The Digital Cell: Statistical tests

Statistical hypothesis testing, commonly referred to as “statistics”, is a topic of consternation among cell biologists.

This is a short practical guide I put together for my lab. Hopefully it will be useful to others. Note that statistical hypothesis testing is a huge topic and one post cannot hope to cover everything that you need to know.

What statistical test should I do?

To figure out what statistical test you need to do, look at the table below. But before that, you need to ask yourself a few things.

  • What are you comparing?
  • What is n?
  • What will the test tell you? What is your hypothesis?
  • What will the p value (or other summary statistic) mean?

If you are not sure about any of these things, whichever test you do is unlikely to tell you much.

The most important question is: what type of data do you have? This will help you pick the right test.

  • Measurement – most data you analyse in cell biology will be in this category. Examples are: number of spots per cell, mean GFP intensity per cell, diameter of nucleus, speed of cell migration…
    • Normally-distributed – this means it follows a “bell-shaped curve” otherwise called “Gaussian distribution”.
    • Not normally-distributed – data that doesn’t fit a normal distribution: skewed data, or better described by other types of curve.
  • Binomial – this is data where there are two possible outcomes. A good example here in cell biology would be a mitotic index measurement (the proportion of cells in mitosis). A cell is either in mitosis or it is not.
  • Other – maybe you have ranked or scored data. This is not very common in cell biology. A typical example here would be a scoring chart for a behavioural effect with agreed criteria (0 = normal, 5 = epileptic seizures). For a cell biology experiment, you might have a scoring system for a phenotype, e.g. fragmented Golgi (0 = is not fragmented, 5 = is totally dispersed). These arbitrary systems are a not a good idea. Especially, if the person scoring is unblinded to the experimental procedure. Try to come up with an unbiased measurement procedure.

 

What do you want to do? Measurement

(Normal)

Measurement

(not Normal)

Binomial

 

Describe one group Mean, SD Median, IQR Proportion
Compare one group to a value One-sample t-test Wilcoxon test Chi-square
Compare two unpaired groups Unpaired t-test Wilcoxon-Mann-Whitney two-sample rank test Fisher’s exact test

or Chi-square

Compare two paired groups Paired t-test Wilcoxon signed rank test McNemar’s test
Compare three or more unmatched groups One-way ANOVA Kruskal-Wallis test Chi-square test
Compare three or more matched groups Repeated-measures ANOVA Friedman test Cochran’s Q test
Quantify association between two variables Pearson correlation Spearman correlation
Predict value from another measured variable Simple linear regression Nonparametric regression Simple logistic regression
Predict value from several measured or binomial variables Multiple linear (or nonlinear) regression Multiple logistic regression

Modified from Table 37.1 (p. 298) in Intuitive Biostatistics by Harvey Motulsky, 1995 OUP.

What do “paired/unpaired” and “matched/unmatched” mean?

Most of the data you will get in cell biology is unpaired or unmatched. Individual cells are measured and you have say, 20 cells in the control group and 18 different cells in the test group. These are unpaired (or unmatched in the case of more than one test group) because the cells are different in each group. If you had the same cell in two (or more) groups, the data would be paired (or matched). An example of a paired dataset would be where you have 10 cells that you treat with a drug. You take a measurement from each of them before treatment and a measurement after. So you have paired measurements: one for cell A before treatment, one after; one for cell B before and after, and so on.

How to do some of these tests in IgorPRO

The examples below assume that you have values in waves called data0, data1, data2,… substitute the wavenames for your actual wave names.

Is it normally distributed?

The simplest way is to plot them and see. You can plot out your data using Analysis>Histogram… or Analysis>Packages>Percentiles and BoxPlot… Another possibility is to look at skewness or kurtosis of the dataset (you can do this with WaveStats, see below)

However, if you only have a small number of measurements, or you want to be sure, you can do a test. There are several tests you can do (Kolmogorov-Smirnoff, Jarque-Bera, Shapiro-Wilk). The easiest to do and most intuitive (in Igor) is Shapiro-Wilk.


StatsShapiroWilkTest data0

If p < 0.05 then the data are not normally distributed. Statistical tests on normally distributed data are called parametric, while those on non-normally distributed data are non-parametric.

Describe one group

To get the mean and SD (and lots of other statistics from your data):


Wavestats data0

To get the median and IQR:


StatsQuantiles/ALL data0

The mean and sd are also stored as variables (V_avg, V_sdev). StatsQuantiles calculates V_median, V_Q25, V_Q75, V_IQR, etc. Note that you can just get the median by typing Print StatsMedian(data0) or – in Igor7 – Print median(data0). There is often more than one way to do something in Igor.

Compare one group to a value

It is unlikely that you will need to do this. In cell biology, most of the time we do not have hypothetical values for comparison, we have experimental values from appropriate controls. If you need to do this:


StatsTTest/CI/T=1 data0

Compare two unpaired groups

Use this for normally distributed data where you have test versus control, with no other groups. For paired data, use the additional flag /PAIR.


StatsTTest/CI/T=1 data0,data1

For the non-parametric equivalent, if n is large computation takes a long time. Use additional flag /APRX=2. If the data are paired, use the additional flag /WSRT.


StatsWilcoxonRankTest/T=1/TAIL=4 data0,data1

For binomial data, your waves will have 2 points. Where point 0 corresponds to one outcome and point 1, the other. Note that you can compare to expected values here, for example a genetic cross experiment can be compared to expected Mendelian frequencies. To do Fisher’s exact test, you need a 2D wave representing a contingency table. McNemar’s test for paired binomial data is not available in Igor

StatsChiTest/S/T=1 data0,data1

If you have more than two groups, do not do multiple versions of these tests, use the correct method from the table.

Compare three or more unmatched groups

For normally-distributed data, you need to do a 1-way ANOVA followed by a post-hoc test. The ANOVA will tell you if there are any differences among the groups and if it is possible to investigate further with a post-hoc test. You can discern which groups are different using a post-hoc test. There are several tests available, e.g. Dunnet’s is useful where you have one control value and a bunch of test conditions. We tend to use Tukey’s post-hoc comparison (the /NK flag also does Newman-Keuls test).


StatsAnova1Test/T=1/Q/W/BF data0,data1,data2,data3
StatsTukeyTest/T=1/Q/NK data0,data1,data2,data3

The non-parametric equivalent is Kruskal-Wallis followed by a multiple comparison test. Dunn-Holland-Wolfe method is used.


StatsKSTest/T=1/Q data0,data1,data2,data3
StatsNPMCTest/T=1/DHW/Q data0,data1,data2,data3

Compare three or more matched groups

It’s unlikely that this kind of data will be obtained in a typical cell biology experiment.

StatsANOVA2RMTest/T=1 data0,data1,data2,data3

There are also operations for StatsFriedmanTest and StatsCochranTest.

Correlation

Straightforward command for two waves or one 2D wave. Waves (or columns) must be of the same length


StatsCorrelation data0

At this point, you probably want to plot out the data and use Igor’s fitting functions. The best way to get started is with the example experiment, or just display your data and Analysis>Curve Fitting…

Hazard and survival data

In the lab we have, in the past, done survival/hazard analysis. This is a bit more complex and we used SPSS and would do so again as Igor does not provide these functions.

Notes for use

Screen Shot 2016-07-12 at 14.18.18The good news is that all of this is a lot more intuitive in Igor 7! There is a new Menu item called Statistics, where most of these functions have a dialog with more information. In Igor 6.3 you are stuck with the command line. Igor 7 will be out soon (July 2016).

  • Note that there are further options to most of these commands, if you need to see them
    • check the manual or Igor Help
    • or type ShowHelpTopic “StatsMedian” in the Command Window (put whatever command you want help with between the quotes).
  • Extra options are specified by “flags”, these are things like “/Q” that come after the command. For example, /Q means “quiet” i.e. don’t print the output into the history window.
  • You should always either print the results to the history or put them into a table so that we can check them. Note that the table gets over written if you do the same test with different data, so printing in this case is a good idea.
  • The defaults in Igor are setup OK for our needs. For example, Igor does two-tailed comparison, alpha = 0.05, Welch’s correction, etc.
  • Most operations can handle waves of different length (or have flags set to handle this case).
  • If you are used to doing statistical tests in Excel, you might be wondering about tails and equal variances. The flags are set in the examples to do two-tailed analysis and unequal variances are handled by Welch’s correction.
  • There’s a school of thought that says that using non-parametric tests is best to be cautious. These tests are not as powerful and so it is best to use parametric tests (t test, ANOVA) when you can.

Part of a series on the future of cell biology in quantitative terms.

The Digital Cell: Getting started with IgorPRO

This post follows on from “Getting Started“.

In the lab we use IgorPRO for pretty much everything. We have many analysis routines that run in Igor, we have scripts for processing microscope metadata etc, and we use it for generating all figures for our papers. Even so, people in the lab engage with it to varying extents. The main battle is that the use of Excel is pretty ubiquitous.

I am currently working on getting more people in the lab started with using Igor. I’ve found that everyone is keen to learn. The approach so far has been workshops to go through the basics. This post accompanies the first workshop, which is coupled to the first few pages of the Manual. If you’re interested in using Igor read on… otherwise you can skip to the part where I explain why I don’t want people in the lab to use Excel.

IgorPro is very powerful and the learning curve is steep, but the investment is worth it.

WaveMetrics_IGOR_Pro_LogoThese are some of the things that Igor can do: Publication-quality graphics, High-speed data display, Ability to handle large data sets, Curve-fitting, Fourier transforms, smoothing, statistics, and other data analysis, Waveform arithmetic, Matrix math, Image display and processing, Combination graphical and command-line user interface, Automation and data processing via a built-in programming environment, Extensibility through modules written in the C and C++ languages. You can even play games in it!

The basics

The first thing to learn is about the objects in the Igor environment and how they work.There are four basic objects that all Igor users will encounter straight away.

  • Waves
  • Graphs
  • Tables
  • Layouts

All data is stored as waveforms (or waves for short). Waves can be displayed in graphs or tables. Graphs and tables can be placed in a Layout. This is basically how you make a figure.

The next things to check out are the command window (which displays the history), the data browser and the procedure window.

Essential IgorPro

  • Tables are not spreadsheets! Most important thing to understand. Tables are just a way of displaying a wave. They may look like a spreadsheet, but they are not.
  • Igor is case insensitive.
  • Spaces. Igor can handle spaces in names of objects, but IMO are best avoided.
  • Igor is 0-based not 1-based
  • Logical naming and logical thought – beginners struggle with this and it’s difficult to get this right when you are working on a project, but consistent naming of objects makes life easier.
  • Programming versus not programming – you can get a long way without programming but at some point it will be necessary and it will save you a lot of time.

Pretty soon, you will go beyond the four basic objects and encounter other things. These include: Numeric and string variables, Data folders, Notebooks, Control panels, 3D plots – a.k.a. gizmo, Procedures.

Getting started guide
Getting started guide

Why don’t we use Excel?

  • Excel can’t make high quality graphics for publication.
    • We do that in Igor.
    • So any effort in Excel is a waste of time.
  • Excel is error-prone.
    • Too easy for mistakes to be introduced.
    • Not auditable. Tough/impossible to find mistakes.
    • Igor has a history window that allows us to see what has happened.
  • Most people don’t know how to use it properly.
  • Not good for biological data – Transcription factor Oct4 gets converted to a date.
  • Limited to 1048576 rows and 16384 columns.
  • Related: useful link describing some spreadsheet crimes of data entry.

But we do use Excel a lot

  • Excel is useful for quick calculations and for preparing simple charts to show at lab meeting.
  • Same way that Powerpoint is OK to do rough figures for lab meeting.
  • But neither are publication-quality.
  • We do use Excel for Tracking Tables, Databases(!) etc.

The transition is tough, but worth it

Writing formulae in Excel is straightforward, and the first thing you will find is that to achieve the same thing in Igor is more complicated. For example, working out the mean for each row in an array (a1:y20) in Excel would mean typing =AVERAGE(A1:y1) in cell z1 and copying this cell down to z20. Done. In Igor there are several ways to do this, which itself can be unnerving. One way is to use the Waves Average panel. You need to know how this works to get it to do what you want.

But before you turn back, thinking I’ll just do this in Excel and then import it… imagine you now want to subtract a baseline value from the data, scale it and then average. Imagine that your data are sampled at different intervals. How would you do that? Dealing with those simple cases in Excel is difficult-to-impossible. In Igor, it’s straightforward.

Resources for learning more Igor:

  • Igor Help – fantastic resource containing the manual and more. Access via Help or by typing ShowHelpTopic “thing I want to search for”.
  • Igor Manual – This PDF is available online or in Applications/Igor Pro/Manual. This used to be a distributed as a hard copy… it is now ~3000 pages.
  • Guided Tour of IgorPro – this is a great way to start and will form the basis of the workshops.
  • Demos – Igor comes packed with Demos for most things from simple to advanced applications.
  • IgorExchange – Lots of code snippets and a forum to ask for advice or search for past answers.
  • Igor Tips – I’ve honestly never used these, you can turn on tips in Igor which reveal help on mouse over.
  • Igor mailing list – topics discussed here are pretty advanced.
  • Introduction to IgorPRO from Payam Minoofar is good. A faster start to learning to program that reading the manual.
  • Hands-on experience!

Part of a series on the future of cell biology in quantitative terms.

Everything In Its Right Place

Something that has driven me nuts for a while is the bug in FIJI/ImageJ when making montages of image stacks. This post is about a solution to this problem.

What’s a montage?

You have a stack of images and you want to array them in m rows by n columns. This is useful for showing a gallery of each frame in a movie or to separate the channels in a multichannel image.

What’s the bug/feature in ImageJ?

If you select Image>Stacks>Make Montage… you can specify how you want to layout your montage. You can specify a “border” for this. Let’s say we have a stack of 12 images that are 300 x 300 pixels. Let’s arrange them into 3 rows and 4 columns with 0 border.

Screen Shot 2016-07-06 at 14.21.53So far so good. We have an image that is 1200 x 900. But it looks a bit rubbish, we need some grouting (white pixel space between the images). We don’t need a border, but let’s ignore that for the moment. So the only way to do this in ImageJ is to specify a border of 8 pixels.

Screen Shot 2016-07-06 at 14.22.27Looks a lot better. Ok there’s a border around the outside, which is no use, but it looks good. But wait a minute! Check out the size of the image (1204 x 904). This is only 4 pixels bigger in x and y, yet we added all that grouting, what’s going on?

The montage is not pixel perfect.

Screen Shot 2016-07-06 at 14.23.38

So the first image is not 300 x 300 any more. It is 288 x 288. Hmmm, maybe we can live with losing some data… but what’s this?

Screen Shot 2016-07-06 at 14.24.49

The next image in the row is not even square! It’s 292 x 288. How much this annoys you will depend on how much you like things being correct… The way I see it, this is science, if we don’t look after the details, who will? If I start with 300 x 300 images, it’s not too much to ask to end up with 300 x 300 images, is it? I needed to fix this.

Solutions

I searched for a while for a solution. It had clearly bothered other people in the past, but I guess people just found their own workaround.

ImageJ solution for multichannel array

So for a multichannel image, where the grayscale images are arrayed next to the merge, I wrote something in ImageJ to handle this. These macros are available here. There is a macro for doing the separation and arraying. Then there is a macro to combine these into a bigger figure.

Igor solution

For the exact case described above, where large stacks need to be tiled out into and m x n array, I have to admit I struggled to write something for ImageJ and instead wrote something for IgorPRO. Specifying 3 rows, 4 columns and a grout of 8 pixels gives the correct TIFF 1224 x 916, with each frame showing in full and square. The code is available here, it works for 8 bit greyscale and RGB images.

Screen Shot 2016-07-06 at 14.55.31

I might update the code at some point to make sure it can handle all data types and to allow labelling and adding of a scale bar etc.

The post title is taken from “Everything In Its Right Place” by Radiohead from album Kid A.