Further Adventures in Statistics
We really hope that you have found this website useful and that you now feel you could perform regression analysis as part of your own research. The techniques outlined on this site provide the most flexible approach to addressing many research questions. Of course, with regards to the wonderful world of quantitative data analysis, there are many other applications and techniques you could explore. Where such techniques or analyses are direct extrapolations from the material we have presented on this site, then they are included in the text (e.g. the discussion of other logistic/ordinal regression models on Page 5.12). Below are some brief descriptions of analyses that you might encounter that may be relevant to the research questions you are asking and some pointers towards resources. So for further adventures in statistics...
These techniques can actually be considered as part of the regression family in many ways but they tend to have a different emphasis and are more widely used for analysing experimental designs. There are six key types of analysis that fall under the umbrella term of ‘general linear model’. You may want to find out more about the following:
ANOVA – Analysis of Variance (One-way): ANOVAs frequently appear within the output for regression analysis so the term should be familiar. The basic ‘one-way’ ANOVA is briefly explained in our foundation module (Page 1.10) but it is always useful to understand how these things work! It is a way to look for statistically significant differences between groups based on the mean value of a continuous outcome (dependent) variable. These groups are often discrete levels of a categorical explanatory (independent) variable. For example, you would use a one-way ANOVA if you wanted to look at whether the mean score on a maths test varies between different ethnic groups (note that you only use an ANOVA if there are more than two levels of the explanatory variable, otherwise you use a T-test – see Page 1.10).
Factorial ANOVA: Don’t let the name fool you - this concept will be fairly familiar to those of you who have mastered the Multiple Linear Regression Module. The Factorial ANOVA is for when you wish to incorporate more than one categorical explanatory variable in to your design. This is very similar to adding multiple dummy variables to a multiple linear regression and allows you to look for interaction effects. Building on the previous example, you might want to look at whether the mean score on a maths test varies between both ethnic and SEC groups and whether these two explanatory variables interact. We have already used a very similar example on this site when describing Multiple Linear regression (see Page 3.11).
Repeated-measures ANOVA: This is for when your outcome variable is ‘within participants’ meaning that you are testing the same participants on numerous occasions. This requires different assumptions to be met and therefore a slight variation on the standard ANOVA. For example, you may want to explore how a measure of reading ability changes over three different time points and would require the same participants to repeat the measure several times.
ANCOVA – Analysis of Covariance:An ANCOVA is basically an ANOVA which includes continuous explanatory variables as ‘covariates’. This is the basis of regression transplanted in to the world of comparing conditions! For example, an ANCOVA would be useful for situations where you wished to compare the means of two groups but wished to include a continuous explanatory variable such as previous exam scores in your design. Essentially it is just a regression by another name (or vice versa!) so you should be familiar with the underlying operations!
MANOVA – Multivariate Analysis of Variance: This is a nautical term, short for MAN-OVER-BOARD! Sorry about that lame joke, the MANOVA is actually a term to describe an analysis of variance in which there are multiple outcome variables. For example, let us say that you wanted to assess the impact of an after school club on the lives of students in a school. You might have two conditions: one group who attend the club and a matched group who do not. However the impact of your after school club might be felt in a number of different domains such as exam performance, attitude to school, aspirations, etc. All of these are outcome variables and it would be good if you could include all of these in the analysis together. A MANOVA allows you to analyse multiple outcome variables and therefore to create such designs.
Mixed Design ANOVA: This refers to a more complicated experimental design in which there are multiple explanatory variables which are a mixture of what we call ‘between’ and ‘within’ participant variables. This means that some of the variables differ between your cases (e.g. gender) and some are measures taken from the same participants (e.g. at different times). As you can imagine this can be rather confusing but luckily SPSS is very adept at disentangling these more complicated designs.
You will notice that throughout our modules we have spoken at length about model diagnostics and assumptions. It is important that these assumptions are met to a satisfactory extent because if they are not your regression model is essentially meaningless. One of the key assumptions that comes up time and time again is whether or not your data is normally distributed. But what can you do with it if it isn’t? We have often suggested some ways around this but in some cases the data is simply not suitable for regression analysis or indeed any type of analysis which assumes normality – so called 'parametric tests'. Luckily there are a range of analyses called non-parametric tests that you can deploy in such distressing circumstances. They are worth learning about!
Multi-level modelling is a technique which has actually sprung up a few times in our regression modules (for example, on Page 2.6). Multi-level regression models allow for the construction of models which include ‘nested’ or hierarchically arranged variables which often better reflect the realities of the social world. For example, student performance is dependent on many factors which vary between individuals but also a number of factors which vary between schools and some which operate at an even higher level (regional or national factors). Multi-level models allow you to factor for these hierarchically arranged sets of variables and explore the way they interact with one another. It is not easy but well worth the effort!
Structural equation modelling is another somewhat advanced technique that is beyond the remit of this website. Basically it uses statistical techniques and a specific set of assumptions to allow the researcher to test for causal relationships - something that cannot be done with the models we have discussed on this site. This is pretty advanced stuff. If you do want to venture into the area we suggest some texts below. There is an excellent software programme called AMOS which is an add-on to SPSS so you do not have to port your data in and out of separate software packages.
On a slightly different theme, factor analysis is a technique for examining commonality within the variance of a set of variables to ascertain whether they may actually be measuring the same underlying factor (or ‘latent variable’). It can be invaluable if you are a fan of using questionnaires in your research as it can allow you to merge sets of questions such that they combine to measure a single factor.
For example, let’s say that you are trying to explore ‘student attitude to school’. There are many different things which may influence a student’s attitude to school: quality of environment, liking for teachers, strength of relationship with peer group, etc. It may be that if you were to measure all of these with a questionnaire you would find patterns in the answers such that all of these items could be combined to get an overall measure of ‘attitude to school’.
There are two main types of factor analysis: exploratory, for when you are looking for factors within a set of measured variables, and confirmatory, for when you are coming at it from the other direction and wish to prove that a set of variables really are all measuring the same overall concept. Confirmatory Factor Analysis is often seen as an aspect of structural equation modelling, so see the reference to SEM above.
That's all Folks...
We hope that these suggestions will be useful pointers if you want to build on what you have (hopefully!) learnt from this site and add further depth and breadth to your research skills. Thanks for visiting our site!