You're right that you don't need to use the normal approximation here. You're almost there, but what you have calculated are probabilities of 8 (or 6) successes out of 10 trials under the null hypothesis. What you really need for a p-value is the probability of 8 (or 6) OR MORE successes.
For the Apple headphones: P = BINOM(8,10;0.5) + BINOM(9,10;0.5) + BINOM(10,10;0.5) = 0.055
For the Shure headphones: P = BINOM(6,10;0.5) + BINOM(7,10;0.5) + BINOM(8,10;0.5) + BINOM(9,10;0.5) + BINOM(10,10;0.5) = 0.377
For a two-sided test, multiply these p-values by 2. Even for a one-sided test, there is not enough evidence to suggest that there is any noticeable difference between the codecs at the 5% significance level. It's important to note that this is not the same as saying that we do have evidence to suggest that the codecs are not different. All we can conclude, as everyone is pointing out, is that this test is worthless.
I've read double-blind studies all the way back to c't in 2000, which said that twelve audiophiles and one sound master at a record company couldn't tell CDs and 256kbps MP3s apart.
Fine, but that has nothing to do with the grandparent's point. The point was that audiophiles will hear a difference between 16-bit 44.1 kHz audio and 24-bit 96+ kHz audio. Nothing to do with MP3 at any bitrate.
(I have no opinion either way, my ears are shot to pieces, I'm just trying to make a stand for logic.)
I still hear people verbalising already painfully long URLs including the "http://", and just recently heard it spelled out "h - t - t - p - semicolon - backslash - backslash..."
But we've had home automation since at least 1984! There were a few bugs in the system (unexpected sentience, etc.) back then, but I'm sure they could have been sorted out by now.
I agree with you that these sorts of reports can be totally uninformative, but I think your stats are misleading. (How do you approximate "error" by 1/sqrt(x), and why do you then +/- x/sqrt(x) == sqrt(x)?)
To estimate the standard error of an estimate like this, you need two things: the sample size and the variation in the sample, neither of which are given here (for 2004 nor for 2005). If the sample size was sufficiently large, and the variation in the sample (a predictor of variation in the population) was sufficiently small, it could well be that this is in fact evidence of a significant (albeit small) change in driving habits.
But we'll never know for sure because, as in all news reports like this, sample means are treated as gospel. A change of one mile in a sample of one driver would probably lead to the same headline.
With my now four month old I am lucky to get in a couple of hours of gaming a week and that is only if my wife and daughter take a nap together while doing other things like working or mowing the lawn.
Your wife and daughter mow the lawn while taking a nap?
I'll second that: stay away from PlusNet. I was aware of the limits and peak times on their "unlimited" plan when I joined, but a couple of months in they changed the rules without warning. The first I heard was an email telling me I was being throttled for what I thought was usage well within the limits.
And now I'm having a hard time cancelling, their customer service leaves a lot to be desired.
Slashdot Mirror
You hear that sound, patent trolls? That's a recording of the world's smallest violin, playing on the world's smallest radio. Just for you.
Very interesting post, but since this is a post about language, I'll allow myself a little Grammar Nazi snark:
You don't need to put, "commas", around every phrase in quotes. It makes your sentences stilted and difficult to read.
You're right that you don't need to use the normal approximation here. You're almost there, but what you have calculated are probabilities of 8 (or 6) successes out of 10 trials under the null hypothesis. What you really need for a p-value is the probability of 8 (or 6) OR MORE successes.
For the Apple headphones:
P = BINOM(8,10;0.5) + BINOM(9,10;0.5) + BINOM(10,10;0.5) = 0.055
For the Shure headphones:
P = BINOM(6,10;0.5) + BINOM(7,10;0.5) + BINOM(8,10;0.5) + BINOM(9,10;0.5) + BINOM(10,10;0.5) = 0.377
For a two-sided test, multiply these p-values by 2. Even for a one-sided test, there is not enough evidence to suggest that there is any noticeable difference between the codecs at the 5% significance level. It's important to note that this is not the same as saying that we do have evidence to suggest that the codecs are not different. All we can conclude, as everyone is pointing out, is that this test is worthless.
Fine, but that has nothing to do with the grandparent's point. The point was that audiophiles will hear a difference between 16-bit 44.1 kHz audio and 24-bit 96+ kHz audio. Nothing to do with MP3 at any bitrate.
(I have no opinion either way, my ears are shot to pieces, I'm just trying to make a stand for logic.)
http://www.veer.com/products/merchdetail.aspx?imag e=vpr0001260
Yeah, you'd almost think it was deliberate, wouldn't you? :)
Youre right! Theres not a single apostrophe in the whole review. However, it's summary does contain a few.
I still hear people verbalising already painfully long URLs including the "http://", and just recently heard it spelled out "h - t - t - p - semicolon - backslash - backslash ..."
No proof? Haven't screenshots been used as "proof" in **AA cases? Wouldn't these watermarks constitute proof just as much as a screenshot does?
From Netflix:
System Requirements:
Windows XP with Service Pack 2
or Windows Vista
Internet Explorer version 6
or higher
But we've had home automation since at least 1984! There were a few bugs in the system (unexpected sentience, etc.) back then, but I'm sure they could have been sorted out by now.
I agree with you that these sorts of reports can be totally uninformative, but I think your stats are misleading. (How do you approximate "error" by 1/sqrt(x), and why do you then +/- x/sqrt(x) == sqrt(x)?)
To estimate the standard error of an estimate like this, you need two things: the sample size and the variation in the sample, neither of which are given here (for 2004 nor for 2005). If the sample size was sufficiently large, and the variation in the sample (a predictor of variation in the population) was sufficiently small, it could well be that this is in fact evidence of a significant (albeit small) change in driving habits.
But we'll never know for sure because, as in all news reports like this, sample means are treated as gospel. A change of one mile in a sample of one driver would probably lead to the same headline.
And then there are distribution assumptions...
"Second comes right after first!"
As does Air France. Google's English translation here.
If this helps keep the Reavers at bay, I'm all for it.
Your wife and daughter mow the lawn while taking a nap?
I know nobody likes grammar nazi's, but you misspelled "hot grits."
You missed the apostrophe in "grit's" :)
Good god. The word is preceded.
Damn kids.
I'll second that: stay away from PlusNet. I was aware of the limits and peak times on their "unlimited" plan when I joined, but a couple of months in they changed the rules without warning. The first I heard was an email telling me I was being throttled for what I thought was usage well within the limits.
And now I'm having a hard time cancelling, their customer service leaves a lot to be desired.