Lecture 1

Why do we need statistics?

Useful advice about this module and the exams….

1. Prepare for the lectures by reading ahead
2. Recommended book: Gravetter & Wallnau (2004) Statistics for the Behavioral Sciences, 6th Edition, Thomas-Wadsworth
3. For the seminars: Brace, N., Kemp, R., & Snelgar, R. (2000) SPSS for Psychologists, MacMilan Press Ltd

Parametric and Non-parametric tests

Non-Parametric tests are:

• relatively easy to calculate
• assumption free
• can use normal and ordinal data

But, are not very powerful because they do not make use of information about the variability of the data. The power of a test reflects how sensitive it is - more sensitive tests will detect a significant difference even if that difference is quite small. The more powerful a test is, the less likely it is to fail to spot a significant difference when one is present (i.e. it avoids Type II errors). Non parametric tests do not use all available information, e.g., Pass or Fail rather than a percentage (failing at 39% is different to failing at 5%).
Parametric tests are more complicated to calculate but are also more powerful:

• use the more informative interval scale
• take advantage of measures of variability, and the properties of the normal distribution

However the data must meet certain assumptions:

• interval scale or higher
• scores must be normally distributed
• samples being compared must have similar variances (homogeneity of variance)

The tests are quite robust; they can cope with some deviation from the ideal conditions.

Q. Why do we need statistics?
A. Because people are variable and our ways of measuring performance are also error prone.

There are many reasons why 2 people who are actually the same on some variable (or even the same person measured twice) will give different scores. People are complicated and their performance will be influenced by a multitude of factors. So, because we expect people who are the same to give us different scores anyway it is difficult to judge when a difference is meaningful or just due to this error variability.

There are 2 ways to deal with error variability:

1. try to eliminate it.
• This is one of the roles of good experimental design.
• Careful matching of participants, control of the environment, accurate measurement techniques, good control of confounding variables
2. try to account for it
• We try to work out how big the error is and take it into account
• Once we have an idea of how much error variability there is, we can see if the effect we have obtained is still meaningful, when error variability has been accounted for……this is where STATISTICS come in

The usual way to estimate the size of error variability in any task is to use the variability within a particular condition. Since everyone within a condition should be the same, any variability here should be due to error. In most tests we simply compare the variability between conditions with the variability within conditions to decide if the difference between conditions is more than could be explained by error variability.

Variability within a condition = ERROR VARIABILITY
Variability between conditions = ERROR VARIABILITY + ANY EFFECT OF TREATMENT

Most statistics (eg, z, f and t) are ratios:
(Variability between conditions) / (Variability within conditions )

Variability provides a quantitative measure of the degree to which scores in a distribution are spread out or clustered together. In order to decide how far apart 2 sample means must be in order to be really different, we must take into account how mch variability