Additive Two-Way ANOVA Model - nonsignificant model but significant parameter estimates?

amarikow57 — Tue, 27 Apr 2021 17:48:37 GMT

My knowledge on two-way ANOVAs is a bit shaky so I'm hoping for some clarification. So it appears my overall model is significant (p < 0.0001). However, I am a bit confused why pressure is nonsignificant and temperature is significant in the Type III ANOVA table. Yet individual levels of pressure are significant and temperature 270 has no values. Are these the difference between main effects and simple effects?

Furthermore, I was going to look at pairwise comparisons, but it that wrong when there is no interaction? That is, I can't really control for temperature when comparing different pressure levels and vise versa.

Data

DATA DATA.Temp;
 input Pressure Temp Strength @@;
 datalines;
 120 250 9.60 120 260 11.28 120 270 9.00
 130 250 9.69 130 260 10.10 130 270 9.57
 140 250 8.43 140 260 11.01 140 270 9.03
 150 250 9.98 150 260 10.44 150 270 9.80
 ;
RUN;

Model Procedure

PROC GLM data = DATA.Temp plots = ALL;
 class pressure temp;
 model strength = pressure temp / clparm noint solution;
 means pressure temp / hovtest = Levene;
 lsmeans pressure temp / pdiff = all adjust = Tukey;
RUN;

Output

Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	6	1164.195417	194.032569	540.51	<.0001
Error	6	2.153883	0.358981
Uncorrected Total	12	1166.349300

Source	DF	Type III SS	Mean Square	F Value	Pr > F
Pressure	3	0.58069167	0.19356389	0.54	0.6727
Temp	2	4.65765000	2.32882500	6.49	0.0316

Parameter	Estimate		Standard Error	t Value	Pr > \|t\|	95% Confidence Limits
Pressure 120	9.482500000	B	0.42366293	22.38	<.0001	8.445834157	10.519165843
Pressure 130	9.309166667	B	0.42366293	21.97	<.0001	8.272500824	10.345832510
Pressure 140	9.012500000	B	0.42366293	21.27	<.0001	7.975834157	10.049165843
Pressure 150	9.595833333	B	0.42366293	22.65	<.0001	8.559167490	10.632499176
Temp 250	0.075000000	B	0.42366293	0.18	0.8653	-0.961665843	1.111665843
Temp 260	1.357500000	B	0.42366293	3.20	0.0185	0.320834157	2.394165843
Temp 270	0.000000000	B	.	.	.	.	.

Re: Additive Two-Way ANOVA Model - nonsignificant model but significant parameter estimates?

PaigeMiller — Tue, 27 Apr 2021 17:52:27 GMT

The Type III test is testing to see if the levels of each variable are different from one another. So the levels of TEMP are different from one another, the levels of PRESSURE are not.

The parameter estimate tests are testing to see if the estimate is different from zero. So for PRESSURE, the estimates are different from zero.

topic Additive Two-Way ANOVA Model - nonsignificant model but significant parameter estimates? in Statistical Procedures

Additive Two-Way ANOVA Model - nonsignificant model but significant parameter estimates?

Re: Additive Two-Way ANOVA Model - nonsignificant model but significant parameter estimates?