# Testing the trajectory of response type - unsure of which analysis to use

#### analogicalmind

##### New Member
Hi everyone,

Hoping someone might be able to help. I want to test a prediction that participants will progress through a trajectory of three different types of response in a matching game as a function of their vocabulary level. I've thought of a couple analyses to test this although I'm unsure of their suitability.

1. Ten trials of a matching game where it is possible to make three types of responses: Type-A, Type-B and Type-C. For each response a participant makes, they will receive a score of 1. After the ten trials, they will receive a score of 10 distributed across the three match types. For example, a participant might have a final score of something like 4 Type-A matches, 5 Type-B matches and 1 Type-C match.

2. A standardise vocabulary assessment with a continuous variable outcome.

The prediction is that participants will progress through a trajectory of making Type-A matches, then Type-B matches, then Type-C matches as a function of their increasing vocabulary.

I know that participants with a lower vocab score will make more Type-A matches, and those with a higher vocabulary will make more Type-C matches; what I am really interested in is testing the hypothesis that they will progress through making the intermediate Type-B matches.

I’ve thought of a couple of ways to test although I’m not completely happy with them.

Method One:

I could group the participants into three groups based on their predominant response type (e.g. predominantly Type-A matchers, predominantly Type-B matchers and predominantly Type-C matchers), then run a one-way ANOVA and pair-wise comparisons with vocab score as the dependent variable and predominant response group as the as the grouping variable. However, this would mean testing enough participants until there are three equal groups. I think this would work however the unknown sample size issue is not ideal it terms of the pragmatics of testing.

Method Two:

The other method I was thinking was to somehow weight the scores on the matching game so that Type-B scores were multiplied by 2 and Type-C scores were multiplied by 3. Each participant would then receive a total continuous score for the matching game that would increase as a function of increasing numbers of Type-B and Type-C responses. I could then use regression with total matching game score as the DV and vocab score as the predictor. However, I don’t think this would be very sensitive in terms of testing the progression through the Type-B matches.

What do you think? Any other ideas re how I could test the hypothesis that there will be a trajectory of Type-A responses - > Type-B responses -> Type-C responses as a function of increasing vocabulary knowledge?

Many thanks.

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#### the42up

##### New Member
This really sounds like a multinomial problem.

If you had only two choice, it would be a simple repeated measures binomial. I.e. choice = language scores + covariates where choice is either one or zero. In this case, they have a third option. So instead of A and B, they also have C.

You have ten repeated measures tests per subject with 10 associated scores. I strongly recommend using a repeated measures design so as not to fall into the trap of pseudo replication.

#### analogicalmind

##### New Member

Indeed. I'm thinking of regression models (vocab predicting the number of matches for each type) which include quadratic terms may be the way to go. The quadratic term should be significant only when vocab score is predicting the number of Type-B matches.

Do you mean repeated measures design as in repeated measures ANOVA?

Many thanks.

#### the42up

##### New Member
So let me see if I understand your design correctly-
you have 10 trials, each trial can have one of 3 possible categorical responses. You want to see if there is a difference in the probability of selecting a category given the subjects language score?

Is this correct?

#### analogicalmind

##### New Member
So let me see if I understand your design correctly-
you have 10 trials, each trial can have one of 3 possible categorical responses. You want to see if there is a difference in the probability of selecting a category given the subjects language score?

Is this correct?
That's correct.

The hypothesis is that they will progress through making Type-A matches, then Type-B, then Type-C as their vocabulary increases.

So number of Type-A matches will be negatively correlated with vocab score, number of Type-C matches will be positively correlated with vocab score, and number of Type-B matches with have a quadratic distribution with neither high nor low vacab score associated with Type-B matches.