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# Chi squared watch

1. This is technically a biology question, but I was hoping there'd be some statisticians here who can help:

I'm a bit puzzled about interpreting results from Chi squared tests. I understand that if the calculated value for chi squared is less than the critical value, we reject the null hypothesis, but I don't understand how to comment on what this means in terms of probability and chance, and how the level of probability comes into it.
Could someone explain this?
2. If the chi-squared value is less than the critical value (which is normally taken at 0.05 by many biologists) we reject the null hypothesis.

Why? Because the difference between observed and expected results is too significant; in other words, the null hypothesis (which normally states there is no significant difference) does not hold up, therefore, difference between results are too large to be dismissed as 'by chance'.

As for the probability part, when we reject the null hypothesis, corresponding probability is usually equal to, or less than, 0.05 (depending on your critical probability), therefore, there is a less than (or equal to) 0.05 chance that the difference is due to chance (in other words, 0.95 certain that difference is caused by some other factor and not chance).

Sorry if it is too lengthy and hopefully it helps!!!

Edit: thanks for giving me the opportunity to brush up my knowledge, as I have a biology practical A level exam on Wednesday ☺.
3. (Original post by Chlktrain135)
If the chi-squared value is less than the critical value (which is normally taken at 0.05 by many biologists) we reject the null hypothesis.

Why? Because the difference between observed and expected results is too significant; in other words, the null hypothesis (which normally states there is no significant difference) does not hold up, therefore, difference between results are too large to be dismissed as 'by chance'.

As for the probability part, when we reject the null hypothesis, corresponding probability is usually equal to, or less than, 0.05 (depending on your critical probability), therefore, there is a less than (or equal to) 0.05 chance that the difference is due to chance (in other words, 0.95 certain that difference is caused by some other factor and not chance).

Sorry if it is too lengthy and hopefully it helps!!!

Edit: thanks for giving me the opportunity to brush up my knowledge, as I have a biology practical A level exam on Wednesday ☺.
Not too lengthy, it's very clear and easy to understand, thank you!
4. Let's go from the top: a statistic is simply a function of the observed data. In this case you're probably using something involving a sum of observed minus expected squared divided by expected - or similar.

Now, the most useful statistics are those for which we can write down a probability distribution; in this case, that sum of observed minus expected squared divided by expected happens to have a probability distribution known as the .

This means that one can look and see where the value of this statistic computed on the observed data lies in the distribution. If it is far out in the tail of the distribution, we take this as meaning that so large a value of the statistic is not likely to be due to chance.

We often take a threshold value of 0.05 (purely conventional, mind you) - so that if the probability of the statistic being as large or larger than that we have actually calculated from our data is less than 0.05 we reject the null hypothesis that the observed value of the statistic was purely due to chance.

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Updated: November 1, 2015
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