.025 [−0.207, 0.257] | 0.01 | 0.21 | .835 | 1.08 |
| Man (versus woman) | 0.190 [−0.347, 0.727] | 0.03 | 0.69 | .488 | 1.08 |
2,514 ratings from 105 people. Person variance 1.59, slope variance 0.00025, residual 2.86. Share of variance between people (ICC) .39. R² .62 from the predictors alone, .76 with the person effects. AIC 10124.3.
Table 12 as a figure. Each dot is one predictor's standardized effect on trust (β) with a 95% interval. The dashed lines mark a small, medium and large effect. Intervals that cross zero are not distinguishable from no effect.
What to look for. Read the standardized β column for which qualities carry the most weight, and compare the doctor row with Table 8 to see how much the gap shrinks.
| Predictor | b [95% CI] | Standardized β | z | p | VIF |
|---|---|---|---|---|---|
| Intercept | 0.459 [−0.390, 1.308] | 1.06 | .290 | ||
| Doctor (versus AI) | 2.253 [1.882, 2.623] | 0.32 | 11.91 | < .001 | 7.07 |
| Quantitative reasoning the decision needs | 0.005 [−0.001, 0.011] | 0.04 | 1.72 | .086 | 1.23 |
| Doctor × need for quantitative reasoning | −0.004 [−0.009, 0.001] | −1.48 | .139 | 5.92 | |
| Age group (1 to 4) | 0.093 [−0.159, 0.344] | 0.03 | 0.72 | .469 | 1.08 |
| Man (versus woman) | 0.037 [−0.542, 0.617] | 0.01 | 0.13 | .900 | 1.08 |
| Intuition | 0.219 [0.176, 0.263] | 0.21 | 9.81 | < .001 | 2.95 |
| Quantitative reasoning | 0.395 [0.352, 0.439] | 0.36 | 17.70 | < .001 | 2.21 |
2,514 ratings from 105 people. Person variance 2.12, slope variance 0.00024, residual 3.18. Share of variance between people (ICC) .39. R² .56 from the predictors alone, .73 with the person effects. AIC 10388.4.
Table 13 as a figure. Each dot is one predictor's standardized effect on trust (β) with a 95% interval. The dashed lines mark a small, medium and large effect. Intervals that cross zero are not distinguishable from no effect.
What to look for. Read the standardized β column for which qualities carry the most weight, and compare the doctor row with Table 8 to see how much the gap shrinks.
| Predictor | b [95% CI] | Standardized β | z | p | VIF |
|---|---|---|---|---|---|
| Intercept | 0.822 [−0.086, 1.729] | 1.77 | .076 | ||
| Doctor (versus AI) | 2.022 [1.824, 2.220] | 0.29 | 19.99 | < .001 | 2.02 |
| Age group (1 to 4) | 0.092 [−0.160, 0.344] | 0.03 | 0.72 | .474 | 1.08 |
| Man (versus woman) | 0.039 [−0.542, 0.620] | 0.01 | 0.13 | .896 | 1.08 |
| Intuition | 0.154 [0.069, 0.239] | 0.15 | 3.54 | < .001 | 11.18 |
| Quantitative reasoning the decision needs | −0.001 [−0.009, 0.007] | −0.01 | −0.35 | .729 | 2.36 |
| Intuition × need | 0.001 [0.000, 0.002] | 1.88 | .060 | 11.90 | |
| Quantitative reasoning | 0.417 [0.325, 0.510] | 0.39 | 8.86 | < .001 | 9.82 |
| Quantitative reasoning × need | 0.000 [−0.002, 0.001] | −0.55 | .581 | 12.55 |
2,514 ratings from 105 people. Person variance 2.17, slope variance 0.00024, residual 3.18. Share of variance between people (ICC) .39. R² .56 from the predictors alone, .73 with the person effects. AIC 10387.5.
Table 14 as a figure. Each dot is one predictor's standardized effect on trust (β) with a 95% interval. The dashed lines mark a small, medium and large effect. Intervals that cross zero are not distinguishable from no effect.
Random intercept for each person, plus a random slope for how much quantitative reasoning the decision needs in every model but the first; restricted maximum likelihood; Wald z tests. R squared is Nakagawa's marginal and conditional version, and the person share is the person variance over person plus residual variance. Standardized betas are b times the SD of the predictor over the SD of trust. AIC refits by maximum likelihood. Age enters as the age group number (1 = 18 to 44, 4 = 70 and over) because the public file does not hold age in years. The notebook's other attempts are not reproduced: one used a person's own average as its outcome and predictor and the notebook records that it was singular.
What explains the gap?
If people trust doctors more because they see them as warmer, more competent, more intuitive or better at quantitative reasoning, then those ratings should carry part of the gap (H4). Taken together, competence carries a clear share (warmth's interval includes zero once competence is in the model), and so do intuition and quantitative reasoning.
What to look for. The last columns. An indirect effect whose interval stays away from zero means that quality carries part of the gap.
| Model | Through | a | b | a × b [95% CI] | z | p |
|---|---|---|---|---|---|---|
| Warmth and competence together | Warmth | 2.02 | 0.31 | 0.63 [−0.24, 1.75] | 1.25 | .212 |
| Warmth and competence together | Competence | 1.47 | 1.07 | 1.58 [0.87, 2.36] | 4.36 | < .001 |
| Intuition and quantitative reasoning together | Intuition | 3.66 | 0.23 | 0.85 [0.21, 1.50] | 2.59 | .010 |
| Intuition and quantitative reasoning together | Quantitative reasoning | 2.65 | 0.37 | 0.97 [0.48, 1.55] | 3.82 | < .001 |
| Warmth alone | Warmth | 2.02 | 0.93 | 1.89 [1.08, 2.94] | 4.21 | < .001 |
| Competence alone | Competence | 1.47 | 1.30 | 1.92 [1.26, 2.66] | 6.11 | < .001 |
| Intuition alone | Intuition | 3.66 | 0.43 | 1.58 [1.01, 2.21] | 5.26 | < .001 |
| Quantitative reasoning alone | Quantitative reasoning | 2.65 | 0.50 | 1.31 [0.81, 1.89] | 5.27 | < .001 |
Paths are within-person: every variable is taken as a distance from that person's own average, so the doctor-versus-AI contrast is a within-person effect. a is the effect of the doctor (versus the AI) on the mediator, b the effect of the mediator on trust with the doctor contrast held fixed, and the indirect effect is a times b. Intervals come from resampling people 2,000 times. z is the delta-method ratio with standard errors that allow for several ratings per person. The notebook ran these as Mplus two-level models; the indirect effects here reproduce its estimates, and its test statistics are close but not identical.
Table 15 as a figure
Each dot is the part of the doctor-versus-AI gap that runs through one quality, in points of trust, with a 95% interval. An interval that stays right of zero means that quality carries a real share of the gap.
Figure 12. Warmth and competence together
Arrows show how doctor versus AI changes trust directly and through each quality. The numbers on the arrows are effect estimates; an arrow with a starred or bold number is reliably different from zero.
Figure 13. Intuition and quantitative reasoning together
Arrows show how doctor versus AI changes trust directly and through each quality. The numbers on the arrows are effect estimates; an arrow with a starred or bold number is reliably different from zero.
Does the gap differ between people?
The gap is large in every group, and the intervals overlap throughout. Nothing here is a finding on its own, but I report it so readers can see how steady the result is.
Figure 14. The doctor-minus-AI gap, by group of people
Each row is a group of people. The dot is the average doctor-minus-AI gap in that group, with a bar for the 95% interval. A dot right of the zero line means the doctor was trusted more.
View as a table
| Group | Trust: average gap [95% interval] | Quantitative reasoning: average gap [95% interval] | Intuition: average gap [95% interval] |
|---|---|---|---|
| 18-44 (n = 19) | 3.2 [1.6, 4.7] | 2.4 [0.5, 4.3] | 2.8 [1.0, 4.6] |
| 45-59 (n = 13) | 4.9 [3.1, 6.7] | 3.5 [0.8, 6.1] | 4.7 [2.6, 6.8] |
| 60-69 (n = 31) | 3.8 [2.7, 4.8] | 3.0 [1.9, 4.1] | 3.8 [2.5, 5.0] |
| 70+ (n = 43) | 4.3 [3.3, 5.2] | 2.4 [1.2, 3.5] | 4.0 [2.7, 5.3] |
| Woman (n = 64) | 4.3 [3.5, 5.1] | 3.2 [2.2, 4.1] | 4.3 [3.4, 5.3] |
| Man (n = 39) | 3.6 [2.8, 4.5] | 2.2 [1.1, 3.3] | 3.1 [2.0, 4.3] |
| No college degree (n = 56) | 4.3 [3.4, 5.2] | 3.3 [2.3, 4.3] | 4.1 [3.2, 5.1] |
| College degree or more (n = 50) | 3.6 [2.9, 4.4] | 2.0 [1.0, 3.0] | 3.4 [2.3, 4.5] |
| Not at all to slightly (n = 36) | 4.5 [3.5, 5.4] | 2.9 [1.5, 4.2] | 4.5 [3.3, 5.7] |
| Moderately (n = 23) | 2.9 [1.8, 4.0] | 2.6 [1.2, 4.0] | 3.7 [1.9, 5.6] |
| More than moderately (n = 47) | 4.1 [3.2, 5.1] | 2.6 [1.5, 3.7] | 3.3 [2.3, 4.4] |
| None or a little (n = 86) | 4.1 [3.5, 4.8] | 2.6 [1.9, 3.4] | 4.1 [3.3, 4.9] |
| Moderate or more (n = 20) | 3.4 [1.8, 5.0] | 2.9 [0.9, 4.9] | 2.6 [0.9, 4.3] |
What to look for. Whether any group differs in its gap. No p value is below .05, so the gap looks steady across these groups.
| Compared by | Groups | Trust | Quantitative reasoning | Intuition |
|---|---|---|---|---|
| Age | 18-44; 45-59; 60-69; 70+ | F(3, 99) = 1.01, p = .392 | F(3, 102) = 0.43, p = .734 | F(3, 102) = 0.74, p = .531 |
| Gender | Woman; Man | t(98) = 1.13, p = .260 | t(101) = 1.33, p = .187 | t(101) = 1.56, p = .123 |
| Education | No college degree; College degree or more | t(101) = 1.09, p = .277 | t(104) = 1.86, p = .065 | t(104) = 0.99, p = .325 |
| How religious | Not at all to slightly; Moderately; More than moderately | F(2, 100) = 2.07, p = .131 | F(2, 103) = 0.05, p = .949 | F(2, 103) = 0.96, p = .385 |
| Experience with AI | None or a little; Moderate or more | t(101) = 1.03, p = .305 | t(104) = −0.27, p = .787 | t(104) = 1.60, p = .112 |
Each dot is the average gap (doctor minus AI) for the people in that group, with its 95% confidence interval. Groups under 10 people are not shown, and race is not shown because only one group has 30 or more people. The tests ask whether the gap differs between the groups shown; they are exploratory and not corrected for the 15 comparisons.
Age: two versions
The one result that moves with age is in the last model (Table 17): the doctor's edge grows with age band (b = 0.160 per band, p .013). The dissertation's Table 8 used age in years. Rerunning that model privately with exact age gives the same main results as here (doctor 1.683, intuition .140, quantitative reasoning .272, warmth .134, competence .578, age .002, man .037), so the age bands lose nothing important. Exact age stays out of the public file because with a sample this size, an exact age together with gender and education could point to one person.
What to look for. The last row. A positive age-by-doctor term means the doctor's edge grows with age band.
| Predictor | b [95% CI] | Standardized β | z | p | VIF |
|---|---|---|---|---|---|
| Intercept | 0.795 [−0.037, 1.626] | 1.87 | .061 | ||
| Age group (1 to 4) | 0.051 [−0.199, 0.301] | 0.02 | 0.40 | .688 | 1.15 |
| Doctor (versus AI) | 1.083 [0.665, 1.501] | 0.15 | 5.08 | < .001 | 8.86 |
| Age group × doctor | 0.160 [0.033, 0.286] | 2.48 | .013 | 7.86 | |
| Man (versus woman) | −0.031 [−0.593, 0.531] | −0.00 | −0.11 | .915 | 1.09 |
| Quantitative reasoning the decision needs | 0.002 [−0.003, 0.008] | 0.02 | 0.85 | .397 | 1.00 |
| Intuition | 0.139 [0.089, 0.188] | 0.13 | 5.50 | < .001 | 3.51 |
| Quantitative reasoning | 0.279 [0.229, 0.328] | 0.26 | 11.09 | < .001 | 2.69 |
| Warmth | 0.140 [0.018, 0.261] | 0.06 | 2.25 | .024 | 5.05 |
| Competence | 0.558 [0.412, 0.705] | 0.21 | 7.46 | < .001 | 4.67 |
2,454 ratings from 105 people. Person variance 1.90, slope variance 0.0003, residual 3.08. Share of variance between people (ICC) .39. R² .58 from the predictors alone, .74 with the person effects. AIC 10073.6.
Table 17 as a figure
Each dot is one predictor's standardized effect on trust (β) with a 95% interval. The age-by-doctor term has no standardized β, so look to the table for it.