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The Mann-Whltney test. Some problems concerning approximation of critical values and tied ranks

100%

Guraj-Kaczmarek K., Parys D., Tomaszewicz A. S., University of Łódź I. o. E. a. S.

Acta Universitatis Lodziensis. Folia Oeconomica

1993

vol. 132

The nonparametric Mann-Whitney test [Mann-Whitneу (1947)] is one of commonly used two sample tests. The problem of tied ranks exists in the case of discrete distributions. It makes the analysis of distribution of Mann-Whitney test quite complicated. There is continuing interest in the properties of this test's statistics. It can be seen from many of papers concerning the distribution of this statistic according to the assumption of equality of distributions about the critical values tables and test s power. In this paper we shall present an approximation of Mann-Whitney statistics, critical values, compared with the most often used approximation by normal distribution. We will determine the unconditional distribution of U-statistics for P=1/2 in the case of tied ranks. We will compare the interpolated quantiles of these distributions with the case of continuous distribution without the tied ranks.

Nieparametryczny test Manna-Whitneya (1947) należy do najczęściej stosowanych testów dla dwóch prób. W tym artykule prezentujemy dokładny aproksymację wartości krytycznych statystyki Manna-Whitneya w porównaniu z aproksymacją za pomocą rozkładu normalnego. Tablice 2 i 3 zawierają błędy aproksymacji dla 14 poziomów istotności. Obliczone kwantyle interpolowane, ich aproksymację za pomocą rozkładu normalnego oraz błędy aproksymacji dla czterech poziomów istotności prezentujemy w tablicach 4-7.

Społeczno-ekonomiczne korzyści z prowadzonej przez rolników pozarolniczej działalności gospodarczej

63%

Ostromęcki A., Zając D., Mantaj A.

Zagadnienia Ekonomiki Rolnej

2015

issue 2(343)

40-60

The paper aims at identifying and assessing the opinions of farmers concerning the socio-economic benefits from non-agricultural activity they conduct towards their agricultural holding, farming family and rural areas on the territory where these units operate. The empirical material for the paper was provided by surveys carried out in 2011-2012, i.e. questionnaire-based interview, among 210 farmers – owners of individual agricultural holdings – running additional non-agricultural economic activity from the area of south-eastern Poland, namely the following three voivodeships: Świętokrzyskie, Małopolskie and Podkarpackie. The classification of the surveyed farms into two groups, which was based on the conditions of the aforementioned opinions, and analysis of differences in the assessment of benefits between these groups, using the Mann-Whitney test, allowed to define the key determinants of farmers’ opinions on the socio-economic significance of the non-agricultural economic activity they conduct. An important determinant was the share of income from non-agricultural economic activity of farmers in the structure of their family’s sources of income. The surveys showed that, in the opinion of farmers, the higher the ratio for the share, the greater the significance of the analysed socio-economic benefits following from non-agricultural activity conducted by them.

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1 Acta Universitatis Lodziensis. Folia Oeconomica

1 Zagadnienia Ekonomiki Rolnej

1 2015

1 1993

1 Guraj-Kaczmarek K.

1 Mantaj A.

1 Ostromęcki A.

1 Parys D.

1 Tomaszewicz A. S.

1 University of Łódź I. o. E. a. S.

1 Zając D.

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The Mann-Whltney test. Some problems concerning approximation of critical values and tied ranks

Społeczno-ekonomiczne korzyści z prowadzonej przez rolników pozarolniczej działalności gospodarczej