Question

The following two-way table gives data for a 2 × 2 factorial experiment with two observations per factor-level combination: The data are saved in the LM.TXT file. 

Factor B Level 1 2 Factor A 1 29.6, 35.2 47.3, 42.1 2 12.9, 17.6 28.4, 22.7 

a. Identify the treatments for this experiment. Calculate and plot the treatment means, using the response variable as y-axis and the levels of factor B as the x-axis. Use the levels of factor A as plotting symbols. Do the treatment means appear to differ? Do the factors appear to interact? (3) 

b. Construct an ANOVA table for this experiment. (3) 

c. Test to determine whether the treatment means differ at the α=0.05 level of significant. Does the test support your visual interpretation from part a? (3) 

d. Does the result of the test in part c warrant a test for interaction between the two factors? If so, perform it, using α=0.05. (3) 

e. Do the results of previous tests warrant tests of the two factor mean effects? If so, perform them, using α=0.05. 

LM.TXT FILE: 

> I need help on this too. How do I even start solving this?

> I am struggling with question a the most so if someone could please help me that would be amazing.

Answer 1

. Two factors Two each at two levels & having two replicates. A level 1 levels ' 29.6,362 41.3 42.) Α 2 12.9, 17.6 28.4, 22:7 Treat combn total Peplicades 2) (2) 29.6 35.2 64.8 12.9 17.6 (a) (6) 30.5 49.3 42.1 894 (ab) 28.4 22.7 51:1 (1) - - - A and B at level i A at levels 2 x B at level, A at level 14 B at level 2 A y B at level 2 b ab in' no. of replicates =2 main effect of A A = an [abra-b-(1) 2 ( 5141+30.5 - 89.4 - 64-8)

2 -18.15 main effect of B. Bakon, (ab+b-a-ci) :(5161789.4–30.5 -648) - 11.3 Omteraction effect AB. z än (ab+(1)-a-b) - ( 511 +64.8= 30.5-89.4) = -1 Sum of squares for A f SSA - (ab+a-6-(0) un) - (5141+ 30.5 - 89.4-64.8) 4(2) = 658.845 Sum of squares B. SSB , (ab+b-a-), (51.1+8904-30.5-6408 4(2) 2 un 2 255.38

Sum of square for AB. SSABB , (ab+)-a-6) un - (51.1 +64.8-30.6–89.45 Total Sum of squares. § z SST 2 § Ý - y... isk - y.... - Grand Total 12/ J21 ks! 2 972.715 - 7922.92- 235.81 Srxox Sum of 34aes. SSE - SST - SSA - SSB - SSAB 2 56.49 ANOVA mean Soss source of vagiation Sum of squares degree of freedom Взлате - 658.845 658.845 255. 38 255.38 F2 = MSSAB mssc 2 20:14 CrಶOY 56.49 14.1225 Total 972:715 -un-1