A beginner's guide to statistics for PhD research

By James Hayton,
August 16, 2013
I'm James, I'm a former physicist (PhD, Nottingham, 2007) and author of "PhD: An Uncommon Guide to Research, Writing & PhD Life".
Since 2010, I've been helping PhD students all over the world overcome barriers in their research and writing
My strategies have helped thousands of PhD students just like you to build confidence, write better and finish on time

Statistics can be invaluable for adding a level of rigour to your analysis, but they can be extremely technical and difficult for non-specialists.

This is not by any means a comprehensive guide, but I will try to give some basic working principles to help reduce the pain and avoid the most common mistakes.

Plot your data

Before doing statistical analysis, wherever possible create a visual representation of your data.

This will give you a much better intuitive understanding of what is going on.For example, if you have survey data using a Likert scale, where answers to questions are given as;

  1. Strongly disagree
  2. Disagree
  3. Neither agree nor disagree
  4. Agree
  5. Strongly agree

You may want to see how the answers to a specific question are distributed across all respondents. You can do this by plotting a histogram showing the number of responses at each point in the scale. Here are 3 examples of possible distributions:

likert histogram 1

likert histogram 2

likert histogram 3

Without doing any statistics, you can instantly see how the data is distributed, and you can use this as a basis for your analysis

What does the mean mean?

If you take the means of each of the three distributions above, you will get values of 3.7, 3 and 2.8.

But what do these values mean? In the top histogram, 3.7 clearly correlates to the peak at 4. In the second, the distribution is flat, so the mean just represents the middle of the range, and in the third, the mean is the least selected option.It is up to you to then interpret what the mean means, but you can only do that when you can see the distribution of the data.

Standard deviation

The standard deviation is a measure of the spread of data around the mean. It is widely used, but you need to be careful. If you use the standard deviation without plotting your data, then you can end up with a meaningless number.

Standard deviation is best used when you have something approximating a normal distribution of data (the classic "bell curve" below)

from http://en.wikipedia.org/wiki/File:Standard_deviation_diagram.svg

When you say the standard deviation = x, this indicates that about 68% of the data lies within ± x of the mean.

But what if you have a graph with 2 peaks? Then the standard deviation becomes meaningless, even though a statistical program will still give you an answer.

from http://en.wikipedia.org/wiki/File:Bimodal.png

Don't include numbers you don't understand

When you use statistical analysis software, it will spit out countless different results, some will be useful, some not.

Do not include in any report or table of results numbers you don't understand. Imagine an examiner asking, "what do these numbers mean?" and if you can't answer, either find out or don't include them.

How many decimal places?

Another potential hazard is that stats software will often give you numbers to many decimal places.

For example, let's say you measure the height of every adult human being on earth and look for the mean. With several billion data points, your calculation of the mean might look something like 1.68234597864422 m (I just made this number up as an example). If you copy and paste this number, you are effectively claiming that you can measure the height of a human being to an accuracy of  0.00000000000002 m, which is much smaller than the radius of an atom.

Much better to give the value as 1.68 or 1.682, since this reflects the accuracy with which you can make a single measurement.

Quoting errors

The same is true when giving an estimate of the error on a measurement. Giving an error of ± 2.336598774654654 is ridiculous! You can't be that precise in an error estimate! Stick to one (or two at the most) significant figures.

Do analysis at a small scale early in your research

If you have 1 month left to submit your thesis, and you are doing analysis for the first time, it's going to be difficult.

So do some analysis early, on a small scale, so you have some experience before you do the full analysis. You will be able to take your time, while the pressure is still low. Most mistakes happen when doing things in a rush at the last minute, especially if you have never done that type of analysis before.

If you know what methodology you are going to use, do a small trial run and analyse the data you get. Not only will this help you refine your methodology, but it will make the final analysis much, much easier.

Any questions?

I am not an expert in statistics, and cannot answer questions on specific analytical techniques or software, but am happy to answer questions on these basics.If any statisticians want to contribute, you are more than welcome!

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