Learning Java

Whatever bad things some people say about Microsoft, in the olden days they brought to market a raft of products, which were accessible, easy to use, and useful. MS Access is an example. It may have limitations as a commercial database engine, but as a sketch pad, a tool for collecting one's thought's, it is, in my opinion, hard to beat. My current task is to design a set of iterations through scoring rate data to render the scoring rate as an objective measure of student ability and item difficulty. The raw data is set out in a single table, as shown in my last blog . On this I have written two queries: SELECT [HAItemB].[sessidx], Avg([HAItemB].[rate]) AS AvgOfrate FROM HAItemB GROUP BY [HAItemB].[sessidx]; and SELECT HAItemB.item, Avg(HAItemB.rate) AS AvgOfrate FROM HAItemB GROUP BY HAItemB.item ORDER BY HAItemB.item; These queries calculate the average raw scoring rate for each session and each item. The item query looks like this: Item AvgOfrate ...

I have now transformed the raw data from my VB Application - Active Math so that it looks like this: 7/28/2000 12:41:55 PM11 3+3 1 27 7/28/2000 12:41:55 PM11 2+2 1 27 7/28/2000 12:41:55 PM11 1+1 1 35 7/28/2000 12:41:55 PM11 4+4 1 32 7/28/2000 12:41:55 PM11 5+3 1 8 I'll refrain from posting the code, but the important links were first the Character Streams lesson, especially the example from the lower half of the page entitled Line-Oriented I/O. Also from the same thread was the lesson entitled Scanning . This has nothing to do with flat bed scanners, and in VB would probably be called parsing. From this lesson I followed the link to the scanner class in the API and reversed up to the parent package (java.util) and then back down to the StringTokenizer class . Useful forum threads were this one , which gave me the idea of using...

My blog will become more blog like again for a while now, and more about learning Java, because I haven't a clue where I am going next. Already I have rebuilt the bare bones of an application, once created in VB6, and posted it as an applet on a web page . I have also revisited some raw theory , which had been floating around in the back of my mind for years. I am now satisfied that I know what I want to estimate, and I know in theory how I want to estimate it. But translating that into practice will be a bit harder. I have a pile of data collected years ago from the VB app. The data was never used at the time and was invisible to the user. The code to collect it was tacked on as an afterthought, "just in case" I ever got around to using it. I had an idea what data I needed to collect, but I had no idea how I would process it, so the data layout was designed purely for ease of collection - i.e. with a minimum of code and in a format which took up a minimal amoun...

Rasch expressed the expected reading rate in a reading test in relation to expected reading rate in a reference test as follows: ε i = λ vi / λ v1 where λ vi is the reading rate of the generic or typical student v in the reading test in question, and λ v1 is the reading rate of the generic or typical student v in the reference test. That translates fine into an estimation methodology, if you have very large data set, where all students address all tests, and the tests themselves are substantial enough for averaging to happen within them. You simply average the results to get your ratio. It doesn't work so well if you are interested in estimating the difficulty of individual test items, and especially not if you are working with data from a modern computer based test, where the items themselves are generated randomly within difficulty levels, and where the difficulty levels are set by student performance. If such a test is working prope...

If the probability of an event occurring in a very short interval of time is θ , the probability that the event occurs a times in n intervals may be estimated by the Poisson distribution: p{a|n} ≈ n θ a e - n θ /a! (10) Suppose n intervals may be aggregated into a time period of interest. For a telephone exchange, this might be a period of peak demand. For a reading test it might be five or ten minutes, however long the test lasts. Now imagine another time period used to define frequency of events λ . Rasch ( op. cit. page 34) uses a 10 second interval, I prefer a minute, most physicists use a second, but as mentioned in the previous blog, it make no difference to the essence of the argument. Note, however, in just a few lines we have referred to three distinct time intervals. First there is the very short time interval, used to define θ, and during which the event will only ever occur once. Rasch ( op. cit. page 35...

The next chapter in the Rasch book addresses reading rates. This is traditionally one of my favourite chapters and I once published a paper based on it . I like scoring rates because I believe intuitively that they yield a more reliable estimate of ability than raw scores. Many years ago I presented a somewhat inane paper at a fortunately sparsely attended WAIER forum . I have long been looking to find a more substantive argument, and I believe I am getting quite close. My inspiration comes from this web page . Let's imagine two students sitting a test comprising a single dichotomous item. Imagine the ability of the first student (Student A) in relation to the difficulty of the item is such that the probability of a correct answer is 55%. Imagine the ability of the second student (Student B) in relation to the difficulty of the item is such that the probability of a correct answer is 45%. What is the probability that these students will be properly ranked b...

On page 18 of the text , Rasch has defined the misreadings in two tests as a vi1 and a vi2 , and the sum of the two as a v . He has also equated the observed number of misreadings in test i with λ vi , the expected number. And from equation 20 in my previous blog: λ vi = τ i /ζ v (20) So if: a vi = λ vi and: a v = a vi1 + a vi2 then: λ v = (τ i1 + τ vi2 )/ζ v (24) Rasch calls this the "additivity of impediments" ( op. cit. page 16). Leaving aside the fact that additivity is not listed in the (MS) dictionary, I can't see the point in this nomenclature just yet. He also rearranges the equation, and suddenly replaces his bold equality with an approximation: ζ v ≈ ( τ i1 + τ vi2 )/a v (25) I shall not discuss the remaining text on that page, because it relates solely to reading tests, and...