Statistics 1: Contingency Tables

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Questions and Answers

What do the sums of frequencies or relative frequencies in rows define?

  • The joint distribution of X and Y
  • The marginal distribution of the variable X (correct)
  • The variance of X
  • The conditional distribution of Y given X

What is the meaning of fi. in the context of contingency tables?

  • The joint frequency of X and Y
  • The variance of X
  • The relative frequency of the group of individuals presenting modality xi of X (correct)
  • The relative frequency of the group of individuals presenting modality yi of Y

What is the formula for the relative frequency fij?

  • fij = nij / (ni. * nj.)
  • fij = nij / n (correct)
  • fij = nij / (ni. * n.j)
  • fij = nij / nij

What is the meaning of n.j in the context of contingency tables?

<p>The subtotal of the frequencies of the groups of individuals in the j-th column (A)</p> Signup and view all the answers

What is the sum of the relative frequencies fij over all i and j?

<p>1 (D)</p> Signup and view all the answers

What is the name of the distribution defined by the sums of frequencies or relative frequencies in columns?

<p>The second marginal distribution (A)</p> Signup and view all the answers

What is the purpose of correlation coefficients, scatterplots, and regression equations?

<p>To summarize and interpret the strength and direction of the relationship between the quantitative variables. (B)</p> Signup and view all the answers

What is X in the context of contingency tables?

<p>The response of an individual to the variable X. (A)</p> Signup and view all the answers

What is represented by nij in a contingency table?

<p>The frequency of the group of individuals presenting both modality xi of X and modality yj of Y. (B)</p> Signup and view all the answers

What is the purpose of a contingency table?

<p>To summarize the frequency of different groups of individuals presenting different modalities of two variables. (A)</p> Signup and view all the answers

What is the graphical representation of the relationship between two quantitative variables?

<p>Scatter plot (A)</p> Signup and view all the answers

What are the elements of a contingency table?

<p>Rows representing the modalities of X and columns representing the modalities of Y. (A)</p> Signup and view all the answers

What does the conditional distribution given the number of rooms is 4 represent?

<p>The probability of the surface area given the number of rooms (C)</p> Signup and view all the answers

What is the formula to calculate the conditional variance?

<p>V (X|Y = yi ) = k X fX=xi |Y =yj x2i − m2X|Y =yi (B)</p> Signup and view all the answers

What is independence in the context of statistical variables?

<p>The absence of a relationship between two statistical variables (B)</p> Signup and view all the answers

What is the condition for two variables to be independent?

<p>fij = fi..f.j , ∀i = 1,.., k and j = 1,.., l (D)</p> Signup and view all the answers

What is represented in a contingency table?

<p>The joint probability distribution of two variables (A)</p> Signup and view all the answers

What is an example of a statistical problem that can be represented by a contingency table?

<p>The relationship between the number of rooms and surface area of dwellings (B)</p> Signup and view all the answers

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