The evaluation of departments or universities has become common place for nowadays academia. Different indicators are used for such purposes, while research is emphasized in many cases (Hazelkorn, 2011). Scientific productivity can be measured using different indicators, such as the number of published articles, the number of received citations,

In Shen et al. (2017), we asked when the arithmetic mean of a sample set, or some other kind of average score, be used to represent the set, and under which conditions a comparison based on such measures of central tendency can be reliable? When does the comparison of arithmetic means indicate a grouping of academics, such as a department or a university, performs better than the one it is compared to? In order to answer this question, we proposed a definition of the minimum representative size

Given, for example, two sets of data, (1) and (2), whose averages are in an ordinal relation e.g. the average of data set (1) is higher than that of data set (2), what is the probability that a random sample from the first data set has a higher average than a random sample from the second? If the two data sets are skewed, the probability is often not high. For the very purpose of increasing this probability when it is possible to increase it, we introduced in Shen et al. (2017) the definition of _{i}

An alternative approach is to truncate the distribution and to consider a particular segment when comparing a set of populations. That particular segment has the property of smaller variation and thus renders the comparison between populations more reliable. In this case, theoretical arguments for choosing a specific segment as being representative of the entire population are strongly required. We pursued this stream of research in Proteasa et al. (2017).

In this article, we apply the former analytical approach in an empirical context: we calculate the minimum representative size for six medicine departments in Romania in order to allow for reliable comparisons between them as collective units.

Let us denote a skewed data set _{j}_{j}_{j}_{j}

where _{i}_{i}_{i}_{i}_{j}_{i}_{j}

where, _{i}_{i}_{i}

We also know that the average of

Equation (2) can be solved by bootstrap sampling (Wasserman, 2004) (see Shen et al. (2017) for further details). For data sets _{i}_{j}_{i}_{j}

For given values of _{i}_{j}

Pair matching is performed on

If (4) conditions are satisfied, then the pairs values (_{i}_{j}_{i}_{j}_{i}_{j}

If _{i}_{i}_{i}_{j}_{j}_{i}_{i}_{j}_{j}_{i}_{i}

We increase _{i}_{j}_{i}_{j}

In this article, we study 3374 academics from the departments of medicine within the six health studies universities in Romania: Cluj, Bucharest, Timişoara, Iaşi, Craiova and Tg. Mureş.

The personnel lists were compiled from public sources: websites and reports in 2014. We collected publication data from the Scopus data-base for the population of academics we established. We collected information regarding publications, citations, and Hirsch’s

University | N | Citation | |||||
---|---|---|---|---|---|---|---|

‹ | ‹ | ‹ | |||||

Cluj | 596 | 24.75 | 124.66 | 1.69 | 2.23 | 2.53 | 4.03 |

Bucharest | 1119 | 18.41 | 80.81 | 1.45 | 1.99 | 2.15 | 3.56 |

Timişoara | 505 | 15.93 | 57.61 | 1.42 | 2.03 | 1.93 | 3.16 |

Iaşi | 547 | 15.86 | 75.22 | 1.54 | 1.90 | 2.06 | 3.08 |

Craiova | 280 | 14.19 | 40.95 | 1.50 | 1.91 | 1.98 | 2.90 |

Tg. Mureş | 327 | 5.40 | 22.19 | 0.83 | 1.28 | 1.08 | 2.04 |

We illustrate the skewness of the six distribution in Fig.1, where we plotted the distributions of total citations of each of the academics affiliated to the six universities. A visual inspection of the plots reveals that the first quartile and minimum citation of the six universities are all close to zero thus cannot be seen in the figure, since a considerable number of academics received no citations in the time window during which citations were collected. The six distributions are skewed and present a high degree of overlapping, as indicated by their large standard variance and by the large difference between medians and means.

In the following section we will engage with two research questions, conceptualized in the section dedicated to the outlining the method: (1) Is the mean a reliable measure of central tendency for the purpose of establishing a hierarchy of the six medical schools, which can account for the quality of the academics affiliated with them? (2) How can the six medical schools be compared using the minimum representative size?

A first statistic treatment we perform includes pairwise comparison of the six medicine faculties. In this respect, we used distributions of citations(

The distributions of the Bootstrap average

The complete results of pairwise comparison based on the three indexes, citation,

A visual inspection of Fig.3 reveals that most of the circles corresponding to pairwise comparisons between faculties are leaning towards the dark ends of the spectra. We interpret this observation as proof of the incapacity of the mean scores to account for the differences between the six faculties, when compared in pairs. More than this, some of the values

In a second statistical treatment, we compare one faculty

_{rest}_{rest}_{rest}_{rest}_{rest}

University | N | Citation | |||||
---|---|---|---|---|---|---|---|

‹_{rest} | ‹_{rest} | ‹_{rest} | |||||

Cluj | 596 | 15.50 | 480 | 1.40 | 183 | 1.95 | 145 |

Bucharest | 1119 | 16:50 | 5283 | 1:44 | > 10^{4} | 2.00 | 1664 |

Timişoara | 505 | 17:35 | 4900 | 1.45 | 9066 | 2.08 | 1378 |

Iaşi | 547 | 17:38 | 7187 | 1.43 | 893 | 2.06 | > 10^{4} |

Craiova | 280 | 17:40 | 477 | 1.42 | 3375 | 2.06 | 3634 |

Tg. Mureş | 327 | 18:39 | 2 | 1.51 | 12 | 2.16 | 13 |

The faculty from Cluj has the highest mean score in all the comparisons we performed, regardless of the index. The corresponding values of the minimum representative size, _{rest}

In a nut-shell, this contribution consists in applying the minimum representative size, a methodology developed in Shen et al. (2017), to a new empirical context— that of the faculties of medicine in the health studies universities in Romania, previously studied by Proteasa et al. (2017). The “quality” of the academics affiliated to the six faculties located in Cluj, Bucharest, Timişoara, Iaşi, Craiova, and Tg. Mureş is measured by the total citations received by each academic, and the respective values of the

One might think that these results which substantiate that the faculties located in Cluj and Tg. Mureş are quite different from the rest, while the others are rather similar is trivial. It can be argued that a similar conclusion can be reached by a simple comparison of the mean scores in Table 1. We emphasize that the method we unfolded in this article which builds on the concept of the minimum representative size (

We consider our findings are particularly relevant in situations when aggregate scores are computed for the purpose of ranking data sets associated with different collective units, such as faculties, universities, journals etc. Whenever one wants to distinguish the performance of two collective units, the minimum representative size of pair-wise comparison should be calculated first as an indication of the reliability of the comparison of the means. When

#### Basic statistics. For each university, its name, number of academics(N), mean score(‹•›), standard variance (σ) of the corresponding index, are shown

University | N | Citation | |||||
---|---|---|---|---|---|---|---|

‹ | ‹ | ‹ | |||||

Cluj | 596 | 24.75 | 124.66 | 1.69 | 2.23 | 2.53 | 4.03 |

Bucharest | 1119 | 18.41 | 80.81 | 1.45 | 1.99 | 2.15 | 3.56 |

Timişoara | 505 | 15.93 | 57.61 | 1.42 | 2.03 | 1.93 | 3.16 |

Iaşi | 547 | 15.86 | 75.22 | 1.54 | 1.90 | 2.06 | 3.08 |

Craiova | 280 | 14.19 | 40.95 | 1.50 | 1.91 | 1.98 | 2.90 |

Tg. Mureş | 327 | 5.40 | 22.19 | 0.83 | 1.28 | 1.08 | 2.04 |

#### Values of κrest. For each university, its name, mean score of the rest university (‹c›rest, ‹h›rest, ‹g›rest), and minimum number of representative academics (κrest), calculated by the corresponding index, are shown.

University | N | Citation | |||||
---|---|---|---|---|---|---|---|

‹_{rest} | ‹_{rest} | ‹_{rest} | |||||

Cluj | 596 | 15.50 | 480 | 1.40 | 183 | 1.95 | 145 |

Bucharest | 1119 | 16:50 | 5283 | 1:44 | > 10^{4} | 2.00 | 1664 |

Timişoara | 505 | 17:35 | 4900 | 1.45 | 9066 | 2.08 | 1378 |

Iaşi | 547 | 17:38 | 7187 | 1.43 | 893 | 2.06 | > 10^{4} |

Craiova | 280 | 17:40 | 477 | 1.42 | 3375 | 2.06 | 3634 |

Tg. Mureş | 327 | 18:39 | 2 | 1.51 | 12 | 2.16 | 13 |