[Statistics Notes] Decision-making criteria for various statistical tests

The compared subscript of the statistic gets the subscript of the statistic (that is, ${with}_{a}Or$${with}_{a/2}$The subscript of) is determined based on a one-sided test or a two-sided test! !
其实就是：单侧时α的分子是 1，双侧时α的分子是 2

• For one-sided inspection: use $\alpha$ ;
• The two-sided test is: use $\alpha /2$。

Here the subscripts of the agreed statistics are all $A$：

var A = 统计量下标;
if(单侧检验)
	A = α;
else
if(双侧检验)
	A = α/2;

---

Of course $t_A、F_{a/2}$The value of etc. still needs to be determined according to the degree of freedom of the specific topic (of course, for the z statistic, it is 1.645, 1.96 and 2.58)

---

z statistics

• $|z|<|z_A|$：Do not reject the null hypothesis$H_0$；
• $|z|>|z_A|$ : Reject the null hypothesis$H_0$。

---

t statistic

• $|t|<|t_A|$：Do not reject the null hypothesis$H_0$；
• $|t|>|t_A|$ : Reject the null hypothesis$H_0$。

---

${\chi }^2$ statistics

${\chi }^2$ Statistics are usually one-sided test, so here$A=\alpha$ , directly use$\alpha a$

• ${\chi }^2<{\chi }_a^2$: Do not reject the null hypothesis $H_0$；
• ${\chi }^2\ge {\chi }_a^2$: Reject the null hypothesis $H_0$。

---

F statistics

• One-sided inspection:
  • $F<F_a$: Do not reject the null hypothesis $H_0$；
  • $F>F_a$: Reject the null hypothesis $H_0$；
• Two-sided inspection:
  • $F_{1-a/2}\le F\le F_{a/2}$: Do not reject the null hypothesis $H_0$。
  • $F<F_{1-a/2}OrF>F_{a/2}$: Reject the null hypothesis $H_0$。

---

P value test

• $P>A$ : Do not reject the null hypothesis$H_0$；
• $P<A$ : Reject the null hypothesis$H_0$。