Chapter 12 Formulas and Vocabulary

• Analysis of variance (ANOVA) (p. 666)
• $F_{\text{crit}}$ (p. 677)
• $F_{\text{data}}$ (p. 673).
  

  $F_{\text{data}}=\frac{\text{MSTR}}{\text{MSE}}$

• Hypotheses for analysis of variance (p. 673).

  
  

  $H_0:{\mu }_1={\mu }_2=\cdots ={\mu }_k$

  versus

  $H_a:\text{not all the population means are equal}$

• Mean square error (MSE) (p. 671).
  

  $\text{MSE}=\frac{\sum (n_i-1)s_i^2}{n_t-k}$

• Mean square treatment (MSTR) (p. 671).
  

  $\text{MSTR}=\frac{\sum n_i{({\overline{x}}_i-\overline{x})}^2}{k-1}$

• Overall sample mean, $\overline{x}$ (p. 670).
  

  $\overline{x}=\frac{(n_1\overline{x}+n_2{\overline{x}}_2+\cdots +n_k{\overline{x}}_k)}{n_t}$

• $p$-Value (p. 673)
• Sum of squares error (SSE) (p. 671).
  

  $\text{SSE}=\sum (n_i-1)s_i^2$

• Sum of squares treatment (SSTR) (p. 671).
  

  $\text{SSTR}=\sum n_i{({\overline{x}}_i-\overline{\overline{x}})}^2$

• Total sum of squares (SST) (p. 671).
  

  $\text{SST}=\text{SSTR}+\text{SSE}$

• Bonferroni adjustment (p. 686)
• Experimentwise error rate ${\alpha }_{\text{EW}}$ (p. 686)
• Multiple comparisons (p. 686)
• Number of pairwise comparisons (p. 686).
  

  $c={(}_k{C}_2)=\frac{k!}{2!(k-2)!}$

• Rejection rule for using confidence intervals to perform Tukey's test (p. 689)
• Test statistic for Bonferroni method (p. 687).
  

  $t_{\text{data}}=\frac{{\overline{x}}_1-{\overline{x}}_2}{\sqrt{\text{MSE}\cdot \left(\frac{1}{n_1}+\frac{1}{n_2}\right)}}$

• Test statistic for Tukey method (p. 689).
  

  $q_{\text{data}}=\frac{{\overline{x}}_1-{\overline{x}}_2}{\sqrt{\frac{\text{MSE}}{2}\cdot \left(\frac{1}{n_1}+\frac{1}{n_2}\right)}}$

• Tukey critical value $q_{\text{crit}}$ (p. 688)

• Blocking factor, or block (p. 694)
• Randomized block design (p. 694)

• Interaction (p. 702)
• Interaction plot (p. 702)