Thank you for your question, Davis.

At pre-test, there are categories 0,1,2,3
but at post-test there are categories 0,1,2,3,4
This difference makes comparisons difficulty.

Please look at http://www.rasch.org/rmt/rmt101f.htm - that Research Note discusses this situation.

Thank you for your plots, Davis.

It is easier to make inferences from this type of plot if they include the confidence bands. Winsteps can do this with the "Plots", "Scatterplot" function. http://www.winsteps.com/winman/index.htm?comparestatistics.htm

Looking at the plots, the points appear to be statistically collinear. To help with interpretation I have drawn in some lines.

PART 1: there is probably a ceiling effect on the Pre-test that causes the 3 points to the right and the weird x-y scaling. Suggestion: omit items with extreme scores from PART 1 plot and make the x-axis and y-axis ranges the same.

PART 2: we can see that there are two trend lines. This is typically a treatment effect. Items that are taught become relatively easier than the other items. We expect that items along the blue arrow were a focus of the treatment.

PART 3, 4, 6: the points approximate the expected trend (blue line). We would know better if we had confidence bands. I have circled two points in red. These may indicate floor and ceiling effects or merely be accidents.

PART 5: this shows a small change in discrimination (red arrow), probably not enough to have substantial impact on inferences. But it may require a choice. Which is decisive? The pre-test item difficulties (medical applications where treatment decisions are made at admission) or post-test item difficulties (educational applications where pass-fail decisions are made at the end of the "treatment").

Davis: There are two considerations here.

1. How do the items interact with the treatment? This is what your plots show. We expect that items directly related to the treatment will get relatively easier. Do they?
Is the treatment intended to make your person performance more uniform across the items? Remediation does this. Then we expect the items to become closer together in difficulty at post-test.
Is the treatment intended to to make person performance more different across the items? Athletic training does this. Then we expect the item difficulties to spread out more.

2. If you want to measure how much the persons change due to the treatment, then you must decide which is the crucial time-point. Pre? or Post? Then anchor the items at the item difficulties for that time-point at both time-points. Measure everyone at the two time-points, and then use conventional plots and statistics to compare the two sets of measures.

OK?

Mike,
I determined person levels for pre test. After then I determined person levels for post test. I used Andrich Thresholds for levels. intervention group and control group statistically same at pre-test. Intervention group is better than control group at post test. I focused on intervention group. Some items are relatively easier than pretest for intervention group.That's why item difficulties are different pre and post. (Not constant). Items are took place at different levels at pre and post.

I want to see how much the persons change due to the treatment, then I must decide which is the crucial time-point. Pre? or Post? I didn't decide. I don't know which is important (pre or post). This study about education on midde school student. I suppose we choosed one of them (pre or post). How to anchor the items for pre and post test. Will I do such as attached?

Davis, for educational applications, post-test is usually the more important because we don't care where the students are when they start, but where they end is crucial.

So, in Winsteps, we would analyze the post-test data:
output IFILE=if.txt and SFILE=sf.txt

Then analyze the pre-test data:
input the anchor files: IAFILE=if.txt and SAFILE=sf.txt