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CSS Statistics QUESTION #2012
Question 1
In the LSD (Least Significant Difference) test for comparing treatment means in ANOVA, two means \(\bar{y}_i\) and \(\bar{y}_j\) are declared significantly different if:
  • Their difference exceeds \(t_{\alpha/2, df_E} \cdot s_e\)
  • Their difference exceeds \(t_{\alpha/2, df_E} \cdot \sqrt{\dfrac{2 MS_E}{b}}\)✔️
  • Their difference exceeds \(F_{\alpha, 1, df_E} \cdot MS_E\)
  • Their difference exceeds \(z_{\alpha/2} \cdot SE\)
Correct Answer Explanation
The LSD test declares means significantly different if \(|\bar{y}_i - \bar{y}_j| > LSD\), where \(LSD = t_{\alpha/2, df_E} \cdot \sqrt{\dfrac{2 MS_E}{b}}\). This is the critical difference computed from the t-distribution with error degrees of freedom and the standard error of the difference between two means.