Analysis by design Statistics is involved in the analysis of data generated from an experiment. It is essential to spend time and effort in advance to ensure that the experiment will generate the right type of data, and enough of it, to answer the key questions of interest. Remember that Statistics CANNOT SALVAGE a BADLY DESIGNED experiment

Analysis by design Desirable features of a good experiment are that:- The results should be valid in terms of for instance estimation of parameters; The results to be reliable, i.e. they should be applicable to the target population. This requires that we select a representative sample of that population; The results should be as precise as possible.

Definitions Experimental unit: the individual test tube or item in the experiment on which observations are made. Treatments: the factors of major interest which are to be compared in the experiment. Response: measurements from the experimental units. Replicates: sets of more than one experimental unit allocated to the same treatment. They are presumed 'identical'. Block: usually a set of 'similar' experimental units. Randomisation: the assignment of treatments to units in a random manner, sometimes in field studies formal randomisation may not be possible. In such cases extreme care should be taken to avoid introducing any biases.

Definitions Control group: a group receiving a standard treatment. Generally interest is in comparing all other treatments with the control. Factor: a collection of levels (e.g. doses) of a specific treatment. Fixed Effect: a factor, levels of which are chosen in a non-random way and therefore cannot be expected to represent the population as a whole; such effects are generally found in experiments where the amount of drug applied is not chosen randomly from all possible amounts, but is chosen systematically so that the effect of drug on response can be modelled. Random Effect: a factor, levels of which are chosen randomly from all the possible levels and the levels used thus can be expected to represent the population as a whole.

Three principles of experimental design Replication Randomisation Blocking

Types of design Three basic types of designed experiment are:- a completely randomised design a randomised block design a factorial design.

Treatment structure Most can be analysed by Analysis of Variance (ANOVA) If there is structure to the treatments, this often means that differences (even small ones) between the treatments will be more easily detected.

The completely randomised design In this experiment, we have a number of treatments, and experimental units are randomly allocated to a treatment. The objective of the experimental design is to identify and quantify significant differences in the mean response amongst the different treatments. Assumptions –Normality –Linearity –additivity

The randomised block design One of the sources of variation is the differences in experimental units, we could control this source of variation by grouping together similar units, ie blocking. the precision of the experiment is increased by identifying a number of homogeneous groups of experimental units (blocks). The treatments are then randomly allocated to units within blocks. In a blocked experiment, we in effect are carrying out the whole experiment in microcosm in each block. We are not particularly interested in the differences between the blocks. What we are really interested in the differences amongst the treatments.

A Factorial design In the designs considered so far, there has been only one treatment factor. This is not always the case. Simplest case is if we have two main factors each with two levels, and a number (preferably the same) of experimental units appearing in the 4 categories. A 2x2 design But can generalise to many factors, with interactions

A randomised block in GLM

Blocking

CR versus RB

Interactions - getting more complex

Interactions in essence Simple additive/linear story, separate story for each factor? or more complicated story involving both factors? Two factors interact if the effect of one factor on response depends on the level of the other.

Analysis of factorial experiments

Leprosy- Interactions with continuous variables

Different slopes

Interactions with continuous variables