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" although the arguing from experiments and observations by induction be no demonstration of general conclusions, yet it is the best way of arguing which the nature of things admits of." Newton, I. 1704 quoted Losee, J. 1972 p.81

In general terms, we use the word experiment in two ways. We can mean trying out new things, or testing by experience. A man wearing lipstick might be experimenting in both ways. He could be trying out something new for him. He might also be testing public reaction. His activities might be described as a social experiment, but they are not what we normally consider a scientific experiment.

A scientific experiment is a procedure constructed to discover, demonstrate or test significant truth about reality, under controlled conditions, in a way that can be repeated by other people with similar results. Like the man wearing lipstick, constructing the experiment requires imagination. Like the man wearing lipstick, experience is providing something that imagination on its own could not.

With a scientific experiment, however, the "truth" that we are discovering, demonstrating or testing will have to be carefully formulated, the conditions of the experiment will be carefully specified and the rational connection between the truth discovered, demonstrated or tested, and the experimental results, will be logically laid out. Newton formulated his truths mathematically and most scientific experiments are quantitative.

By saying that the truth should be significant, I mean that it should relate to a general body of theory that can be seen to rationally and usefully explain the world in a way acceptable to scientists. It may relate by just showing that an accepted scientific theory does not adequately explain reality - but it must relate in some way to scientific theory.

Statistical Experiments

Statistical experiments are common in many sciences, including biology, psychology, medicine and ecology. In Simple Statistics, Frances Clegg gives this "Summary of experimental procedure".

1. Have an idea ( theory) about the effect of one variable upon another.

2. Define the independent variables and the dependent variables

3. Decide how the variables will be quantified. (What the units of measurement are)

4. Express the idea formally as an experimental hypothesis .

5. Decide what kind of statistical analysis will be appropriate.

6. Specify a significance level and sample size.

7. Select the sample to be used from the parent population which is under scrutiny.

8. Divide the sample into two

9. Apply the experimental treatment to one part of the sample, and treat the other as a control group.

10. Collect the results. These will be two sets of scores, one for the experimental group and one for the control group, showing how the dependent variable altered as the independent variable was altered.

11. Analyse the data
    
    
    • Establish the null hypothesis
    • Apply an appropriate statistical test or technique
    • Accept or reject the null hypothesis in the light of the last step

    • Draw a conclusion about whether the experimental hypothesis has been confirmed or not.

Independent and Dependent Variables

The first variable (the one we alter to affect the other) is called the independent variable. The variable we predict will be altered is called the dependent variable.

Example "Drug x is good for making people with colds better" predicts that the independent variable "Drug x" will tend to make the dependent variable, "people with colds", better.

Non-directional hypotheses A non-directional hypothesis does not predict which way the independent variable will affect the dependent variable.

Example "Drug x will have an affect on people's colds"

This does not predict if it will make the colds better or worse.

Directional hypotheses A directional hypothesis predicts the way the independent variable will affect the dependent variable.

Examples:

"Drug x will make people's colds worse"
OR
"Drug x will make people's colds better"

The slang term for a non-directional hypothesis is a "two-tailed" hypothesis because the experimenter predicts correctly whether the people with colds get better or worse. A directional hypothesis is called a one-tailed hypothesis. As with tossing a coin that has one head and one tail, only one out of two predictions can be correct.

But notice that, with experimental hypotheses, there is a third possibility. The independent variable may have no effect. The drug may not influence the colds in any way. This possibility is called the null hypothesis


Statistical Tests
Tests of Significance

Statistical tests are used to see if samples of numbers appear to have come from one or from two populations. The statistical test will also say what the likely margin of error is.

Another way of saying this, is that the statistical test tests whether a difference observed between two samples is likely to reflect a real difference between two populations.

For example:

One sample of twenty people with colds was given drug x. A control sample of twenty people with colds was not given any treatment. 10 of the first sample had stopped sneezing two hours after taking drug x. At the same time, 8 of the control sample were found to have stopped sneezing.

It would appear that drug x works. But is the difference between samples likely to reflect a real difference between the (hypothetical) population of all people with colds who might take drug x, and the (hypothetical) population of the (same) people with colds, but without taking drug x?

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