## 1 Introduction  
The freezing point is one of the analyses regularly performed on milk and corresponds to the temperature at which freezing occurs, which varies depending on the milk osmotic pressure, the concentration of ions and the levels of lactose, potassium, sodium and chlorides [1, 2]. This measurement allows for the detection of whether the milk has been adulterated by adding water to increase its volume [3]; the amount of water added is calculated based on the difference between the freezing point of the sample and the expected value for milk. However, the freezing point of milk may vary for natural reasons related to several factors, such as feeding, lactation stage, presence of mastitis, water consumption, weather, regional or seasonal conditions or carbon dioxide concentration;thus, the generally expected standard freezing point may vary between countries [2]. Milk acidity caused by lactic acid fermentation and the effect of pasteurization have also been found to be the cause of milk composition changes [4]. The European Union and other individual countries have produced directives or regulations regarding the freezing point of milk. The Chilean Food Sanitary Regulation is an example of such guidelines [5], which establishes a range for the freezing point of milk from \(-0.512\) up to \(-0.550\)\({}^{\circ}\)C (\(-512\) m\({}^{\circ}\)C to \(-550\) m\({}^{\circ}\)C). Several authors have studied the relationship between the freezing point and the amount of water added; a study published by [PERSON] et al. [4] states that, for each percentage point of water addition, the freezing point goes up by \(0.006\)\({}^{\circ}\)C.  
The different analytical methods used by laboratories to determine the freezing point of milk are as follows: the cryoscopic thermistor method, for which there is a reference method established by the ISO 5764:2009 standard (IDF 108:2009) [6] and the NCH 1742:1998 standard [7], and the MIR mid-infrared spectroscopy method [8]. The reference method for the calibration of the latter is the one described in the ISO 5764:2009 standard (IDF 108:2009) [6]. The reference method is based on supercooling the milk sample to a suitable temperature and inducing its crystallization by imposing sufficient conditions to cause an instantaneous release of heat that results in the heating of the sample to a temperature plateau [6]. The plateau is considered to have been reached when the temperature increase is no more than \(0.5\) m\({}^{\circ}\)C for the last 20 s. This temperature would correspond to the freezing point of the sample [6]. In Chile, most laboratories use the thermistor method, although the MIR mid-infrared spectroscopy method has been moderately adopted in recent years. The laboratories responsible for determining the freezing point can participate in proficiency tests (PTs) to corroborate the validity of their analytical results, which are required for the control of the milk quality in all its stages, from primary production onwards. Proficiency testing (PT), or \"evaluation of participant performance against pre-established criteria by means of interlaboratory comparisons\" [9], is of utmost importance for analytical laboratories in the agrifood sector, and regular participation in testing is a requirement for laboratories working under the ISO/IEC 17025:2017 standard [10]. According to [PERSON] and [PERSON] [11], control laboratories are required to participate in PT schemes that comply with the ISO/IEC 17043 standard. In order to analyze the results and to produce reports for each participant, the standard ISO 13528, which describes the statistical methods that must be followed to assess the participants' performance, must be referred to. The PT providers evaluate the performance of the participants according to specifically predetermined criteria and compare their results with a reference or assigned value [9], which can be established using different approaches.