W.M. Kalmijn (Wim)
http://repub.eur.nl/ppl/25509/
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RePub, Erasmus University RepositoryHappiness is not normally distributed: A comment to Delhey and Kohler
http://repub.eur.nl/pub/37188/
Sun, 01 Jan 2012 00:00:01 GMT<div>W.M. Kalmijn</div>
Delhey and Kohler assume that the happiness distribution at the population level is essentially normal, but that this is distorted by the fact that happiness is measured in samples using scales that are discrete and two-sided bounded. This assumption is tested using the probit method and rejected. From Discrete 1 to 10 Towards Continuous 0 to 10: The Continuum Approach to Estimating the Distribution of Happiness in a Nation
http://repub.eur.nl/pub/30581/
Wed, 12 Oct 2011 00:00:01 GMT<div>W.M. Kalmijn</div>
Happiness is often measured in surveys using responses to a single question with a limited number of response options, such as 'very happy', 'fairly happy' and 'not too happy'. There is much variety in the wording and number of response options used, which limits comparability across surveys. To solve this problem, descriptive statistics of the discrete distribution in the sample are often transformed to a common discrete secondary scale, mostly ranging from 0 to 10. In an earlier publication we proposed a method for estimating statistics of the corresponding continuous distribution in the population (Kalmijn 2010). In the present paper we extend this method to questions using numerical response scales. The application of this 'continuum approach' to results obtained using the often used 1-10 numerical scale can make these comparable to those obtained on the basis of verbal response scales. Quantification of Happiness Inequality
http://repub.eur.nl/pub/21777/
Thu, 02 Dec 2010 00:00:01 GMT<div>W.M. Kalmijn</div>
Happiness is considered to be an important aspect of human life and this
is reflected in a growing interest of social sciences during the past decennia.
Happiness research is only possible if happiness can be measured and quantified.
The measurement of happiness, more specifically the way observation results
are further processed, is discussed in this dissertation, which is intended to be a
methodological contribution to happiness research. Happiness in this context
is defined as “the degree to which an individual judges the overall quality of
his/her life-as-a-whole favorably”.
Traditionally, this happiness is measured by simply asking the person to
rate it. A frequently used method is to ask a closed question, e.g. “Taking
all together, how happy would you say you are ?” and to offer a limited
number (3 – 7) of response categories, one of which has to be ticked, e.g.
“pretty happy”. In particular such happiness questions with textual response
categories, shortly referred to as “verbal scales”, form the object of the
investigation presented here.
Investigators of happiness are not just interested in individual happiness
scores, they are also interested in happiness in communities. In this dissertation
we shall refer to “nations”, but our findings are equally applicable to other
defined collectivities. Not all individuals are equally happy. With respect to
this happiness inequality, we have to distinguish between within-nations and
between-nations inequality. To collect information on both, social scientists
examine samples from the population or a sub-population, e.g. from all adult
citizens. This sampling should be done at random, but in reality this never
happens. Nevertheless, we assume that all samples discussed in this study can
be considered as if sampling has been at random, since information on the
happiness distribution within the population represented by that sample can
only be obtained under that assumption.Measures of Inequality: Application to Happiness in Nations
http://repub.eur.nl/pub/32756/
Mon, 01 Feb 2010 00:00:01 GMT<div>W.M. Kalmijn</div><div>L.R. Arends</div>
What is a good measure for happiness inequality? In the context of this question, we have developed an approach in which individual happiness values in a sample are considered as elements of a set and inequality as a binary relation on that set. The total number of inequality relations, each weighed by the distance on the scale of measurement between the pair partners, has been adopted as an indicator for the inequality of the distribution as a whole. For models in which the happiness occurs as a continuous latent variable, an analogous approach has been developed on the basis of differentials. In principle, this fundamental approach results in a (zero) minimum value, and, more importantly, also in a maximum value. In the case where happiness is measured using a k-points scale, the maximum inequality is obtained if all 1/2N sample members select the lowest possible rating (Eq. 1) and the other 1/2N the highest possible one (k). This finding even applies to the truly ordinal case, i.e., if the distances between the successive ratings on the scale are unknown. It is, however, impossible to quantify the inequality of some measured sample distribution, unless all distances of the k categories of the scale of measurement are known or at least estimated, either on an empirical basis or on the basis of assumptions. In general, the numerical application of the method to continuous distributions is very complicated. An exploration on the basis of a relatively simple model with a linear probability density function suggests that the inequality of a beta probability distribution with shape parameters a and b increases as the value of these parameters decreases. A contour plot, obtained by numerical integration, demonstrates this relationship in a quantitative way. This approach is applicable to judge the aptness of common statistics of dispersion, among which the standard deviation and the Gini coefficient. The former is shown to be more appropriate than the latter for measuring inequality of happiness within nations. Happiness Scale Interval Study. Methodological Considerations
http://repub.eur.nl/pub/20939/
Fri, 01 Jan 2010 00:00:01 GMT<div>W.M. Kalmijn</div><div>L.R. Arends</div><div>R. Veenhoven</div>
The Happiness Scale Interval Study deals with survey questions on happiness, using verbal response options, such as 'very happy' and 'pretty happy'. The aim is to estimate what degrees of happiness are denoted by such terms in different questions and languages. These degrees are expressed in numerical values on a continuous [0,10] scale, which are then used to compute 'transformed' means and standard deviations. Transforming scores on different questions to the same scale allows to broadening the World Database of Happiness considerably. The central purpose of the Happiness Scale Interval Study is to identify the happiness values at which respondents change their judgment from e.g. 'very happy' to 'pretty happy' or the reverse. This paper deals with the methodological/statistical aspects of this approach. The central question is always how to convert the frequencies at which the different possible responses to the same question given by a sample into information on the happiness distribution in the relevant population. The primary (cl)aim of this approach is to achieve this in a (more) valid way. To this end, a model is introduced that allows for dealing with happiness as a latent continuous random variable, in spite of the fact that it is measured as a discrete one. The [0,10] scale is partitioned in as many contiguous parts as the number of possible ratings in the primary scale sums up to. Any subject with a (self-perceived) happiness in the same subinterval is assumed to select the same response. For the probability density function of this happiness random variable, two options are discussed. The first one postulates a uniform distribution within each of the different subintervals of the [0,10] scale. On the basis of these results, the mean value and variance of the complete distribution can be estimated. The method is described, including the precision of the estimates obtained in this way. The second option assumes the happiness distribution to be described as a beta distribution on the interval [0,10] with two shape parameters (α and β). From their estimates on the basis of the primary information, the mean value and the variance of the happiness distribution in the population can be estimated. An illustration is given in which the method is applied to existing measurement results of 20 surveys in The Netherlands in the period 1990-2008. The results clarify our recommendation to apply the model with a uniform distribution within each of the category intervals, in spite of a better validity of the alternative on the basis of a beta distribution. The reason is that the recommended model allows to construct a confidence interval for the true but unknown population happiness distribution. The paper ends with a listing of actual and potential merits of this approach, which has been described here for verbal happiness questions, but which is also applicable to phenomena which are measured along similar linesInequality-adjusted happiness in nations: egalitarianism and utilitarianism married in a new index of societal performance
http://repub.eur.nl/pub/7204/
Fri, 06 Jan 2006 00:00:01 GMT<div>W.M. Kalmijn</div><div>R. Veenhoven</div>
According to the utilitarian creed, the quality of a society should be judged using the degree of happiness of its members, the best society being the one that provides the greatest happiness for the greatest number. Following the egalitarian principle, the quality of a society should rather be judged by the disparity in happiness among citizens, a society being better if differences in happiness are smaller. Performance on these standards can be measured using cross-national surveys, where degree of happiness is measured using the mean response to a question about happiness and disparity expressed as the standard deviation. In this paper we marry these measures together in an index of 'Inequality-Adjusted Happiness' (IAH) that gives equal weight to either criterion. It is a linear combination of the mean happiness value and the standard deviation and it is expressed as a number on a 0 to 100 scale. We applied this index to 90 nations for the 1990s and observed large and systematic differences, IAH being higher in rich, free and well governed countries. We also considered the trend over time for 14 rich countries and found that IAH has increased over the last 30 years.Measuring inequality of happiness in nations. In search for proper statistics.
http://repub.eur.nl/pub/16429/
Thu, 01 Dec 2005 00:00:01 GMT<div>R. Veenhoven</div><div>W.M. Kalmijn</div>
ABSTRACT<br/>
Comparative research on happiness typically focuses on the level of happiness in nations, which is measured using the mean. There have also been attempts to compare inequality of happiness in nations and this is measured using the standard deviation. There is doubt about the appropriateness of that latter statistic and some prefer to use the statistics currently used to compare income inequality in nations, in particular the Gini coefficient.
In this paper, we review the descriptive statistics that can be used to quantify inequality of happiness in nations. This review involves five steps: (1) we consider how happiness nations is assessed, (2) next we list the statistics of dispersion and considered their underlying assumptions; (3) we construct hypothetical distributions that cover our notion of inequality; (4) we define criteria of performance and (5) we check how well the step-2 statistics meet the step-4 demands when applied to the step-3 hypothetical distributions We then applied the best performing statistics to real distributions of happiness in nations.
Of the nine statistics considered, five failed this empirical test. One of the failed statistics is the Gini coefficient. Its malfunction was foreseen on theoretical grounds: the Gini coefficient assumes a ratio level of measurement, while happiness measures can at best be treated at the interval level. The Gini coefficient has been designed for application to 'capacity' variables such as income rather than to 'intensity' variables such as happiness.
Four statistics proved to be satisfactory; these were (1) the standard deviation, (2) the mean absolute difference, (3) the mean pair difference and (4) the interquartile range. Since all four statistics performed about equally well, there is no reason to discontinue the use of the standard deviation when quantifying inequality of happiness in nations.