Film Coatings

Step 1: Graphs
Graph > Boxplot > with Groups, Graph variable= Thickness, Categorical variable= Temperature

Graph > Boxplot > with Groups, Graph variable= Thickness, Categorical variable= Pressure

Step 2: Summary Statistics

Stat > Basic Statistics > Display Descriptive Statistics, Variable= Thickness, By variables= Temperature

Temperature
	n	Mean	Std
Low	9	43.667	2.291
Mid	9	38.0	2.345
High	9	37.667	2.915

Stat > Basic Statistics > Display Descriptive Statistics, Variable= Thickness, By variables= Pressure

Pressure
	n	Mean	Std
Low	9	38.111	2.848
Mid	9	39.11	4.37
High	9	42.111	2.804

Step 3: Interaction

Stat > ANOVA > Interactions Plot, Response= Thickness, Factors= Temperature Pressure

Test for Interaction:
1) α=0.05
2) H₀: g₁₁=g₁₂=...=g₃₃=0 (no interaction)
3) H₀: g_ij≠0 (some interaction)
4) p-value= 0.012 < α
5) We reject H₀, there is some interaction

Step 4: Tests for Factors
Stat > ANOVA > Twoway, Response=Thickness, Row Factor= Temperature, Column factor= Pressure, Graphs > Residual vs. Fits and Normal plot

Test for Temperature:

1) α=0.05
2) H₀: α₁ = .. =α₃=0 (no difference in the mean Thicknesss of different Temperatures)
3) H_a: α_i≠0 for some i (some differences in the mean Thicknesss of different Temperatures)
4) p-value= 0.000 < α
5) We reject H₀, there are some differences in the mean Thicknesss of the Temperatures

Test for Pressure:

1) α=0.05
2) H₀: β₁ = .. =β₃=0 (no difference in the mean Thicknesss of different Pressures)
3) H_a: α_i≠0 for some i (some differences in the mean Thicknesss of different Pressures)
4) p-value= 0.000 < α
5) We reject H₀, there are some differences in the mean Thicknesss of the Pressures

Step 5: Multiple Comparison
What we need is to find the best combination of pressure and temperature, but the two-way command does not have a multiple comparison box. Here is what we can do:
Make a new variable TP with each Temperature-Pressure combination:
Data > Concatenate > Concatenate text columns: Temperature Pressure, Store in TP
Stat > ANOVA > Oneway, Response=Thickness, Factor= TP , Comparisons > Check Tukey

Here we don't need the complete results, we only need to find which combinations(s) are best, that is have the thinnest films. The combination with the thinnest film is Temperature=High, Pressure=Mid (34.667). Then we find in the order of the means:

Combination	Mean	Lower	Upper	Stat. Different ?
Mid - Low	35.667	-3.197	5.197	No
High-Low	37.333	-6.864	1.530	No
Mid Mid	38.333	-0.530	7.864	No
Mid High	40.000	1.136	9.53	Yes

Clearly all others are also stat. different.

Another way to do this is using a new command, General Linear Model. This is a generalization of the ANOVA method:
Stat > ANOVA > General Linear Model, Responses: Thickness, Temperature Pressure
But this does not include an interaction term!

• Two-way ANOVA: fits interaction by default
• General Linear Model: fits additive model (no interaction) by default

Here is how we include an interaction term in the General Linear Model:
Stat > ANOVA > General Linear Model, Responses: Thickness, Temperature Pressure Temperature*Pressure

And now for the multiple comparison:
Stat > ANOVA > General Linear Model, Responses: Thickness, Temperature Pressure Temperature*Pressure, Comparisons > Terms: Temperature*Pressure, uncheck box Test

The result is the same as above.