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...

I have decided that I really don't like the Rasch personal and item parameters, because they seem counter intuitive, and I don't like his use of the Poisson Distribution, because the assumptions required by it are unrealistic, certainly if you broaden the discussion beyond a very easy reading test. But I have resolved to continue anyway. I've been thinking about this for years, and at last I've bought the book , so I don't have to worry about library or other loan returns. I can take as long as I like, and I have resolved to understand every equation in the book, if only to disagree with it, or at least with it's use. I mentioned at the end of my last blog that Rasch refers to the "probability of misreading" ( op. cit. page 16) in a test, but he is a bit vague as to whether this a single error or several. The vagueness continues into the next section ( op. cit. page 17), when he refers back to his equation 2.1, which is my equation 12: ...

Returning to the original Rasch definition of person and item parameters, given by: θ vi = δ i /ζ v (12) Rasch puts flesh on them by defining a test, test zero, for which δ is unity. In this case: θ v 0 = 1/ζ v (16) He then says: "the ability of the person is the reciprocal of the probability of misreading in the reference test". Let's not think too hard about the reference test for a minute, but say the probability is estimated at 5%. I've initially chosen a low value, because Rasch uses Poisson estimation, which relies on low values. That returns a value of 20 for ζ . Rasch then looks for a person with unit ability. Rasch uses this conceptual person to estimate test/item difficulty as follows: θ 0i = δ i (17) He then adds the verbal definition: "the difficulty of a test is the probability that the standard person makes a mistake in the test...

Rasch was very clear on one thing. All these measures are relative. "Neither δ nor ζ can be determined absolutely" ( op. cit. page 16). Rasch emphasises the arbitrary nature of units, even in physical science: "1 Ft = the length of the king's foot" ( op. cit. page 16). This answers my own question posed in the fourth paragraph of this blog , which was that if the difficulty parameters for three items were found to be 1, 2 and 5 using one population, would they be exactly the same for another population or in the same proportion. The answer is the latter. It also confirms my own gut feeling that those writers who have developed the habit of talking about "logits", in the context of Rasch parameters, should desist from doing so, because stipulating units flies in the face of the original Rasch argument. Sometimes I think Rasch is oversold by the enthusiasts. If all you want to do, with say three children, Flossy, Gertrude, and Samantha, is esti...

Chapter two of the the Rasch book continues with the introduction of individual and item parameters. On my first reading of this, my powers of analysis were reduced to jelly because Rasch used the Greek letter ζ to represent ability. He also came up with the pronouncement. θ vi = δ i /ζ v (12) where θ vi is the probability of individual v making an error on item i. He introduces this expression by saying "Let us ... think of the probability of making a mistake in a test as a product of two factors ( op. cit. page 16, his italics, but my emphasis, because he italicised the whole statement). I mentioned earlier that, while at school, I studied Newtonian or macro-mechanics, which is classically deterministic. I also did econometric units at uni, which used linear algebra in essentially deterministic models of the economy. So had I been Rasch, I would have said: "Let us think of the probability of making a mistake as a ...