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Statistical inference allows researchers to learn things about a population using only a sample of data from that population. But if it isn't a random sample, inference becomes tricky or outright impossible, as Norbert Hirschauer, Sven Grüner, Oliver Mußhoff, Claudia Becker and Antje Jantsch explain

Besides the inferential errors that abound in the interpretation of p-values, the probabilistic pre-conditions (i.e. random sampling or equivalent) for using them at all are not often met by observa-tional studies in the social sciences. This paper systematizes different sampling designs and discusses the restrictive requirements of data collection that are the sine-qua-non for using p-values.

There is a lot of research on the relationship between income and happiness, but little research into the relationship between wealth and happiness. Knowledge about the effects of wealth on happiness is required for informed decision making in matters of saving and consumption. In order to answer the questions of how and to what extent wealth relates to happiness, we take stock of the available research findings on this issue, covering 119 research findings observed in 72 studies. We use a new method of research synthesis, in which research findings are described in a comparable format and entered in an online 'findings archive', the World Database of Happiness, to which links are made from this text. This technique allows a condensed presentation of research findings, while providing readers access to full details. We found mostly positive relationships between assets and happiness, and negative relationships between debt and happiness. The size of the relationships is small, variations in wealth explain typically less than 1% of the variation in individual happiness. The correlations are slightly reduced when controlled for income and socio-demographic factors. The few longitudinal studies suggest a causal effect of wealth on happiness. We found little differences across methods used and populations studied. Together, the available research findings imply that building wealth will typically add to your happiness, though not by very much.

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