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I am working on sample size of 70 . My observed and expected values are different (Observed 586, 648, 526, 662, 658, 502, ..... so on for 70 samples and expected 570 634, 513, 647, 644, 490, .....so on for 70 samples). I used Chi-sq test to check the null that there is no difference in observed and expected value. And I got a p-value of 0.99 which means I can't reject null. Can I use any other test for this kind of problem since I can see that for all the 70 samples observed is higher than expected but I cant show this result statistically.

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  • $\begingroup$ What are your values? As you say your sample size is 70, they must be measurements, not counts? $\endgroup$ – Peter Ellis Dec 17 '12 at 10:15
  • $\begingroup$ @PeterEllis These are all counts not measurements. $\endgroup$ – manjovial Dec 17 '12 at 10:19
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    $\begingroup$ Did the idea to look at the shift come after you saw that these data were like this, or before? (If it came before, why did you do a chi-square?) If you mainly want power against simple alternatives like a shift in the mean, why on earth do a vanilla chi-square? It has terrible power against such alternatives. $\endgroup$ – Glen_b Dec 17 '12 at 11:29
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Sounds like you need a paired t-test (which will use the difference between each observed and actual observation), or a non-parametric equivalent (which would pick up on the fact that more of the observed numbers are larger than expected than would be expected if it were a 50-50 chance).

To be fancy you could adjust for the fact that the observations are counts and hence unlikely to be normally distributed. This would require, for example, a model whereby each observation has a poisson distribution and hence the variance increases as the mean increases. In practice, if your example data reflects the overall set, you will get a similar result to a paired t-test.

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    $\begingroup$ could be right if what you want to test is whether the observed and expected have different means. But in one place you just say "different" without defining exactly what you intend. Did you want to test for a difference in means? $\endgroup$ – Peter Flom Dec 17 '12 at 11:11

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