Understanding inferential statistics
Inferential statistics allow psychologists to draw conclusions from their findings. These concusions are based on the probability that a particular pattern of results could have arisen by chance or not. Consider the example about gender differences in ability to read maps. One study might test 20 women and 20 men to see who had a better understanding of maps. The findings showed a difference favouring the women. The big question is:Is this deifference due to chance? Or is there a real effect (i.e. women are actually better than men). If the findings are not due to chance, then the pattern is described as significant i.e. there is a real effect.
Samples and populations
Consider the following example from the psychologist and statistician Hugh Coolican (2004): At my local chippy I am convinced that they save money by giving some people rather thin chips (because they then can get more chips from each potato). There are two chip bins under the counter - the owner of the chippy claims the two bins contain the same kind of chips but I suspect they are different. So I (sadly) tried an experiment. I asked for one bag of chips from each of the chips bins, and I went home and measured the width of the chips in each bag.
Belief 1 is 'The two bins cotain chips of an equal avergae width'.
Belief 2 is 'One bin has thinner chips o average than the other'.
In fact I found a very small difference between the average width of the chips in each bag, but nothing to shout about.
We would expect small differences between samples (bags of chips) jst because things do vary a little - this is simply random variation or 'chance'. What we are lookings for is a sufficiently large difference between the samples to be sure that the bins (the total population) are actually different. Otherwise we assume the bins are the same, i.e. the samples are drawn from a single population rather than from two different populations.
- The bins are populations - in the earlier example about gender differences in map reading, the population is all the men and women in the world.
- The bags of chips are samples - in out other example, the 20 women and 2 men comprise our samples.
- The belief that the two bins contain chips of the same width or the belief that there us no gender difference in map reading is called the null hypothesis. This is a statement of no effect - the samples are not different.
- The alternative belief is that one bin has thinner chips or that women are better than men - this is called the alternative hypothesis. This is a statement that something is going on, there is an effect - the samples…