Fisher's paradigm

Fisher was focused on significance testing. He introduced the p-value as a measure of evidence against the null. His general procedure was

• Choose a test-statistic $T$
• Compute the p-value under the null: $\mathbb{P}(T(X)\ge t)$ where $t$ is the observed value of the test-statistic
• Reject $H_0$ if the p-value is small.

Note that in Fisher’s paradigm, there is no notion of a significance level $\alpha$ (unlike the Neyman-Pearson paradigm), and there is no alternative hypothesis.