Chi-square - Determining Probability Values

Deana Namuth-Covert Author

01/13/2019 Added

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Video tutorial showing how to read a chi-square distribution table to determine probability values that experimental data supports a tomato breeding hypothesis.

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[00:00:00.260]Hi, this is Dr. Deana.
[00:00:09.300]In this video clip, we'll be taking our chi-squared value that we calculated in the previous
[00:00:14.840]clip and looking at how we interpret that number.
[00:00:18.460]Does it support our hypothesis or should we reject it?
[00:00:22.560]So did we see differences in data which were too great, so we should reject our hypothesis?
[00:00:29.280]Or can we accept it?
[00:00:31.240]So in our case that we're looking at with our tomato breeding experiment, we had calculated
[00:00:36.880]a chi-score value of 1.2335.
[00:00:40.880]So what do we do with that number?
[00:00:42.280]We consult a chi-score distribution table, such as one like this.
[00:00:47.880]So we'll see here on the left, this first column, there's a category called degrees
[00:00:53.260]of freedom.
[00:00:55.520]Now what degrees of freedom are, there's a simple formula.
[00:00:59.060]It's just the number of classes in your experiment minus one.
[00:01:04.600]Alright, so let's look at our particular example, and we have two different classes.
[00:01:11.940]We have resistant tomato plants, and we have tomato plants which are susceptible to bacterial
[00:01:17.780]spot disease.
[00:01:19.640]So our degrees of freedom is n minus one, so in our case it would be two minus one.
[00:01:28.840]Which is one.
[00:01:32.980]So in our case we have one degree of freedom.
[00:01:35.640]Now let's go back to our chi-square table.
[00:01:40.400]Here let's write down our numbers which are key.
[00:01:44.080]So we have one degree of freedom, and our chi-square is 1.2335.
[00:01:53.780]Okay, so the first thing you do is go to the degrees of freedom
[00:01:58.620]column, and read down until you find your degrees of freedom for
[00:02:03.700]your particular experiment.
[00:02:05.980]So we don't have to go far, we just go to one.
[00:02:08.100]And then you're gonna read over to the right until you find your chi-square
[00:02:13.300]value, or where it would fall.
[00:02:15.100]So I'm looking for 1.2335.
[00:02:18.880]All right, it's a little bit bigger than .455, but it's less than 1.32.
[00:02:24.360]So it would fall somewhere here [scribbles between the .455 and 1.32 values].
[00:02:26.020]And then what you do is you read up
[00:02:28.400]to this other set of numbers [at the top of the table], and these set of numbers are the probability values.
[00:02:36.580]Okay, so you may see it as p equals something.
[00:02:40.440]So it is the probability.
[00:02:41.760]Okay, so what does that mean?
[00:02:44.680]What that means is if we were to repeat our experiment,
[00:02:47.940]what's the probability that we would see a larger chi-squared value?
[00:02:54.120]And remember, if you have a larger chi-squared, that means your data from
[00:02:58.180]your experiment deviated even further from what you expected
[00:03:02.080]than your current experiment, okay so what's the probability that if we were to repeat
[00:03:06.800]our experiment that we would get even greater deviations and yet be able to still accept
[00:03:11.800]our hypothesis?
[00:03:13.680]So in our case we're going to have a probability value that is greater than 0.25 but it's less
[00:03:26.200]than 0.5 by consulting this chart.
[00:03:32.780]So somewhere between 25 and 50 percent of the time if we were to repeat the experiment
[00:03:37.960]we would see data similar to what we had in this particular experiment or even deviating
[00:03:43.180]greater from what we expected and still we'd be able to accept our hypothesis.
[00:03:48.920]So what is the cutoff value?
[00:03:51.440]Well it turns out scientists have determined that this [circles 0.05] is
[00:03:56.100]the cutoff value.
[00:03:56.100]It's a critical value in most cases.
[00:03:59.700]So they're willing to accept a .05 value, meaning that 5% of the time if they were to
[00:04:05.980]repeat their experiment they would have greater deviations than what they saw and still the
[00:04:11.500]hypothesis would be correct.
[00:04:14.120]So sometimes that's a little bit hard to understand, but for our purposes just know .05 is our
[00:04:20.480]critical value.
[00:04:22.140]So if you have a chi-squared that falls to the right on this
[00:04:26.000]table [p-value is less than 0.05], what you're going to do is reject your hypothesis.
[00:04:31.400]You're going to go back and determine, you know, maybe there's some other kind of genetic
[00:04:36.440]inheritance pattern that's going on, for one example.
[00:04:41.200]So any chi-squared values that fall to the left of this .05 probability value [they are greater than .05], then we
[00:04:48.060]can accept our hypothesis and we know then that our data from our experiment actually
[00:04:55.900]supports what we were hypothesizing.
[00:05:00.360]Now it's important that students sometimes think that this proves your hypothesis is
[00:05:04.120]true, but it doesn't, it just gives you the probability that your data supports it.
[00:05:09.080]And the only way you can really prove an idea is to do repeated experiments and some real
[00:05:13.920]thorough investigation.
[00:05:16.100]So just make sure you know that chi-square doesn't prove anything is true, but it does
[00:05:21.720]give you a probability value that your data actually supports your hypothesis.
[00:05:25.800]Alright, so this is how you can solve a chi-square distribution table and being able to interpret
[00:05:32.940]your chi-squared calculation results and it will help you know what the significance is
[00:05:38.260]of your data.
[00:05:39.680]Are any differences that you saw statistically significant so that you should reject your
[00:05:45.240]hypothesis so they fall to this side of the chart [p-value less than 0.05]?
[00:05:48.880]Or does your data support your hypothesis?
[00:05:51.920]So that would be over here on the left side [p-value greater than 0.05].
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Chi-square - Determining Probability Values

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