2.2 Special types of Correlation
2.3 Point Biserial Correlation rPB
2.3.1 Calculation of rPB
2.3.2 Significance Testing of rPB
2.4 Phi Coefficient (φ )
2.4.1 Significance Testing of phi (φ )
2.5 Biserial Correlation
2.6 Tetrachoric Correlation
2.7 Rank Order Correlations
2.7.1 Rank-order Data
2.7.2 Assumptions Underlying Pearson’s Correlation not Satisfied
2.8 Spearman’s Rank Order Correlation or Spearman’s rho (rs)
2.8.1 Null and Alternate Hypothesis
2.8.2 Numerical Example: for Untied and Tied Ranks
2.8.3 Spearman’s Rho with Tied Ranks
2.8.4 Steps for rS with Tied Ranks
2.8.5 Significance Testing of Spearman’s rho
2.9 Kendall’s Tau (ô)
2.9.1 Null and Alternative Hypothesis
2.9.2 Logic of Kendall’s Tau and Computation
2.9.3 Computational Alternative for Kendall’s Tau
2.9.4 Significance Testing for Kendall’s Tau
38. 𝒓 𝒃 =
𝒀 𝟏 − 𝒀 𝟎
𝑺 𝒀
𝑷 𝟎 𝑷 𝟏
𝒉
𝑊ℎ𝑒𝑟𝑒,
𝒀 𝟏 = the sample mean of the y variable for those individuals for whom x = 1
𝒀 𝟎 = the sample mean of the y variable for those individuals for whom x = 0
𝑺 𝒀 = the standard deviation of the y values
𝑷 𝟏 = the proportion of individuals with x = 1
𝑷 𝟎 = 1 − 𝑷 𝟏 = the proportion of individuals with x = 1
𝒉 = ordinate or the height of the standard normal distribution at the point
which divides the proportions f P0 and P1