# Anyone good with statistics?

Anyone good with statistics??

I've conducted an experiment looking at phonetic symbolism in Japanese words.
Thirty participants listened to 40 Japanese words and had to choose out of a choice of two possible English translations which one they thought was the correct answer.

I'm trying to find out whether or not the participants could give the correct answer at an above-chance expectancy level.

Since they didn't know Japanese, we can assume that they had a 50% chance of giving the correct answer (since there were two possible answers for each word- a correct and incorrect one).

There were 705 correct answers out of 1200 possible correct answers (30 x 40).
This is more than half, but is it significantly more than half?

I wasn't sure of the correct statistical test to use, but I used a Chi-square test and followed the instructions on this page: visualstatistics.net/SPSS%20workbook/chi-square_goodness_of_fit.htm

Obviously they use a different example but I'm pretty sure it's the same thing: comparing observed frequencies with expected frequencies.

The results suggested that it was massively significant. However, even if they only got 614 correct and 586 incorrect, it still reports a significant difference (Chi square = .653, Asymp. Sig. = .419).

This doesn't seem right to me, it seems very low.
If I tossed a coin 1200 times and it landed heads 614 times, then that means the coin is weighted??

705/1200 is only 58.75%, and that's significant?

I'm surely doing something wrong..

ssd
Perform standard statistical test for binomial proportion.

sotonandy
I'm not sure whether this is implemented in any of the standard statistical packages, but I write some code in R to calculate the probability of getting any given number right (out of 1200, using the binomial distribution), then had it add up the probability of getting more than 705. It was tiny. In fact, the probability of getting more than 641 is less than 0.01 (significant at 1% level). A result of just 629 would be significant at the all-important 5% level.

When the number of samples is very large, the proportion of coin tosses that are heads tends to 50%, and the probability of ending up a long way off becomes very small (the laws of large numbers). The percentage required to be significant becomes only a little bit more than 50. As an aside, the proportion of human babies that are male, about 51%, is accepted as statistically different from 50% due to the huge amount of data being considered.

If you have Matlab or similar you to do a simulation to convince yourself.

There is an approximation to the binomial test here:

http://www.dimensionresearch.com/resources/calculators/normal.html

If you can use R or S-plus I could give you the code I wrote if you want.