This video explains what a p-value is and how to determine if one is statistically significant using both alpha = .05 and .01.
Video Transcript: In this video we'll take a look at how to interpret a p-value. So what is a p-value? P-value stands for probability value; it indicates how likely it is that a result occurred by chance alone. If the p-value is small, it indicates the result was unlikely to have occurred by chance alone. These results are known as being statistically significant. A small p-value means that it's greater than chance alone, something happened; the test is significant. Whereas a large p-value indicates that the result is within chance or normal sampling error, or in other words nothing happened, the test is not significant. And p values range from 0 to 1. Let's go ahead and take a look at some p-values of popular computer output. So here's SPSS and the p-value is given where it says Sig. (2-tailed) and it's very small in this example at .002. Now we'll formalize this in a minute, but for now, that's beyond chance, it's quite small, so we would say that the result is statistically significant. Taking a look at another example, here we see a p-value, reported as Sig. once again in SPSS, as .268. Now that's not really that small, so that's within normal sampling error we would say, or it's not beyond chance. So the result is not statistically significant. Now to formalize this, we want to look at what is known as alpha. And when we interpret whether a p-value is significant, that is beyond chance or not, we need to know the level of alpha being used for the test. The two most common levels are .05 for alpha, or .01.Alpha is decided beforehand by the researcher or analyst. So if we use an alpha of .05, the following rule applies: If p or Sig., as you saw in our output, is less than alpha or less than .05 in this case, the test is significant. Whereas if p or Sig. is greater than .05, the test is not significant. So, as an example, if we had a p-value or a Sig. of .03, using the rule up above, with an alpha of .05, would the test be significant or not? Well the test would be significant, right, because .03 is less than .05. Let's go ahead and take a look at another example. So if we have a p of .12 now with alpha .05, try and assess whether or not that test would be significant. It would not be significant because .12 is greater than .05, so it's not significant, or it's not beyond sampling error. And here's a table of some different outcomes, so looking at this first row, if we had a p of .04, and we use alpha .05 in all decisions, this is less than .05 so we would say it's significant. Our second value, .075, that's greater than .05 right, so we would say that's not significant. .049, that's very close, but it is less than .05, so that would be significant. And then .523, that's definitely greater than .05, so it's not significant. And then finally, .001, definitely less than .05, so this result is significant. Now if we look at alpha of .01 we use really the same decision rule, if p is less than alpha, this time alpha's .01 though, the test is significant. Whereas if p is greater than alpha, the test is not significant. So if we have an example here with a p of .04, using an alpha of .01, we would see that the test is not significant, because .04 is greater than .01. If we had an example of .003, we would see that it is significant in this case, because .003 is less than .01. So let's go and take a look at some examples as well with alpha .01. So here we have a p of .001, that's definitely less than alpha of .01, so it's significant. .02, it's close, but it's greater than .01, so it's not significant. .009, once again, quite close, but less than alpha of .01, so it's significant. .523 is greater than .01, so it's not significant. And then finally, .012, close once again, but it is greater than .01, so it's not significant. OK let's look at a p-value again in SPSS. So now we have a p of .002, and it's very small, let's assess this for significance using alpha .05. So because .002 is less than .05, the test is significant at alpha .05. Now before we close ask yourself would it have been significant if alpha .01 was used. Well since .002 is less than .01, the test would be significant if an alpha .01 was used as well.