Scales of measures and statistical methods

Relations between measurement scales and statistical methods are very often neglected in the social sciences. I hope you will not make this mistake.
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Dembitskyi S. Scales of measures and statistical methods [Electronic resource]. - Access mode:
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.
Task of Statistical Analysis
Determining typical value or mean
Determining heterogeneity of distribution
Analysis of relationship strength (correlation coefficient)
Group comparison
Index of Qualitative Variation (IQV)
Phi, Cramer’s V, Lambda (all charted)*
Sample proportion comparison**
Gamma (charted), Spearman’s, Kendall’s
Nonparametric tests***
Arithmetic mean
Mean deviation, standard deviation
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.

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