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Alternative hypothesis (h1):
If the null hypothesis is true, then the distribution of means of samples of a particular size would have the same mean as the hypothesised population, so the two distribution curves would be centred on the same point.
If the null hypothesis is not true, then your sample mean will be noticeably different. At some point the null hypothesis becomes so unlikely that you can reject it.
Then you have some justification for inferring that population is centred around the observed sample, as the best information that you have. This would not amount to proof that you have discovered the truth: it would be the alternative hypothesis.
Click here to see an illustration.
Analysis of covariance:
A significance test that takes account of influencing factors. In the example given in Statistics for the Terrified, there are two sources of influence at work:
- 1 between the teachers of two classes, and
- 2 due to the influence of the pupil's IQ
In the illustration, the exam scores are plotted against the IQ, and an overall line fitted to the data. The differences from the line for each data point (the residuals) are shown against the x axis. This removes the infuence of IQ, and makes it clear that teacher A better than teacher B.
Click here to see an illustration.
Analysis of variance (anova):
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A perversely titled technique to test whether there is a difference between a set of sample means. The simplest form of analysis of variance looks at the means classified by just one factor, eg. the factor UK nationality would produce four means: English, Irish, Scottish and Welsh. Two-way analysis of variance can handle a second factor as well, eg. Gender: male, female. This way you can look at both factors simultaneously, effectively English male, English female, Irish male, Irish female, etc. Anova is very similar to the two-sample t test, but is used when there are more than two samples. In ANOVA, we look at the variance within the groups, and the variance between the group means. If the means are quite far apart, that would suggest that at least one of the groups may be significantly different to the others. However, we need to look at how varied the data is within the groups as well. |
| In Statistics for the Terrified we introduce a visual approximation which shows how far the variation within the groups (represented by grey lines) obscures the variation between the group means (represented by red lines). | |
Area under the curve (auc):
A single value summary of something measured repeatedly over time. It consists of a series of lines connecting adjacent points. The area underneath these lines is used as a summary of the values shown by these points. It can be calculated from the baseline established by the first measurement (usually preferable) or from zero. (The name of the technique is a misnomer, because there is no curve.)
Click here to see an illustration.
