A restaurant asked a focus group to rate 5 new dishes, each of which features either beef, chicken, fish, pork,...

Owning the Dataset

Table 1: Text Analysis

Table 2: Chart Analysis

Key Insights

Tofu is the clear favorite, winning every possible comparison and appearing as the preferred choice in every matchup it appears in. Pork is the least preferred, losing in every comparison and never being selected as the favorite in any pairing. Chicken and fish are equally preferred in the middle, while beef wins only one comparison. The clear preference order is: Tofu > Chicken = Fish > Beef > Pork.

Step-by-Step Solution

Question 1: Identify the Dish Preferred Over All Others

Complete Statement:

The focus group preferred the dish featuring ______ to every other dish.

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: preferred the dish featuring ______
    • Meaning: Looking for the one dish that was chosen over the others
    • Relation to Chart: The matrix shows which dish won in each head-to-head comparison
    • Important Implications: We need to find the dish that was always picked as the winner in each matchup
• Statement Breakdown 2:
  • Key Phrase: to every other dish
    • Meaning: The chosen dish must have beaten all the other options
    • Relation to Chart: Check for a row/column (for that dish) showing only that dish as winner across all matchups
    • Important Implications: Only one dish can be the universal winner in all comparisons
• What is needed: Which single dish won every pairwise comparison against all other dishes

Solution:

• Condensed Solution Implementation:
  Scan the matrix and see which dish appears as the preferred one in all its paired comparisons.
• Necessary Data points:
  The number of times each dish is listed as the preferred dish in comparisons with other dishes.
  • Calculations Estimations:
    Tofu is the winner in all its four comparisons (4 wins). No other dish achieves this.
  • Comparison to Answer Choices:
    Tofu has 4 wins, Beef 1, Chicken 2, Fish 2, Pork 0. Only tofu is universally preferred.

FINAL ANSWER Blank 1: Tofu

Question 2: Identify the Dish Least Preferred by the Group

Complete Statement:

The focus group preferred every other dish to the dish featuring ______.

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: preferred every other dish
    • Meaning: All the other dishes were chosen above this dish in comparisons
    • Relation to Chart: This dish never appears as a winner in the matrix
• Statement Breakdown 2:
  • Key Phrase: to the dish featuring ______
    • Meaning: The dish in the blank lost all its direct comparisons
    • Relation to Chart: Check for a row/column for a dish that shows it as loser in every matchup
• What is needed: Which dish lost every pairwise comparison against all other dishes

Solution:

• Condensed Solution Implementation:
  Review the comparison matrix for a dish that never appears as the winner.
• Necessary Data points:
  The number of times each dish is listed as the loser (or never as the winner) in pairwise matchups.
  • Calculations Estimations:
    Pork is never the preferred dish in any of its four matchups (0 wins).
  • Comparison to Answer Choices:
    Only Pork has zero wins; all other dishes have at least one win.

FINAL ANSWER Blank 2: Pork

Summary

By reviewing the pairwise preference matrix, it's clear that tofu was selected over every other dish (winning every matchup), and pork was never selected as the winner (losing every matchup). Thus, tofu fills the first blank, and pork fills the second.

Question Independence Analysis

The two questions are independent; one asks for the universally preferred dish while the other asks for the universally least preferred. Each requires identifying a distinct pattern (all wins, or all losses) in the comparison matrix.