If a result is significant at 5%, it means:
👉 “There is less than a 5% chance that we’d get this result if the null hypothesis were true.”
Therefore we reject the null hypothesis.
👉 “There is less than a 5% chance that we’d get this result if the null hypothesis were true.”
Therefore we reject the null hypothesis.
Conduct and interpret unpaired t-tests when variances are unknown but equal (Student's two-sample t-test) and when variances are unknown and unequal (Welch's t-test).
https://www.liverpool.ac.uk/courses/fully-funded-epsrc-dtp-phd-studentship-in-mathematics-open-to-all-research-areas
Follow us: https://t.iss.one/mathandresearch
Follow us: https://t.iss.one/mathandresearch
www.liverpool.ac.uk
Fully Funded EPSRC DTP PhD Studentship in Mathematics – Open to all research areas | Courses | University of Liverpool
The Department of Mathematical Sciences at the University of Liverpool invites applications for Doctoral Training Partnership (DTP) studentships leading to a PhD and commencing study from the 28 September 2026.
Prism | A free, LaTeX-native workspace for scientists | OpenAI
https://openai.com/prism/
OpenAI introduced LaTeX-native workspace that integrated GPT‑5.2 directly into scientific writing and collaboration.
https://openai.com/prism/
OpenAI introduced LaTeX-native workspace that integrated GPT‑5.2 directly into scientific writing and collaboration.
Openai
Prism | A free, LaTeX-native workspace for scientists
Write, edit, and collaborate on scientific documents in LaTeX with Prism—a free workspace integrating GPT-5.2 into research and writing.
Paul Dirac: The Silent Genius Who Spoke Through Equations 🤫⚛️
Paul Dirac was famously shy — so uncomfortable with attention that social gatherings terrified him, and he avoided small talk like the plague.
His colleagues joked that his conversation rate could be measured in words per hour. (They even invented a unit called the "dirac" = 1 word/hour! 😄)
Yet, his mind was revolutionary.
In 1928, he formulated the Dirac equation, beautifully merging quantum mechanics with special relativity. It described the electron with stunning accuracy... and astonishingly predicted antimatter (the positron) years before anyone observed it.
This became a cornerstone of quantum field theory and modern particle physics.
When he won the Nobel Prize in Physics in 1933 (shared with Schrödinger), the publicity horrified him. He seriously considered refusing it to avoid the spotlight.
He was only convinced to accept after being told: refusing would create even more attention than quietly receiving it. Logic won — silence did not.
Paul Dirac was famously shy — so uncomfortable with attention that social gatherings terrified him, and he avoided small talk like the plague.
His colleagues joked that his conversation rate could be measured in words per hour. (They even invented a unit called the "dirac" = 1 word/hour! 😄)
Yet, his mind was revolutionary.
In 1928, he formulated the Dirac equation, beautifully merging quantum mechanics with special relativity. It described the electron with stunning accuracy... and astonishingly predicted antimatter (the positron) years before anyone observed it.
This became a cornerstone of quantum field theory and modern particle physics.
When he won the Nobel Prize in Physics in 1933 (shared with Schrödinger), the publicity horrified him. He seriously considered refusing it to avoid the spotlight.
He was only convinced to accept after being told: refusing would create even more attention than quietly receiving it. Logic won — silence did not.