Analysis: Do people reply to emails slower on Friday afternoons? (draft v7)

Ticket DS-4471, opened as "quick question". Time spent: 3 weeks. Status: Inconclusive (high confidence).

TL;DR

Directionally, possibly, after adjustment, in some mailboxes: unadjusted hazard ratio for replying to a Friday-afternoon email is 0.31 (95% CI 0.29–0.33). Once the weekend is controlled for, the effect is p = 0.051. The weekend may be the effect.

Background

On Monday, Susan suggested that people reply more slowly on Friday afternoons because they have gone home. Anecdote is not evidence. This analysis corrects for Susan.

Data

61,204 threads from email_latency_final_v2_FIXED.csv, January 2024 to June 2026. The join on thread_id fanned out to 212,880 rows because of reply-all. 9,114 "replies" came 0.3 s after receipt and were out-of-office autoreplies, the only fast responders in the building. Timestamps were stored in server UTC, so 16:00 Friday in Sydney was being counted as Friday morning in London. A manual followed_up_on field contained "next Tues" 211 times and "lol" once.

Humans should not be allowed to enter data. They should not be allowed to generate it either, but here we are.

EDA

Friday PM reply latency (h)
0–4    ████████████
4–24   ████
24–48  ██
48–72  ████████████████████   <- mode: 64 h
72+    ███

There is a mode at 64 hours, which is Monday at 09:00. Nobody predicted this.

Methods

1. Difference in medians. It compares two numbers, which is the level at which this question was asked.
2. Welch t-test on log latency. It allows the two groups to have different variances (heteroscedasticity), but I wouldn't expect you to follow that.
3. OLS of log latency on day × hour dummies with sender fixed effects. Every sender is treated as a sensor with its own calibration error.
4. Cox proportional hazards, with unanswered threads right-censored. This is the correct model, and it was run fourth.
5. LightGBM on 400 engineered features, predicting a reply within 4 h.
6. Bayesian hierarchical model with partial pooling by department. Partial pooling shrinks noisy groups toward the mean, the way the organisation does with its staff.
7. IV using cake_in_breakroom as an instrument for Friday. First-stage F = 3.1, below the usual threshold of 10. Cake also delays replies directly, so the exclusion restriction fails. It is a confounder with frosting.

Results

LightGBM wins by 0.0003.¹ It took 41 GPU-hours to tie a regression.

¹ Difference 0.0003, 95% CI −0.0011 to 0.0017.

Feature importance

Mean |SHAP| ranks hours_until_monday first. Feature 312 is is_tuesday_and_raining_and_susan_in_office. The top driver of slow Friday replies is the approach of the weekend, and this is reported here as a discovery.

Significance

After adjusting for weekend_in_reply_window, the Friday coefficient on log latency is 0.041, SE 0.021, z = 1.95, 95% CI −0.0002 to 0.0822, p = 0.051. That is marginally significant, trending, approaching significance. Adjusting for the mechanism removed the effect, which is what adjusting for a mediator does.

For threads first opened on a Tuesday, β = 0.112, SE 0.0545, z = 2.06, 95% CI 0.0052 to 0.2188, p = 0.040. That was 1 of 48 subgroups tested; Bonferroni would require p < 0.00104. It was not applied. The Tuesday result stands, unsupervised.

Caveats

1. Unanswered emails are censored, and some are censored forever.
2. Remote work introduced covariate shift in 2025.
3. The direction reverses within finance (Simpson's paradox). Finance replies on Friday to avoid Monday.
4. Reply latency measures the timestamp, not the reading.
5. "Read, will reply Monday" is a reply, technically.
6. Sender fixed effects absorb rudeness, which is not stationary.
7. Thursday afternoon is already partially Friday.
8. Daylight saving time moved Friday twice a year.
9. The final_v2_FIXED file has never been fixed.
10. The presence of humans.

The residuals are you.

You filed this ticket at 16:47 on a Friday, so it has been added to the treatment arm.

Recommendation

Further study, more data, fewer humans in the loop. A/B test: randomise delivery of non-urgent email to Friday PM or Tuesday PM.

σ = 1.9 (log h), δ = 0.041, α = 0.05 two-sided, power = 0.80:

n per arm = 2σ²(1.96 + 0.84)² / δ² = 2 × 3.61 × 7.84 / 0.001681 = 33,674

The team mailbox produces 12 eligible emails per Friday afternoon, so 33,674 / 12 = 2,807 Fridays, or 53.8 years. Expected completion is 2080. We recommend starting immediately.

Dashboard

<dashboard link>: twelve tiles, hourly refresh, zero viewers. Its usage analytics are on another dashboard, which also has zero viewers. Both refresh on Fridays without anyone noticing.

Deliverable: analysis_FINAL_final_v7_USE_THIS.ipynb, 340 cells. Cell 1 is Susan's answer.

Acknowledgements

Thanks to Susan for the original hypothesis, which has now been made less certain.

Analysis: Are Mondays bad? (draft v7)

Ticket DS-4471, opened as "quick question". Time spent: 3 weeks. Status: Inconclusive (high confidence).

TL;DR

Mondays are directionally, modestly and only conditionally worse than other weekdays, at least for this sample: adjusted mood effect −0.4095 points on a 10-point scale (95% CI −0.8211 to 0.0021, p = 0.0512). The interval includes zero by two thousandths of a point, and so does your week.

Background

On Monday, Susan suggested that Mondays are bad. Anecdote is not evidence. This analysis corrects for Susan.

Data

The source is 6,240 rows from pulse_survey_final_v2_FIXED.csv: a daily 1–10 mood question answered by 41 employees between January 2025 and June 2026. After cleaning, 4,977 rows remain.

The cleaning took eleven days. A join to the HR table fanned out on duplicate employee IDs and tripled one person, who was having a bad quarter. The survey tool logged timestamps in UTC, so 212 Friday-evening responses from the Pacific office turned up as Saturdays. Fourteen respondents typed their mood as a word, including "monday" (9 times) and "next Tues" (twice). Humans should not be allowed to enter data. They should not be allowed to generate it either, but here we are.

EDA

Monday mood distribution:

1-2  ████████
3-4  ██████████████
5-6  ████████████████████
7-8  ███████████████
9-10 ████

Mood rises across the week and peaks on Friday. This is presented as a finding because the ticket required one.

Methods

1. Weekday means. These are arithmetic averages. You will follow this one.
2. Welch t-test, Monday vs. rest. It compares two means without assuming equal variances. Raw Δ = −0.58, p < 0.0001, but it ignores that the same 41 people answered roughly 121 times each. Repeated measures are a real problem, and I wouldn't expect you to follow why.
3. OLS with respondent fixed effects and SEs clustered by respondent. Each person is compared with their own baseline. This step produced the headline number.
4. Gradient boosting on 400 engineered features, predicting a bad day (mood ≤ 4).
5. Bayesian hierarchical model with day-of-week effects partially pooled across teams. Posterior Monday effect −0.38, 95% CrI −0.83 to 0.07.
6. Instrumental variable. Bank holidays are used as an instrument for whether a day counts as Monday, because they move Monday to Tuesday. The exclusion restriction fails because holidays improve mood directly. The instrument is not an instrument.

The correct framing is reinforcement learning: the agent learns to dread a state it cannot leave.

Results

Gradient boosting wins by 0.0003 AUC.¹ Most of the R² is noise from the people who answered the survey.

¹ The 95% CI of the AUC difference is −0.0041 to 0.0047.

Feature importance

SHAP ranks is_monday first among 400 features. The question we were asked turns out to be the most important variable in its own analysis. Feature 312 is is_tuesday_and_raining_and_susan_in_office, and it ranks above sleep.

Significance

The adjusted Monday effect has p = 0.0512, which is marginally significant and trending. In the subgroup of teams with a Tuesday 9 a.m. standup, the effect is −0.6150 (95% CI −1.2030 to −0.0270, p = 0.0404). We tested 23 subgroups, so a correction for multiple comparisons applies. It has been noted.

Caveats

1. Mood is self-reported by a sensor that lies.
2. People who leave the survey (nonresponse) are disproportionately those having a bad Monday.
3. Fridays have a ceiling effect.
4. Residual variance differs by team (heteroscedasticity), and I wouldn't expect you to follow that.
5. The pooled trend may reverse within teams (Simpson's paradox). It hasn't yet.
6. Respondents who know the survey is about Mondays answer differently on Mondays.
7. The UTC fix may have moved some Mondays into Sunday.
8. Forty-one people are a non-stationary process with opinions.
9. One respondent rated every day 1, including their holiday.
10. The presence of humans.

Your intuition was correct, and it was confirmed on the 15th Monday of the analysis.

Recommendation

We recommend further study, more data and fewer humans in the loop. We also recommend an A/B test that randomizes which day is treated as Monday:

• σ = 2.14, δ = 0.10, α = 0.05, power = 0.80
• n per arm = 2 × (1.96 + 0.84)² × σ² / δ² = 2 × 7.84 × 4.5796 / 0.01 = 7,181 team-Mondays
• 14,362 team-Mondays across 6 teams = 2,394 weeks = 16,758 days
• Completion: Q3 2072

We recommend starting immediately.

Dashboard

<dashboard link> has twelve tiles, refreshes hourly and has zero viewers. Its usage analytics are on a second dashboard, which also has zero viewers.

Acknowledgements

Thanks to Susan for the original hypothesis, which has now been made less certain.