Does carbon dating work only on (used to be) living things

Carbon dating only works on organic material, such as wood or bone.

Your archaeologists probably used other methods for that site; perhaps geological information in the various strata.

A factor is a categorical predictor variable. Factors are composed of levels. For example, treatment is a factor with the various types of treatments comprising the levels. In the type of analyses discussed here, a subject should appear under only one level. In this case, it would mean that a subject is given only one of the many possible treatments.

While I've yet to see it stated explicitly in any textbook, it is important to be aware of two different types of factors--those where subjects are randomized to the levels and those where no randomization is involved. The same statistical methods are use for analyzing both types of factors, but the justification for the use of statistical methods differs, just as for intervention trials and observational studies. When subjects are randomized to levels, as in the case of treatments, the validity of the analysis comes from the act of randomization. When subjects are not randomized to levels, as in the case of sex or smoking status, the validity of the analysis follows either from having random samples from each level or, more likely, from having used an enrollment procedure that is believed to treat all levels the same. For example, a door-to-door study of adults with and without children in primary school conducted in the early afternoon is likely to produce very different results from what would be obtained in the early evening.

The terms Single Factor Analysis of Variance, Single Factor ANOVA, One Way Analysis of Variance, and One Way ANOVA are used interchangeably to describe the situation where a continuous response is being described in terms of a single factor composed of two or more levels (categories). It is a generalization of Student's t test for independent samples to situations with more that two groups.

I have sometimes been guilty of putting a hyphen in single-factor analysis of variance. This was prompted by a reviewer who confused the analysis of variance with another statistical technique, factor analysis, and asked why we had failed to report the results of the single "factor analysis" of variance