Noise and Air Filters

Step 1: Graphs
Graph > Boxplot > with Groups, Graph variable=Noise, Categorical variable=Size
Graph > Boxplot > with Groups, Graph variable=Noise, Categorical variable=Filter
Graph > Boxplot > with Groups, Graph variable=Noise, Categorical variable=Side
Windows > Project Manager, Click on Graphs inleft Panel, CTRL-click the three graphs, right-click, choose Layout tool > Finish

Step 2: Tables

Stat > Basic Statistics > Display Descriptive Statistics, Variable= Noise, By variables=Size

Noise by Size

n Mean Std

Small 12 824.2 7.64

Medium 12 833.75 13.51

Large 12 772.50 10.34

Noise by Size
	n	Mean	Std
Small	12	824.2	7.64
Medium	12	833.75	13.51
Large	12	772.50	10.34

Stat > Basic Statistics > Display Descriptive Statistics, Variable= Noise, By variables=Filter

Noise by Filter

n Mean Std

Octel 18 804.72 25.64

Standard 18 815.56 32.22

Noise by Filter
	n	Mean	Std
Octel	18	804.72	25.64
Standard	18	815.56	32.22

Stat > Basic Statistics > Display Descriptive Statistics, Variable= Noise, By variables=Side

Noise by Side

n Mean Std

Left 18 810.00 34.81

Right 18 810.28 23.36

Noise by Side
	n	Mean	Std
Left	18	810.00	34.81
Right	18	810.28	23.36

Step 3: Interactions Stat > ANOVA > Interactions Plot, Response= Noise, Factors= Size Filter Side, check Display full interactions plot matrix

Tests for interaction:

Stat > ANOVA > General Linear Model, Responses= Noise, Model = Size Filter Side Size* Filter Size* Side Filter* Side
Results (Short) Size*Filter p=0.000, reject H₀, there is interaction
Size*Side p=0.000, reject H₀, there is interaction
Filter*Side p=0.286, fail to reject H₀, there is no interaction

Step: Tests for Factors
Stat > ANOVA > General Linear Model, Responses= Noise, Model = Size Filter Side Size* Filter Size* Side, Graphs > Residual vs. Fits
Windows > Project Manager, Click on Graphs in left Panel, CTRL-click the two graphs, right-click, choose Layout tool > Finish

Size
1) a=0.05
2) H₀: a₁ = .. =a₃=0 (no difference in the mean noise of different sizes)
3) H_a: a_i≠0 for some i (some differences in the mean noise of different sizes)
4) p-value= 0 < a
5) We reject H₀, there are some differences in the mean noise of different sizes

Filter
1) a=0.05
2) H₀: b₁ = b₂=0 (no difference in the mean noise for different Filters)
3) H_a: b_i≠0 for some i (some differences in the mean noise of different Filters) 4) p-value= 0 < a
5) We reject H₀, there are some differences in the mean noise by Filters

Side
1) a=0.05
2) H₀: g₁ = g₂=0 (no difference in the means for different sides)
3) H_a: g_i≠0 for some i (some differences in the means for different sides) 4) p-value= 0.868 > a
5) We fail to reject H₀, there is no evidence for stat. signif. differences in the means for different sides

Multiple Comparison No need, there are only two filters, and they are different.