# •Comparing groups - which test should I use（t-test or ANOVA)

#### xiaohui

##### New Member
The general infomation is:
We have 6 kinds of material and have 4 group for each material now(please see the attached table)
we cut one tooth to two halves(A and B) and bonded two composite cylinder to each half(cylinder 1 and 2). half A is control group(just following the normal bonding process) and half B is treated group(treated with one of the material first and then following the normal bonding process).That means, In total, we make four cylinder on one tooth.(A1.A2,B1,B2). We test the shear bonding strength after 24h(A1 and B1) and after 1week(A2 and B2)

In general:

A1 = ControlGroup after 24h
A2 = Control Group after 1w
B1 = Experimental Group after 24h
B2 = Experimental Group after 1w

we want to test:
1. if all of the material will have influence on the shear bond strength(bonding effect)
2. how the shear bond strength changes following the storage time(24h and 1w)

I have think about several methods:
1) use the paired t-test to analyze the relationship between A1 and A2, B1 and B2(different time)
use the independent t-test to analyze the relationship between A1 and B1, A2 and B2(with treatment and without treatment)

2) just use one way ANOVA to analyze all the four group per each material. This method can not analyze the difference within different materials.

3）use two-way ANOVA(time and treatment is two factors).(the problem is we can got the result about if "time" or "treatment" has influence, but we can not see the details between A1 and A2, B1 and B2, A1 and B1,A2 and B2)

4) use repeated-measures ANOVA to analyse(time is within-subject factor, treatment is between-subject factor)

5) if we also want to analysis the difference between different solution, maybe we should choose three-way ANONVA.( time, treatment, different materials as three factor, the problem is the same with 3), we can not get the details between A1 and A2, B1 and B2, A1 and B1,A2 and B2)

I really can not decide which method is suitable for my data, I am very appreciated if you can give me some advice. Thank you very much!

#### xiaohui

##### New Member
In brief, there are 4 variables in this study. three independent variables are different materials(6 levels), untreatment or treatment(2 levels), time(2 levels)
one dependent variables are shear bond stress(Newton)
we want to test how can these three independent variables influence dependent variables.

#### victorxstc

##### Pirate
I would suggest a repeated-measures two-/three-way ANOVA. Do not use the t-test here; use an ANOVA post hoc, instead.

(the problem is we can got the result about if "time" or "treatment" has influence, but we can not see the details between A1 and A2, B1 and B2, A1 and B1,A2 and B2)
It is a weak point of some statistical packages like SPSS which sometimes do not allow the user to test for some of the pairwise comparisons. You can use more flexible packages such as R.

Besides, I think shear bond strength is related with the pressure (not the force) and is computed mostly in MegaPascal (MPa) unit which is Newton/mm^2. If you want to assess the force only (in Newtons), it will disregard the size of the bonding area. If the bonding areas for different specimens are not the same, comparing shear bond strengths in Newton might be problematic.

#### xiaohui

##### New Member
I would suggest a repeated-measures two-/three-way ANOVA. Do not use the t-test here; use an ANOVA post hoc, instead.

It is a weak point of some statistical packages like SPSS which sometimes do not allow the user to test for some of the pairwise comparisons. You can use more flexible packages such as R.

Besides, I think shear bond strength is related with the pressure (not the force) and is computed mostly in MegaPascal (MPa) unit which is Newton/mm^2. If you want to assess the force only (in Newtons), it will disregard the size of the bonding area. If the bonding areas for different specimens are not the same, comparing shear bond strengths in Newton might be problematic.

Thank you for your suggestion! Do You mean I should use two way ANOVA for each material. ( I think two-way ANOVA is enough because we only have two factor:time and treatment). and when the material changes, just repeat this statistic method again and again for different material?

Yes, you are right, actually when I analyze the data I will transfer the force to Mpa according to Newton/mm^2. Because we have all the same area for every test(about 4 mm^2), I guess maybe the result should be the same. Thank you to remind this.

#### victorxstc

##### Pirate
Thank you for your suggestion! Do You mean I should use two way ANOVA for each material. ( I think two-way ANOVA is enough because we only have two factor:time and treatment). and when the material changes, just repeat this statistic method again and again for different material?
You are so welcome. It would be better to include the material (the solution) into a three-way ANOVA framework, instead of repeating a two-way ANOVA for each solution.

Yes, you are right, actually when I analyze the data I will transfer the force to Mpa according to Newton/mm^2. Because we have all the same area for every test(about 4 mm^2), I guess maybe the result should be the same. Thank you to remind this.
Sure. #### xiaohui

##### New Member
You are so welcome. It would be better to include the material (the solution) into a three-way ANOVA framework, instead of repeating a two-way ANOVA for each solution
this is the result from three-way Anova

Tests of Between-Subjects Effects
Dependent Variable :Mpa
Source Type III Sum of Squares df Mean Square F Sig.
Corrected Model 4464.285a 15 297.619 7.525 .000
Intercept 9 7364.522 1 97364.522 2461.838 .000
time 58.395 1 58.395 1.476 .225
treatment 3049.014 1 3049.014 77.094 .000
material 769.448 3 256.483 6.485 .000

time * treatment 41.211 1 41.211 1.042 .308
time * material 275.883 3 91.961 2.325 .075
treatment * material238.922 3 79.641 2.014 .112
time * treatment * material 31.412 3 10.471 .265 .851
Error 12023.053 304 39.550
Total 113851.860 320
Corrected Total 16487.339 319
a. R 方 = .271（Adjusted R Squared = .235）

I know I should do post hoc test for material and treatment.
But treatment has only 2 level, SPSS said that it can not do it because level are less than three.and I really want to compare treatment at different time point(1w and 1d)for different material. How can I do it ?
And In your opinion,for material, whick post hoc test should be done?

Thank you very much for your kind help!

#### GretaGarbo

##### Human
It seems to me, from the first post, that factor A vs B and the time could be evaluated as a repeated measures design. (From my understanding of the experiment I don't think a 3 way anova is correct.)

I don't understand how the third factor, I believe it is the material, enters the experiment.

Is it possible to do a cross table of treatment(A and B) versus material? Was it made a randomization among these combinations?

Is this an application within the area of a dentist? 