Chi-square - Plugging in Numbers to Calculate Chi-square Values for F2 Phenotype Data

Deana Namuth-Covert Author

01/13/2019 Added

6170 Plays

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Tutorial clip demonstrating how to calculate expected F2 ratios and individuals in classes for a chi-square analysis.

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[00:00:00.200]Hello, this is Dr. Deana, and we're continuing on with our video clip series for the chi
[00:00:14.240]square analysis.
[00:00:15.240]In our earlier clip, we talked about taking a true breeding-resistant tomato plant that
[00:00:21.280]was resistant to bacterial spot disease, and we crossed it with a susceptible one.
[00:00:26.520]Our hypothesis is this was due to a single gene, and the gene was dominant.
[00:00:32.120]So in our F1, all of our genotypes are big R little r.
[00:00:36.880]We allowed that to self-pollinate, and so now we're looking at our F2 generation, and
[00:00:42.200]we have those growing, and we want to see if the numbers that we have observed fit with
[00:00:47.380]what we expected.
[00:00:49.300]So we were expecting a ratio of three resistant to one susceptible plant.
[00:00:54.500]Okay.
[00:00:55.500]So let's continue on.
[00:00:56.500]and fill out that table that you saw in your text.
[00:00:59.660]Okay.
[00:01:00.660]So the best way to do a chi-squared is make some sort of table like this [see text resource for setup]
[00:01:05.560]We're going to put in this first column our different classes that we're going to be looking
[00:01:09.680]at.
[00:01:10.680]So in our case, we're going to have resistant plants and also susceptible ones [writes them into their own rows]
[00:01:22.280]Okay.
[00:01:24.940]We know from the text that
[00:01:26.480]we observed when we went out and phenotyped them
[00:01:30.160]we saw that we had 141 of our F2 plants were resistant and 56 were susceptible.
[00:01:42.540][writes them into the table] Alright.
[00:01:45.280]So now what we have to do is plug in our numbers that we expected and when we did that calculation,
[00:01:53.000]we had expected 147 [writes into table]
[00:01:56.460]I'll go ahead and put the 147.75 in to be resistant [writes in table] and then for susceptible we expected 49.25 [writes into table].
[00:02:09.400]Now when people are first learning this chi-squared analysis, they sometimes want to put the ratios
[00:02:15.220]in here [the expected column], put like 3 resistant to 1 susceptible, but what you want to put is the actual number
[00:02:21.760]of individuals that you expect, not the ratios of them.
[00:02:25.540]And to double check your math
[00:02:26.440]if you add up your observed, 141 plus 56, that gives you 197, so you counted a total
[00:02:35.400]of 197 F2 plants, well you should also come up with 197 expected.
[00:02:42.960]So when you add your 147.75 plus the 49.25, you'll come up with 197.
[00:02:51.160]So that's a good way to double check your math and make sure you're correct at this
[00:02:55.420]point.
[00:02:56.420]Okay now the next step is we're going to take the number that we observed and subtract the
[00:03:01.480]number that we expected for each class.
[00:03:04.600]So for a resistant, we're going to come up with a minus 6.75 [writes it into the table]
[00:03:13.980]Okay and that's 141 that we observed minus 147.75 that we expected.
[00:03:22.580]So we end up with minus 6.75.
[00:03:25.260]Same thing with susceptible, take 56 minus 49.25.
[00:03:30.360]In this case, we're going to have a plus 6.75 [writes it into the table].
[00:03:33.960]OK, so we take observed minus expected.
[00:03:42.120]This is called the deviation.
[00:03:45.680]So you may be running across that word
[00:03:50.260]as you're reading in the literature
[00:03:52.780]or you're going through other classes.
[00:03:55.480]OK, so observed minus expected is the deviation.
[00:03:59.500]So now the next step is we take observed minus expected
[00:04:02.800]and square that.
[00:04:04.100]So we take minus 6.75 times minus 6.75,
[00:04:10.360]and that gives us 45.5625.
[00:04:19.320]OK, so this is a way that we
[00:04:20.260]get rid of our negative sign.
[00:04:21.960]So minus 6.75 times minus 6.75 gives us the 45.5625 [writes into resistant row].
[00:04:30.760]We take positive 6.75 times positive 6.75,
[00:04:36.120]and that also gives us 45.5625 [writes into susceptible row].
[00:04:42.100]OK, now for this last column, we're taking our observed minus
[00:04:45.640]expected squared number and divide it up by the expected.
[00:04:50.240]OK, so for this first column, we're going to take our 4.5625
[00:04:56.720]number, divide it by what was expected, which is 147.75.
[00:05:05.000]OK, so 45.5625 divided by 147.75, and that comes up with 0.3084 [for resistance row].
[00:05:18.720]OK, same thing for our susceptibility.
[00:05:20.220]We take our observed minus expected squared number, so our 45.5625.
[00:05:28.220]This time we're going to divide it by 49.25.
[00:05:32.520]Okay, so you work with the numbers within the class, and this gives us 0.9251 [for susceptible row]
[00:05:41.100]Okay, so 45.5625 divided by 49.25 gives us 0.9251.
[00:05:51.400]Now what we want to do is add up these two numbers then, this one [0.3084] and this one [0.9251].
[00:05:59.200]So if we add up 0.3084 plus 0.9251, that gives us 1.2335.
[00:06:09.440]And this number then is critical.
[00:06:11.080]This number would be known as our chi-squared value, okay?
[00:06:17.740]Or the sum of all of our chi-squares from our classes.
[00:06:21.400]In our next video clip then, we're gonna figure out what we do with this number.
[00:06:25.940]We'll actually be looking at a chi-squared distribution table.
[00:06:29.420]And then that gives us some kind of probabilities then that our data fits what we expected.
[00:06:41.060][music]
[00:06:41.560][music]
[00:06:43.620][music]

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Chi-square - Plugging in Numbers to Calculate Chi-square Values for F2 Phenotype Data

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