Now, if I were to use a parametric test, in the instances of numerical data, and my sample data did not come from a population at a normal distribution for that variable. Then I am going to get erroneous p values. You're able to calculate those p values, but they might be wrong. There might be some error in it. It might not reflect the true difference in groups that do exist. And that makes non-parametric tests very very useful. There is a little price to pay for that. A non-parametric test are slightly less slightly to pick up small differences between groups that might be statistically significant. It's going to miss just that little fine edge, but really not a lot. And then, many cases much safer to use non-parametric tests, and then, in some cases absolutely necessity to use non-parametric tests. Use parametric test under those circumstances you are not going to tell the truth and then the full picture of the research that is being done. Now, the question is, if you have numerical data, how do you know what is can you do to make sure that sample data comes from a population parameter that is normally distributed? Now, there's some non-fancy ways and there's some fancy ways and there's very fancy ways. All of them though, are very subtle. It's in the end irrespective of the analysis that you do, it is a judgment call, there's a bit of judgment in that when to decide that something is parametric or from a normal distribution or not. Now the first place is to take your sample later for each group, the white cell count for one group, the white cell count for the other group, and just make a histogram plot then. There you see a histogram superimposed, the fine line there your kernel density estimate, and you can see there's quite a bit of skewness there. Now this is just a sample data, this is not a population data out there, billions of data points. It's just our sample data. If you just do a histogram of it and you see there is quite a bit of skewness. Now this is a right tail, it tails off to the right, to the positive side and you see the skewness for this particular graph as 1.82, positive 1.82. There's quite a bit of skewness there. And you'll have to be circumspect to use a parametric test if one of your group at least looks like this. The other more visual way of doing it is what is called a q-q plot. There you see an example of a q-q plot and I'll explain what's going on there. The q stands for a quantile. Just to explicitly tell you what a quantile is. On this kind of plot is you take any value and you plot the percentage of values that are less than that in the data set. So it's value versus its quantile. The quantile is the percentage of values in the whole set that is less than that. And those are all the blue dots. The red line, we asked the computer there to draw that red line, and that is the line of a normal distribution. So all the blue dots that fall on that red line would be part of a normal distribution. And you can clearly see our data points which are represented by those small little blue dots, they didn't follow that red line at all. So we can clearly say, and this is the data from the previous histogram that I showed you. Clearly, that sample, we can say, we can all visually decide there that that sample data is not taken from population parameter that is normally distributed. Look at this. Here we have some sample data for a group and you can clearly see the histogram there with a superimposed kernel density estimate that it looks beautifully symmetrically distributed. And we see a skewness of only -0.01 there. So that's a normal distribution. And look at the Q-Q plot there. There we can see when our data points follow that red line visually. We can see, we make the judgment call that sample data they came from a population variable that has a normal distribution, and so k in this instance to use a parametric test like a t test. Remember all of the groups will have to have that kind of distribution. So this q-q plot actually, as a visual way, it works very well. Now [COUGH] really in the first example we didn't follow that grid line, the q-q plot. It would be really wrong to use that kind of parametric test, and for this specific reason when to use what test, it would be lovely if all data was open access data. If we could have access to all the data from all the journal articles that we've viewed. And I think that's something very important to strive towards, to have open access data so that we can make a call as to whether the correct test was used in any kind of analysis in the general literature out there. In the next section we'll do a bit of a deeper discussion into how to start looking at non-parametric tests.