Statistical Inference for the Relationship Between Two Variables

  • Babak Shahbaba
Part of the Use R! book series (USE R)


In this chapter, we continue our discussion of hypothesis testing methods. Here, we only consider hypotheses that are expressed in terms of a relationship between two variables. We start our discussion by focusing on situations where one variable is numerical and the other variable is binary. Typically, the numerical variable, called the response variable, is regarded as the primary variable of interest that captures a specific characteristic of the population that we are investigating. The binary variable, called factor, on the other hand, divides the population into two groups. Therefore, to evaluate the hypothesis regarding the relationship between the numerical variable of interest and the binary variable that defines the two groups, we investigate the difference between the two groups with respect to the characteristic represented by the numerical variable. Next, we discuss situations where both variables are binary. Finally, we talk about the situations where both variables are numerical.


Tail Probability Population Proportion Population Means Normal Body Temperature Output Window 
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  1. 14.
    Kettunen, J.A., Harilainen, A., Sandelin, J., Schlenzka, D., Seitsalo, S., Hietaniemi, K., Malmivaara, A., Kujala, U.M.: Knee arthroscopy and exercise versus exercise only for chronic patellofemoral pain syndrome: a randomized controlled trial. BMC Med. 5, 38 (2007) CrossRefGoogle Scholar
  2. 16.
    Levine, P.H.: An acute effect of cigarette smoking on platelet function: a possible link between smoking and arterial thrombosis. Circulation 48(3), 619–623 (1973) Google Scholar
  3. 19.
    Mackowiak, P.A., Wasserman, S.S., Levine, M.M.: A critical appraisal of 98.6°F, the upper limit of the normal body temperature, and other legacies of Carl Reinhold August Wunderlich. JAMA 268, 1578–1580 (1992) CrossRefGoogle Scholar
  4. 35.
    Teasdale, N., Bard, C., Larue, J., Fleury, M.: On the cognitive penetrability of posture control. Exp. Aging Res. 19(1), 1–13 (1993) CrossRefGoogle Scholar
  5. 39.
    Witte, A.V., Fobker, M., Gellner, R., Knecht, S., Floel, A.: Caloric restriction improves memory in elderly humans. Proc. Natl. Acad. Sci. USA 106(4), 1255–1260 (2009) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of California, IrvineIrvineUSA

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