The bell-shaped curve: Normal distribution

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Understanding Clinical Research: Behind the Statistics

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University of Cape Town

Understanding Clinical Research: Behind the Statistics

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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

Building an intuitive understanding of statistical analysis

There is hardly any healthcare professional who is unfamiliar with the p-value. It is usually understood to have a watershed value of 0.05. If a research question is evaluated through the collection of data points and statistical analysis reveals a value less that 0.05, we accept this a proof that some significant difference was found, at least statistically.In reality things are a bit more complicated than that. The literature is currently full of questions about the ubiquitous p-vale and why it is not the panacea many of us have used it as. During this week you will develop an intuitive understanding of concept of a p-value. From there, I'll move on to the heart of probability theory, the Central Limit Theorem and data distribution.

Patterns in the data: Distributions2:52

The bell-shaped curve: Normal distribution3:37

Plotting a sample statistic: Sampling distribution7:08

Standard normal distribution: Z distribution9:52

Estimating population parameters: t-distribution3:11

(Optional) Generating random data point values using spreadsheet software6:22

Case study 217:29

Rencontrer les enseignants

Juan H Klopper
Dr
Department of Surgery

So lets start talking about distributions.

Distributions of data points for a variable in a population.

Now there are many, many, many different distribution types and

they are quite different for discreet data types and for continuous data types.

The one that we are going to be interested in, obviously is for

continuous data types.

That is the format in which the data types where most of the analysis that we do

in medical statistics come in is continuous data types and

most important of all of those is the normal distribution.

Now the normal distribution really is the most common type of random variable

distribution and it passes that there's some pattern to this distribution to

the actual data points such that there's a high frequency of certain values.

So certain actual values occur much more commonly than others.

The further away, the bigger the difference between an individual value and

those values that occur very commonly, the less common they become.

Now that means that there is some symmetry to this is you get

father away from both sides away from the mean, you get less and less common values.

This curve is a bell shape, usually referred to as being bell shaped and

that symmetry in the bell shape of the curve

allows us to come up with a rule of thumb that is called the empirical rule.

Now have a look at this.

Let me remind you just of the standard deviation.

Remember?

And we had a set of sample data points and we can plot them all on an x-axis and

we can also plot exactly where the mean is.

The standard deviation is the average distance of all of values and the mean.

So we just look at all the values.

The difference between that value and the mean, we sum all of them up and

divide it by how many there are, so a type of mean.

The mean or the average in distance away difference with the mean.

So look at the bell-shaped curve, a normal distribution at the bottom.

It says, the following if we include all values that are within one

standard deviation,

that's the average distance away average difference away from the mean.

If we included all values that are within one standard deviation away from the mean.

If the values are normally distributed, we'll get about 68% of all the values.

If we include all values that are within two standard variations away from

the mean, we're gonna include about 95%.

Now that's going to ring a bell with you, that should ring a bell with you.

If we were to include 95% of all values, that means we're left with five and

five on either side means 2.5 on either side,

0.025 on each side, 2.5% on each side.

So if we found a value that's further than two standard deviations away from

the mean, those were values would occur very infrequently.

We might be talking about values, there that are very significant to find and

that's exactly how we're going to look at Statistical tests.

It's the same principle.

Lastly, if we go about three standard deviations away from the mean,

we include all of those values, that would be about 99.7%.

So this is just a rule of thumb.

We can't use this rule when we do statistical analysis, but

we're going to work on this kind of premise.

I just want to remind, you might come across the standard normal distribution,

that is really where we have a mean of zero and

a standard deviation of exactly one.

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