They calculate the adjusted residuals with the output shown below. What does this indicate?

bunnyland otherland wilderness
doggie 3.40249826 0.04766563 -3.35278341
kevin -3.40249826 -0.04766563 3.35278341

Question

They calculate the adjusted residuals with the output shown below. What does this indicate?

bunnyland   otherland  wilderness
  doggie  3.40249826  0.04766563 -3.35278341
  kevin  -3.40249826 -0.04766563  3.35278341

BlackTom AI · Accepted Answer

Adjusted residuals are standardized z-scores for each cell in a contingency table: a positive residual means the observed count is higher than expected, a negative means lower than expected, and magnitudes larger than about 1.96 are statistically significant at the 5% level (≈2.58 for 1% and ≈3.29 for 0.1%). Given the table: - Doggie: Bunnyland = 3.40249826, Otherland = 0.04766563, Wilderness = -3.35278341 - Kevin: Bunnyland = -3.40249826, Otherland = -0.04766563, Wilderness = 3.35278341 Step-by-step reasoning: 1. Compare each adjusted residual to the usual significance cutoff of |z| = 1.96. - Doggie in Bunnyland: 3.4025 → |3.4025| > 1.96 (in fact > 3.29), highly significant positive. - Doggie in Wilderness: -3.3528 → |3.3528| > 1.96 (also > 3.29), highly significant negative. - Doggie in Otherland: 0.0477 → |0.0477| << 1.96, not significant. - Kevin’s cells are exact opposites by symmetry and hence show the corresponding significant negative/positive values in the same cells (negative in Bunnyland, positive in Wilderness). 2. Interpret signs: Doggie’s positive residual in Bunnyland means Doggie leads there more often than expected; Doggie’s negative residual in Wilderness means Doggie leads there less often than expected. Kevin shows the reverse pattern (less in Bunnyland, more in Wilderness). 3. Therefore the only statistically significant differences are Doggie overrepresented in Bunnyland and underrepresented in Wilderness, with Kevin overrepresented in Wilderness and underrepresented in Bunnyland. Otherland shows no significant difference for either. Why other choices are wrong: - Options claiming Doggie leads less in Bunnyland or that differences are only in Otherland contradict the signs and significance. - The choice asserting no significant differences is false because two cells exceed significance thresholds. Conclusion: The correct interpretation is that Doggie leads more in Bunnyland and Kevin leads more in the wilderness (option 4).

They calculate the adjusted residuals with the output shown below. What does this indicate? bunnyland otherland wilderness doggie 3.40249826 0.04766563 -3.35278341 kevin -3.40249826 -0.04766563 3.35278341Single choice

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