Comments on: Anova p-value without tables
http://ask.metafilter.com/96416/Anova-pvalue-without-tables/
Comments on Ask MetaFilter post Anova p-value without tablesSat, 12 Jul 2008 12:04:05 -0800Sat, 12 Jul 2008 12:04:05 -0800en-ushttp://blogs.law.harvard.edu/tech/rss60Question: Anova p-value without tables
http://ask.metafilter.com/96416/Anova-pvalue-without-tables
I'm trying to streamline my Mum's business processes and part of that is moving her statistical analysis online. Based on her notes I've created the <a href="http://www.hazelryan.co.uk/anova.php">anova table</a>. Now I need to find the exact p-value where my F is significant <br /><br /> Its been 7 years since I did this at school so I don't remember all the exact terms but even then we just picked a significance level, looked up the value in the table and then said it was significant or not significant which isn't enough for what my mum does. <br>
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I've googled around all I can find are online calculators that will calculate it for you (and sadly none of them were javascript) so I know its possible and feasible but I just can't find any algorithms or methods described anywhere. The standard answer seems to be to look it up in a table or use some ready made software.post:ask.metafilter.com,2008:site.96416Sat, 12 Jul 2008 11:56:10 -0800missmagentaanovap-valueBy: missmagenta
http://ask.metafilter.com/96416/Anova-pvalue-without-tables#1406446
Forgot to add that her notes indicate she's using a chi-squared test.comment:ask.metafilter.com,2008:site.96416-1406446Sat, 12 Jul 2008 12:04:05 -0800missmagentaBy: proj
http://ask.metafilter.com/96416/Anova-pvalue-without-tables#1406461
You haven't specified the significance level. Statistics aren't merely "significant" or "non-significant." You need to pre-specify the level of signficance that will satisfy you. An alpha of .05 is pretty standard, as is .01. You can find out what value F would need to take to be significant at each of those values using a standard F distribution table.comment:ask.metafilter.com,2008:site.96416-1406461Sat, 12 Jul 2008 12:23:37 -0800projBy: proj
http://ask.metafilter.com/96416/Anova-pvalue-without-tables#1406470
I might add here that if she's doing her analysis with any kind of statistical software at all it will tell you the significance level of the F-statistic when it produces it. Reporting the significance level of a statistic is enough for most academic journals, I can't imagine why that wouldn't "be enough" for your mom's business.<br>
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For instance, most journals report statistics in the following way, "F = 42.33 **" with one * indicating that the statistic is significant at the .05 level, two *s indicating significance at the .01 level, three *s at the .001 level, and so on. I don't know that (in the social sciences) I've ever seen "F = 42.33, F would be significant at 41.01, therefore reject the null and conclude significant a the .05 level" or something to that effect.comment:ask.metafilter.com,2008:site.96416-1406470Sat, 12 Jul 2008 12:29:12 -0800projBy: epugachev
http://ask.metafilter.com/96416/Anova-pvalue-without-tables#1406516
The p-values that statistical software reports along with F statistics are computed by integrating the probability density function of what is known as the <a href="http://en.wikipedia.org/wiki/F_distribution">F distribution</a> (which requires 2 parameters to be specified that depend on the nature of your data and the statistical test) from 0 up to the observed F-statistic</a>, and subtracting that value from 1. The integral of the F distribution pdf does not have a simple closed-form solution, so numerical integration is required in practice. Numerical integration can be tricky to do properly and certainly beyond the abilities of a student with a textbook and a calculator, which is why in classes they have you look up values in a table.<br>
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I don't have a cite for the proper way to do the integration. I would recommend trying to find a library where this is already implemented rather than reinventing the wheel yourself.comment:ask.metafilter.com,2008:site.96416-1406516Sat, 12 Jul 2008 13:18:35 -0800epugachevBy: missmagenta
http://ask.metafilter.com/96416/Anova-pvalue-without-tables#1406590
Found a library at phpmaths.com - after looking at the source code I can see why all the articles/tutorials that include an exact p-value skip over that part and just magically come up with the number ;)comment:ask.metafilter.com,2008:site.96416-1406590Sat, 12 Jul 2008 15:29:38 -0800missmagentaBy: singingfish
http://ask.metafilter.com/96416/Anova-pvalue-without-tables#1406596
Your p value is in the table at http://www.hazelryan.co.uk/anova.php<br>
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F(df=1,4) = 37.5, p = 0.3 which means that the ANOVA is non significant and there is no difference between means (well variance actually) across conditions. Actually you seem to have shifted the decimal places over - I had a quick look in Excel with =fdist(37.5,1,4) which indicates that the p value is 0.003 which makes more sense given the size of the F statistic.<br>
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I have no idea what the chi squared test is for - your thinking sounds quite confused about this.<br>
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Once you have an idea of the hypotheses you want to test, you might want to look at <a href="http://r-project.org">R</a> along with <a href="http://oit.utk.edu/scc/RforSAS&SPSSusers.pdf">this document</a>.comment:ask.metafilter.com,2008:site.96416-1406596Sat, 12 Jul 2008 15:34:29 -0800singingfishBy: missmagenta
http://ask.metafilter.com/96416/Anova-pvalue-without-tables#1406613
<em>Your p value is in the table at http://www.hazelryan.co.uk/anova.php</em><br>
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It is <em>now</em>. Also the decimal place wasn't shifted the number you saw was just plain wrong (just coincidentally about 100x the real value) - you happened to look at it in the 30 seconds where I'd put the wrong numbers into the formula ;)comment:ask.metafilter.com,2008:site.96416-1406613Sat, 12 Jul 2008 16:05:40 -0800missmagenta