Scales of measures and statistical methods

Measuring social characteristics >> Scales of measure > Alternative classifications | Scales of measures and statistical methods >> Descriptive statistic

Relations between measurement scales and statistical methods are very often neglected in the social sciences. I hope you will not make this mistake.

For reference

Dembitskyi S. Scales of measures and statistical methods [Electronic resource]. - Access mode: http://www.soc-research.info/quantitative_eng/5-2.html

The scale, in which the variable is displayed, determines which methods can be used in this case, and which cannot. All methods that can be used for "weaker" scales can also be used with "stronger" ones. Thus, the methods suitable for nominal scales are also suitable for ordinal and metric scales. Methods suitable for ordinal scales are suitable for metric scales.

Scale	Task of Statistical Analysis
Scale	Determining typical value or mean	Determining heterogeneity of distribution	Analysis of relationship strength (correlation coefficient)	Group comparison
Nominal	Mode	Index of Qualitative Variation (IQV)	Phi, Cramer’s V, Lambda (all charted)*	Sample proportion comparison**
Ordinal	Median	Index of Qualitative Variation (IQV)	Gamma (charted), Spearman’s, Kendall’s	Nonparametric tests***
Metric	Arithmetic mean	Mean deviation, standard deviation	Pearson’s	Sample mean comparison****, analysis of variance

* Phi and Cramer’s V are based on the use of the chi-square test.
** Sample proportions are compared using Student’s distribution, as well as the normal distribution of sample statistics.
*** Criteria based on the comparison of ranks of values, e.g., Kruskal-Wallis test or Mann-Whitney U test.
**** Sample means are compared using Student's distribution, as well as the normal distribution of sample statistics.

References

default_titleХили Дж. Статистика. Социологические и маркетинговые исследования. - К.: ООО "ДиаСофтЮП"; СПб.: Питер, 2005. - 638 с.
default_titleНаследов А. Математические методы психологического исследования. Анализ и интерпретация данных. - СПб.: Речь, 2004. - 388 с.
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