Checking for normality

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En provenance du cours de University of Cape Town

Understanding Clinical Research: Behind the Statistics

723 notes

University of Cape Town

Understanding Clinical Research: Behind the Statistics

723 notes

If you’ve ever skipped over`the results section of a medical paper because terms like “confidence interval” or “p-value” go over your head, then you’re in the right place. You may be a clinical practitioner reading research articles to keep up-to-date with developments in your field or a medical student wondering how to approach your own research. Greater confidence in understanding statistical analysis and the results can benefit both working professionals and those undertaking research themselves. If you are simply interested in properly understanding the published literature or if you are embarking on conducting your own research, this course is your first step. It offers an easy entry into interpreting common statistical concepts without getting into nitty-gritty mathematical formulae. To be able to interpret and understand these concepts is the best way to start your journey into the world of clinical literature. That’s where this course comes in - so let’s get started! The course is free to enroll and take. You will be offered the option of purchasing a certificate of completion which you become eligible for, if you successfully complete the course requirements. This can be an excellent way of staying motivated! Financial Aid is also available.

À partir de la leçon

Which test should you use?

The most common statistical test that you might come across in the literature is the t-test. There are, in actual fact, a few t-tests, but the one most are familiar with, is of course, Student’s t-test and its ubiquitous p-value. Not everyone, though, knows that the name Student was actually a pseudonym, used by William Gosset (1876 - 1937). Parametric tests have very strict assumptions that must be met before their use is justified. In this lesson we take a closer look at these tests, but perhaps more importantly, their strict assumptions. Once you know these, you will be able to identify when these tests are used inappropriately.

Introduction to nonparametric tests3:18

Checking for normality5:07

Thinking nonparametrically2:27

Comparing paired observations: Signs2:42

Ordering values: Ranking2:33

Paired comparisons: Sign ranks2:22

Summation of ranks: Rank sums6:04

Comparing two populations: Mann-Whitney-U test4:07

More nonparametric tests5:09

Case study 313:40

Rencontrer les enseignants

Juan H Klopper
Dr
Department of Surgery

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.

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