# Statistical test for analyzing 2*3 between-subject design's main & interaction effect

#### AnneLearningStats

##### New Member
Hello,

I am now having trouble analyzing my data since I got stuck on selecting the proper statistical test to use.

My data is a 2*3 between-subject design data. The two IVs are one norminal(with values 0 and 1) and one ordinal(with values 0, 1,2), and my dependent variables are interval (rating scale from 1 to 5).

Since my data doesn't follow normal distribution even after log() or ln() transformation and doesn't have homogeneity of variance, I have to use nonparametric methods. Currently I got recommendations of Friedman test and Scheirer-Ray-Hare Test. But I searched online trying to understand them and found that: Friedman is suitable only for one IV with repeated measures; Scheirer-Ray-Hare Test cannot analyze interaction effect.

Would anyone please correct me if my understanding is wrong? And would any method could be applicable for my data? If you could also provide links with examples using package, that would be great. I had a hard time searching for Scheirer-Ray-Hare Test's ready-to-use package.

Anne

#### Karabiner

##### TS Contributor
Re: Statistical test for analyzing 2*3 between-subject design's main & interaction ef

Since my data doesn't follow normal distribution
Do you mean, your raw data (irrelevant), or data within cells/residuals (sometimes relevant)?
And how large is your sample?
and doesn't have homogeneity of variance
What does that mean, are there very large differences between
the cell sd's? And are there unequal cell sizes?

Maybe you should consider ordinal regression, with your 5-point scale
as ordinal dependent variabe, 1 dummy for your dicotomous and 2
dummies for your ordinal predictor, and 2 interaction variables.

With kind regards

K.

#### AnneLearningStats

##### New Member
Re: Statistical test for analyzing 2*3 between-subject design's main & interaction ef

Hi Karabiner,

Thanks so much!

For your questions, actually each cell has 5 samples and I tested again, they follow homogeneity of variance.

I followed your suggestion to try ordinal regression(logit) in SPSS and Generalized Linear Models with Ordinal Distribution and Logic link function. However, I am so confused with the results mainly because I am not sure how to interpret the p-value for regression coefficients.

Firstly, in Ordinal regression, the goodness of fit, the parallel assumptions both don't get reject. Given that, the p-values for one IV(three-level one) is one > 0.05 and one < 0.05. I suppose this would be the evidence concluding there is no main effect on this IV, right? And the p-values for my dependent variables(four thresholds) are also having such results. Would that be a problem?

Secondly, when using Generalized Ordinal logic regression, it will show the p-values for main-effects and interestion effect. However, confusingly, the p-values shown for each level of IV in Parameter Estimates table is still one>0.05, one < 0.05, but the p-value for that IV in the Test of Model Effect Table is <0.05, significant.

I guess as a summary, I am just not sure how to interpret the results given such not very obvious significant p-value and whether the Generalized methods' results conflict with Ordinal Logic Regression at all.

Thanks so much!
Anne

#### Karabiner

##### TS Contributor
Re: Statistical test for analyzing 2*3 between-subject design's main & interaction ef

Given that, the p-values for one IV(three-level one) is one > 0.05 and one < 0.05. I suppose this would be the evidence concluding there is no main effect on this IV, right?
You mean, one dummy is p > 0.05 and the other is p < 0.05? You have to
interpret this with respect to the third level which (the reference level)
wasn't represented by a dummy. By the way, maybe does the SPSS ordinal
regression procedure offer an opportunity to circumvent the creation of
dummies and declare your ordinal predcitor as "categorical"? In that case
you could have a look at which contrasts serve your purposes.

With kind regard

K.