ANOVA

Assumptions for ANOVA

• For each population, response (dependent variable - measuring; effect), is normally distributed

• Variance of DV, is the same for all populations

• Observations must be independent

  • Null is TRUE (sample means are close)

  • Null is FALSE (sample means are far) - not all populations means are the same (has significant difference)

ANOVA

: used to test equality of three or more population means

1. Completely randomized design

1. treatments are randomly assigned to the experimental units (ONE FACTOR ONLY - ONE INDEPENDENT VARIABLE ONLY)
   
   

2. Between treatments estimate of Population Variance

   1. MSTR - estimate of variance based on the variation of sample means (mean square due to treatments) 

3. Within-treatments estimate of Population Variance

   1. MSE - Estimate of variance based on the variation of sample observations (mean square error)

1. Randomized blocked design

1. Experimental units are the objects of interest in the experiment

2. experimental design where treatments are randomly assigned to the experimental units

3. If experimental units are heterogenous, blocking can be used to form homogeneous groups, thus randomized block design

SST = SSTR (k-1) + SSBL(b-1) + SSE(k-1)(b-1)

TOTAL DF = N(t) -1

1. Factorial experiment

1. Some experiments we want to draw conclusions about more than one variable or factor

2. Factorial term = all combinations possible are included

SST = SSA (a-1) + SSB(b-1) + SSAB(a-1)(b-1) + SSE [ab(r-1)]