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

• The goal of multiple comparisons corrections is to reduce the number of false positives, because false positives can be embarrassing, confusing, and cause you and other people to waste your time.
• The conclusion from p-value depends much on signigicance $\alpha$ (usually $\alpha=0.05$). What if we wanna test multiple tests simultaneously? The same $\alpha$ for all cases?
• Dealing with multiple testing → adjusting $\alpha$.

References

1. Math is fun -- Chi-Square Test.