Basic Statistics question: which test to run?

1. Jan 24, 2012

james121515

Hi everyone!

Lately I have been trying to improve my typing speed, and have been playing a game called Type Race, where you type various short passages (the passages are selected at random from a text bank) and your score in WPM is recorded. What I want to do is determine whether or not my typing speed has improved as a result of playing the game. In particular, I want to test the hypothesis that my scores have increased since I first started playing, statistically speaking. Right now I have completed 2821 races, with mean of 102.4 wpm and a standard deviation of 11.14 wpm. I have all the results saved in an Excel Spreadsheet I graphed my results with a histogram and noticed that my “population” of scores is quite normal. So, given this model of what I want to, what would be the strongest significance test to run on this data? With my very limited knowledge of statistics, I was thinking I could two random samples, one from the first half of my scores, and another from the second half, and testing the hypothesis that there will be a significant increase in wpm in minute. (In other words, the mean of the first half is larger than the second half). However, I think that there are some issues with this, since the initial scores have a direct influence on the later scores due to improvement from practice. In other words, the post “treatment” results were a direct result of having completing the “pre treatment” results in the first place. Sorry if that made NO SENSE whatsoever, again I’m a statistics newbie. What I’m getting at is, if this is case, wouldn’t it be more appropriate to run some kind of test that takes the pooled variance into account? Granted I would prefer to avoid analysis of variance if possible, but again I’m looking to obtain the most statistically robust results possible.

Thanks for any help!

2. Jan 24, 2012

james121515

Was this not the appropriate forum to post this thread in? This is not a homework problem.

3. Jan 24, 2012

Stephen Tashi

Applying statistics is a subjective matter and it is heavily influenced by tradition. (It sounds like you aren't worried about publishing a paper about your experiment, but if you are, it is advisable to look a other papers that got published and see what sort of statistical techniques impressed the editors of the publications.)

You didn't mentioned whether you had plotted your scores as function of either time or the number of the practice sesssion ( first, second, third, etc.). That's where I would start.

You say that you are a statistics newbee, so I don't know whether you understand the technical defintions of terms like "significance", "confidence" etc. The definitions of those concepts are not simple and they are not what a common sense type of person wants to know about real world situations! Is your purpose to apply statistics to the data in order to learn more about statistics? Or is your purpose to find out something about the data? If so, what? (If you are going to say "I want to know if my improvement is statistically significant", then please explain what you understand "statistically significant" to men.)

4. Jan 25, 2012

james121515

Thanks for your response. What I’m doing here is a little project on my own to help me understand statistics at a deeper level (beyond the one freshman level intro class I took two years ago), while at the same time having some fun with it. You mentioned confidence. I want to run this test at a 95% confidence level. Broadly speaking, I want there to only be a 5% chance that any improvement (increase in wpm) was by chance, and chance alone.
I suppose the question now is, given the data I have, what is the most appropriate way to measure “improvement” (or lack thereof)? Again, back to my original idea of taking a sample from the first half of the data, and another from the second half, and then running an independent samples t-test to determine whether or not the increase increase in mean WPM observed was statistically significant (with a CL of .95). My question is whether or not there are things I have not taken into account, which might affect the validity of my model.

Thanks again,
James

5. Jan 25, 2012

Stephen Tashi

The term "confidence" applies when you desire to estimate a parameter. Suppose we take "wpm" to mean the mean wpm of the imagined distribution of all possible typing exercises that you could do ( or do in the first half of your training, or however you wish to restrict the population). If you assume your wpm's are normally distributed and you have a certain number of samples from the population, you can state the radius of a 95% "confidence interval". The radius will be given in wpm and the "confidence" will be that if you repeated the experiment of collecting the same number of samples over and over again then the probability that the sample mean will be with in plus or minus that radius of population mean is 0.95. ( However if you take the particular wpm from your data, like 120.3 wpm you cannot claim that there is a 0.95 probability that this particular sample mean is within plus or minus that radius of the true population mean. That's the rub with using "confidence intervals".)

The statement that there "only be a 5% chance that any improvement (increase in wpm) was by chance, and chance alone" sounds like you wish to do "hypothesis testing". (The 5% is a "significance level" or "critical p-value", not a "confidence" level ). You could assume two samples (like your earlier vs later typing exercises) are drawn from the same normal population and you compute the probability of the difference in the means of the later minus the earlier sample being equal or gretater than the difference you observed. That does tell you whether there was a 5% (or less) probability than the observed result happened by chance, on the assumption that the two distributions are the same. (There is no question about the distributions being the same or not in this calculation. The phrase "by chance alone" isn't tested. It is assumed. There is no allowance for anything but chance. The distributions are assumed to be the same - or, if you wish, they are assumed the same with proability 1. Hence the 5% mentioned in the definition of the test does not tell you that a given outcome implies that is only a 5% probability that the distributions are the same or that there is a 95% probability they are different etc. That's the rub with hypothesis testing. It tells you nothing about the probability that the hypothesis is true or false. It only tells you about the probability of the data given the truth of the hypothesis - not vice versa.)

The above are descriptions of "frequentist" statistics, which is the type usually taught in introductory courses. My personal preference is to use Bayesian statistics. I also prefer to use probability models and simulations as opposed to relying on statistics alone.

Last edited: Jan 25, 2012
6. Jan 30, 2012

moonman239

What you want is a 2-sample t-test, which is used when you don't know the population standard deviation but you are sure that the data has a normal distribution or the sample is large. If the data is pooled - meaning there's no difference between the variances - use the pooled 2-sample t-test. If not, use the non-pooled 2-sample t-test.

Last edited: Jan 30, 2012
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