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The effect of rounding off in samples

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  • M. E. Wise

Abstract

Dit artikel bevat een elementaire behandeling van afrondingseffecten in steekproeven. Zoals men verwacht, neemt de variantie van het steekproefgermddelde door af ronding der waarnemingen toe met een factor 1 +b2/12σx2, waarbij b het afrondings‐ interval enσx2de stamvariantie is, in analogie met de bekende correcties van Sheppard. Verder wordt het effect van afronding op de variantie van de steek‐proefvariantie onderzocht. Er wordt op gewezen, dat de afrondingsfout ε in één steekproef gecorreleerd is met de afwijking van de nauwkeurige — d.w.z. niet afgeronde — stochastische variabele x van zijn gemiddelde μ, hoewel deze correlatie gemiddeld nul is. Het gevolg is, dat de variantie van de steekproefvariantie toeneemt. Bij “gewone” waarschijnlijkheidsverdelingen, die continue naar nul gaan bij x →, is deze toename gelijk aan 1/n(1/3b2σx2+ 1/180b4) waarbij n de grootte van de steekproef is. Bij normale verdelingen is het effect ongeveer twee maal zo groot als de toename volgens de Sheppard's correctie van de afgeronde variantie.

Suggested Citation

  • M. E. Wise, 1954. "The effect of rounding off in samples," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 8(3‐4), pages 169-173, September.
  • Handle: RePEc:bla:stanee:v:8:y:1954:i:3-4:p:169-173
    DOI: 10.1111/j.1467-9574.1954.tb00448.x
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