How do you do a Chi Square?

Question

I have a Chi Square table I have to complete for our fruit fly experiment but I have no clue how to do it. It has rows labeled observed, expected, deviation, deviation squared, and deviation squared divided by expected. It has columns labeled vestigial male, vestigial female, wild male, and wild female. The results from the experiment were no vestigial flies and 73wild male and 67 wild female. My hypothesis was that there wouldn’t be any vestigial. How do you find expected??? THANKS!!!

Answer 1

In order to find the expected, you have to know what the original cross was. If a wild (normal winged) male was crossed with a vestigial winged female, all the F1 generation would have normal wings, but be heterozygous for vestigial wings. If the F1 offspring were crossed to produce an F2 generation, you would expect a ratio of 3 normal winged flies to one vestigial winged fly. The mutation for vestigial wings is not carried on the X chromosome, so it doesn't matter how many males or females there are.
What you would do is apply the ratio to the number of actual flies you had. For example, let's say you got 33 flies with vestigial wings (vg) and 67 with normal wings (+). That is a total of 100. When you apply the ratio, you realize you would have expected 25 vg and 75 +.
Now, you wonder why you got more vg and fewer + than you expected. Did these differences from what you expected come from chance, or was there another problem (like did someone else put another kind of fly in your cross bottle). In order to tell the probability that the differences were due to chance, you use the chi square test.
You plug your values into the Chi square equation(actual - expected) squared over the expected for each phenotype. Thus in the case I mentioned, it would be ((33-25)^2)/25 + ((67-75)^2)/75. You come up with the chi square value, and use it in the table to find the probability.
When there are two phenotypes (vg or +), there is one degree of freedom, and you look along the columns to find where your value would fit. It is usually between two of the columns - for example, 0.9 and 0.5. In that case, there is between a 50% an a 90% chance that the differences were due to chance. Usually, you consider that the differences were due to chance (and not some problem with your experiment) if the probability is more than 5%.

Answer 2

Chi square is a non-parametric test of statistical significance for bivariate tabular analysis (also known as crossbreaks).
There is a tutorial at this site:
http://www.georgetown.edu/faculty/ballc/webtools/web_chi_tut.html