From the book “How not to be wrong” by Jordan Ellenberg

This book explains the concepts of p-value and hypothesis testing brilliantly. You should read this book too.

Note: Reading: How not to be wrong by Jordan Ellenberg

• Key Insights from the Book (Vietnamese)
• Key Insights from the Book (English)

Null hypothesis

• Null hypothesis ⇒ questions scientist want to nullify.
  • Example: $H_0$ = "The world is flat."
• Alternate hypothesis: "The world is round."
• In order to change an opinion, we first prove it wrong!

p-value

• Small p-value ⇒ reject null hypothesis!
• Mostly, we need $p<0.05$ (statistical significance) to reject a null hypothesis.
  • Smaller $0.05$, we are more sure!
• Example: "Gender IS NOT linked to pet preference (cat/dog)." With $p=0.043<0.05$, we reject that hypothesis and conclude "Gender IS linked to pet preference. (ref)

Understand p-value?

• If $p=0.75$, it means that there are $75\%$ the null hypothesis is true! We cannot reject it!

Calculate p-value

In order to calculate p-value, we use Chi-Square Test ($X^2$ test).

• This test only works for categorical data (men, women), not numerical data (height, weight).
• The number of entries must be large enough.

Multiple tests + p-value correction