Differences

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--- t-test [2025/10/08 03:34] – [모집단의 평균과 표준편차를 알고 있을 때] hkimscil
+++ t-test [2026/03/31 23:18] (current) – hkimscil
@@ Line 6: / Line 6: @@
 \begin{eqnarray}
-z\;\;\;\text{or}\;\;\;t = \frac{\overline{X}-\mu}{\sigma_{\overline{X}} }  \\
+z\;\;\;\text{or}\;\;\;t & = & \frac{\overline{X}-\mu}{\sigma_{\overline{X}} }, \; \text{where } \;\; \sigma_{\overline{X}} = \frac{\sigma}{\sqrt{n}} \\
-t = \frac{\overline{X}-\mu}{s_{\overline{X}}  } \\
-t = \frac{(\overline{X_a}-\overline{X_b})-(\mu_a-\mu_b)}{\sigma_{diff}} \\
+t & = & \frac{ \overline{X}-\mu}{s_{\overline{X}} }, \; \text{where } \;\; s_{\overline{X}} = \frac{s}{\sqrt{n}} \\
-t = \frac{\overline{D}-0}{s_{ \overline{D} }} = \frac {\overline{D}}{ \frac{s_D}{\sqrt{N}} }
+t & = & \frac{(\overline{X_a}-\overline{X_b})-(\mu_a-\mu_b)}{\sigma_{\text{diff} }}, \\
+& & \qquad \qquad \text{where } \;\; \sigma_{\text{diff} } = \sqrt{ \frac{s^2_{\text{pooled}}}{n_a}  + \frac{s^2_{\text{pooled}}}{n_b} } \nonumber \\
+& & \qquad \qquad s^2_{\text{pooled}} = \frac {\text{SS}_a + \text{SS}_b} {df_a + df_b} \nonumber \\
+t & = & \frac{\overline{D}-0}{s_{ \overline{D} }}, \; \text{where } \;\; s_{ \overline{D} } = \frac {s_D}{\sqrt{n}} \\
 \end{eqnarray}
 --
@@ Line 20: / Line 26: @@
 위의 4 경우의 공통점은 :
+\begin{eqnarray*}
-$t = \displaystyle \frac{\text{obtained difference}}{\text{difference by random error}}$
+t & = & \displaystyle \frac{\text{obtained difference}}{\text{difference by random error}}
+\end{eqnarray*}
 </WRAP>