I think Junguo is asking how to carry out the analysis with SPSS.  You have two factors, A and B (with 0=No, 1=Yes, for example).  Note that the group that has (A=0, B=0) is your vehicle control group.  The basic syntax will look something like this:

UNIANOVA Y BY A B

  /METHOD=SSTYPE(3)

  /INTERCEPT=INCLUDE

  /EMMEANS=TABLES(A)

  /EMMEANS=TABLES(B)

  /EMMEANS=TABLES(A*B) COMPARE(A)

  /EMMEANS=TABLES(A*B) COMPARE(B)

  /CRITERIA=ALPHA(.05)

  /DESIGN=A B A*B.

The F-test for the A*B term tests a null hypothesis that can be stated in either of the following ways:

• The effect of A (whatever it is) is independent of B
• The effect of B (whatever it is) is independent of A

The last two EMMEANS sub-commands above will show the simple effects of each variable at both levels of the other. 

 HTH.

A synergistic effect would be a superadditive interaction between the two factors.

I think Junguo is asking how to carry out the analysis with SPSS.  You have two factors, A and B (with 0=No, 1=Yes, for example).  Note that the group that has (A=0, B=0) is your vehicle control group.  The basic syntax will look something like this:

UNIANOVA Y BY A B

  /METHOD=SSTYPE(3)

  /INTERCEPT=INCLUDE

  /EMMEANS=TABLES(A)

  /EMMEANS=TABLES(B)

  /EMMEANS=TABLES(A*B) COMPARE(A)

  /EMMEANS=TABLES(A*B) COMPARE(B)

  /CRITERIA=ALPHA(.05)

  /DESIGN=A B A*B.

The F-test for the A*B term tests a null hypothesis that can be stated in either of the following ways:

• The effect of A (whatever it is) is independent of B
• The effect of B (whatever it is) is independent of A

The last two EMMEANS sub-commands above will show the simple effects of each variable at both levels of the other. 

 HTH.

Hi, Bruce, many thanks for your answer, though I still do not know how to do it with SPSS. I read published papers that used two-way anava (SPSS) analysis to give a conclusion if the combo treatment has synergistic effect or not.

Thanks, Stephen. I want to learn how to do it with two-way anova with SPSS to judge if the combo treatment has synergistic effect. I have searched the internet and did not find a particular example like the data mode in my study.

Junguo, if I follow, you can determine whether the interaction effect is synergistic or antagonistic by looking at the simple main effects (which are generated by the last two EMMEANS lines in my syntax).  E.g., if the simple main effect of A increases as the level of B increases, that (I think) is what you are calling a synergistic effect.  On the other hand, if the simple main effect of A decreases as the level of B increases, (I think) you would describe that as an antagonistic effect.  (And for completion, if the simple main effect of A is independent of the level of B, there is no interaction.)

Is this what you're asking about?   

In Psychology and related fields, the same basic ideas have been described using slightly different terminology.  E.g., this is from p. 10 of Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences (3rd Ed.):

"Some behavioral science disciplines have found it useful to discriminate two types of conditional relationships.[4]  Moderation indicates that the strength of the relationship between C and Y is reduced as the value of D increases. [Example omitted]  In contrast, augmentation or synergy means that the strength of the relationship between C and Y is increased as the value of D increases.  Thus, moderation and augmentation describe particular forms of conditional relationships."

"[4] Elsewhere moderation may be used to describe both forms of conditional relationship.  Whether a relationship may be considered to be moderated or augmented in the sense used here is entirely dependent on the (often arbitrary) direction of scoring of the IVs involved."

HTH.

Dear Junguo

If you suppose that the time plays important role in the output data, then I suggest to study the treatment time as a factor, and analyze your data as a factorial experiment with two factors ( drugs 4 levels and treatment time =? ), so you will get the main effect of drugs , and main effect of treatment time , and the interaction between drug × treatment time.

Good Luck

I think what we have here is an issue of terminology. You have to articulate what exact pattern of effects corresponds to a "synergistic" effect (it often helps to draw a plot of your prediction). As Bruce and I mentioned, this probably is a certain kind of interaction: a "synergistic" effect means that the combination effect of A and B is bigger than the sum of effect A and of effect B; in other words, the value you get for condition A2B2 is bigger than what you would expect if you predicted it based on just the effect of A plus the effect of B. You test this by seeing if the interaction term in your model is significant. But as Bruce pointed out, it has to be a certain kind of interaction (you could have an interaction but is significant in the wrong direction, which would be the opposite of synergy; i.e. if the effects of A and B are not additive and not superadditive either). Often the most straightforward way would be to do this in a general linear model (e.g. a regression model) rather than ANOVA, because this way (unlike ANOVA with F-tests) your interaction term will have a sign (positive or negative). Then it becomes much more straightforward, i.e., if the main effect of A is positive and the main effect of B is also positive, then a positive interaction term means a superadditive (synergistic) effect whereas a negative interaction term means the opposite.

Re Stephen's suggestion to use a general linear (or regression) model, if you add the following /PRINT sub-command to the UNIANOVA command I posted earlier, you'll get a table of parameter estimates (or regression coefficients):

  /PRINT = PARAMETER

And Stephen, FYI, UNIANOVA is a GLM procedure, as it allows inclusion of both categorical and continuous explanatory variables.

HTH.

Given the information provided, it is difficult to tell if this is appropriate. However, this sounds like a repeated measures trial. You have patients with tumors and you administer a drug and monitor the effect on the tumor over time.

That said, there are a number of possible experimental issues that might cause trouble. Firstly, if replication was minimal for a standard ANOVA design, then you will not have sufficient replication for the repeated measures analysis. Secondly, I have no idea how to handle a case where the drugs are administered at irregular intervals. If the drugs are administered on Monday of every week that is ok. If there was a week pre-treatment interval then dose 1 was administered, with dose 2 at 4 weeks later, dose 3 2 weeks later, dose 4 at 7 weeks later, and then assessments for 2 years after that ... good luck. Subjects entering or leaving (dying?) the experiment, or missing values will all cause problems.

Good catch, Timothy!  Mea culpa!  I obviously didn't read the original question nearly carefully enough, as I missed the time element.  The UNIANOVA syntax I posted earlier assumed one measurement per patient, and is not appropriate for repeated measures.  In SPSS, the two most common approaches would be GLM-REPEATED MEASURES or MIXED.  The latter is the more flexible approach, and the one I would recommend.  If the OP Googles , several examples & tutorials should come up.  The UCLA "textbook examples" page has examples from Singer & Willett's book Applied Longitudinal Analysis, for example.