What's New in PRIMER 8

PRIMER 8 with PERMANOVA+ is a substantial upgrade on its predecessor, offering a host of marvelou...

Most of the methods in the list below are unique to PRIMER 8 and are not available in any other s...

New default colour palette - The new colour palette for PRIMER graphics ensures distinctive col...

Summary statistics provide essential information to help you get to know your variables, their fu...

Given a set of values $\{ y_1, y_2, ..., y_n \}$ for any individual variable $Y$, the following s...

To show the utility of this tool, we will calculate some summary statistics from a study examinin...

To run summary statistics on your variables separately for multiple groups of data, just choose a...

For environmental data, we might choose to calculate different sorts of summary statistics than t...

Overview What is an empirical distribution? The empirical distribution of a variable is able to b...

To demonstrate the empirical distribution tool in PRIMER, we shall examine a dataset consisting o...

Suppose we have measured a given variable in each of several groups. To visualise the distributio...

Let's re-visit the data on oyster sizes (,). We have already seen some variation in the cumulativ...

studied organisms colonising holdfasts of the kelp, Ecklonia radiata, sampled from four differen...

Overview The Wilcoxon signed-rank test was described by . It is designed for the situation where ...

An example of a paired design with two groups is provided by , who described a study by to inves...

Overview The Mann-Whitney U test was described by and . Here, interest lies in comparing two gro...

As an example of the Mann-Whitney U test, we will look at a dataset consisting of counts of the s...

Overview The Kruskal-Wallis test was described by and . Its purpose is to compare two or more in...

We will use the Kruskal-Wallis test to compare counts of a bivalve species, Abra prismatica, occu...

Overview The Kolmogorov-Smirnov test is a non-parametric test for comparing two distributions of ...

To demonstrate the Kolmogorov-Smirnov test in PRIMER, we shall return to the dataset consisting o...

Overview PRIMER 8 offers several options to achieve a non-parametric bivariate test of associatio...

To demonstrate the test of association, we shall re-visit a dataset of macrofauna assemblages col...

It is instructive to consider some additional examples of the test of association where the varia...

Re-vamped interface To run a PERMANOVA in PRIMER 8, there are two essential steps. From a resembl...

An important assumption of classical analysis of variance (ANOVA) is that the errors come from a ...

The one-way ANOVA model In one-way univariate analysis of variance (ANOVA), interest lies in comp...

Overview The Behrens-Fisher problem (BFP) is one of the oldest puzzles in statistics (; ; ). The ...

Overview In a multivariate context, there are many ways that groups of sampling units can differ ...

Overview described a general dissimilarity-based solution to the multivariate Behrens-Fisher pro...

Let's look now at an example where there is a single factor in the study design, the number of re...

Handling heterogeneity with multiple factors The most important question to answer when you are d...

We shall look at the diets of $N$ = 346 juvenile steelhead / rainbow trout (Oncorhynchus mykiss) ...

ANOVA is one of the most widely used statistical techniques, providing a partitioning of the meas...

Consider the classical one-way linear ANOVA model, as described in section 6.2 above. Specificall...

What is meant by a 'finite' factor? Suppose, for any factor, there are a total of $A$ levels in t...

The study design We consider here a study examining effects of a sewage outfall for $p$ = 151 mol...

Comparison of results treating 'Locations' as random Historical wisdom for such a design would ha...

In some cases, experiments are done in a way that lacks replication, often at the smallest spatia...

The study design An example of a split-plot design is provided by a study of the effect of fire d...

The study design An example of a repeated-measures sampling design (Fig. 8.5) is provided in a st...

There are situations where it may be useful or important to include one or more quantitative co-v...

Natural cycles in biology and ecology Important situations where the treatment of multiple covari...

Consider the study described by consisting of regular surveys of macroalgal cover from a rocky i...

Rationale When considering the response of a whole set of variables (such as the abundances of sp...

What is a 'main effects plot'? In a main effects plot, we calculate and then show in an ordinatio...

What is an 'interaction plot'? Although main effects plots can help us to visualise the main effe...

To further demonstrate the utility of main effects plots and interactions for multi-way study des...

Rationale It is sometimes desirable to remove the effects of a factor or covariable, and examine ...

We shall show the utility of being able to construct a residual distance matrix and, from this, a...

Rationale Suppose you have multivariate data (e.g., abundances of multiple species) sampled repea...

A classical univariate control chart arises in the context of process control for industrial and ...

A suitable criterion for a control chart designed to detect shifts in the population mean vector ...

To demonstrate the use of Hotelling's $T^2$ in a multivariate control-chart setting, it is useful...

Essential steps Suppose we have an $(N \times p)$ data matrix, $\bm{Y}$, and we can capture the i...

We offer here a few additional notes regarding the implementation of control charts in real appli...

We shall implement a control chart on data from the North American Breeding Bird Survey (BBS) ()....

PRIMER 8 offers a host of new options for standardising data (either samples or variables), via t...

Rationale Suppose we have data where the variables consist of different size classes of mussels (...

To implement the new standardisation routine in PRIMER 8 and (simultaneously) demonstrate the uti...

There are many situations where the standardisation of samples is required as a pre-treatment pri...

There is a new tool in PRIMER 8 that permits the end-user to create a set of ordered groups, base...

To demonstrate the creation and use of ordered groups from a continuous variable, we will look at...

Accessibility It is important to make graphics accessible to those with color vision deficiencies...

In PRIMER 8, the options available for selecting samples or selecting variables have been expande...

There are many situations where it would be very handy to be able to change the names of levels o...

In PRIMER 8, there is a new tool that allows us to add customised values and labels to coordinate...

In PRIMER 8 there is a new tool, accessed by clicking Tools > Split Data..., which allows you to ...

There is a new facility in PRIMER 8 to create Line plots in two different ways: with one line fo...

In PRIMER 8, you can now output more detailed statistical information from either dispersion-weig...

In PRIMER 8, it is now possible to output diagnostic plots from the CAP routine (i.e., canonical ...

Background Consider a cloud of $N$ points (sampling units) in a $p$-dimensional multivariate spac...

Overview A plot of the means (or averages) for groups of samples, with error bars capturing some ...

Let's look at an example of a means plot for a one-way case using biotic data ($p$ = 131 taxa) fr...

Let's look at a means plot where we have a two-way nested design. We will examine data consisting...

An example of a two-way crossed design is provided by a study of trawl samples for fish communiti...

The Means Plot procedure in PRIMER 8 will operate just as other univariate plots do (such as hist...