What was the purpose of the study conducted by the psychologist? Were there any differences in the ability to solve puzzles between history majors and mathematics majors? Is there an interaction effect between the major and the type of puzzle?
The psychologist conducted a study to determine if there are differences in the ability to solve puzzles between history majors and mathematics majors. The study involved 25 mathematics majors and 25 history majors from a liberal arts college in Maine. Each group was randomly assigned one of five types of puzzles, and the time taken to complete each puzzle was recorded. A penalty of 10 minutes was added if a student couldn't complete a puzzle within the allocated time. To analyze the data, a line graph was plotted to show the mean time to complete a puzzle for each type by major. Additionally, a Two-Way ANOVA test was conducted at the 0.05 significance level to determine if there was an interaction effect between the major and the type of puzzle.
Plotting Mean Time to Complete Puzzle
Using Excel to analyze the data, a line graph was created to visualize the average time taken to complete a puzzle for history majors and mathematics majors. The x-axis represented the types of puzzles (crossword, cryptogram, logic problem, maize, cross sums), while the y-axis showed the mean time in minutes. By examining the line graph, it becomes easier to compare the puzzle-solving abilities of history majors and mathematics majors across different puzzle types.
Conducting Two-Way ANOVA Test
To determine if there was an interaction effect between the major and the type of puzzle, a Two-Way ANOVA test was performed at the 0.05 significance level. In Excel, the data was organized with each group (history majors, mathematics majors) in separate rows or columns, and each type of puzzle in another row or column. By running the Two-Way ANOVA test using Excel's 'Data Analysis' toolpack and selecting the 'ANOVA: Two-Factor With Replication' option, the interaction significance value ('Pr > F') was obtained from the ANOVA table.
Interpreting the Results
If the 'Pr > F' value in the ANOVA table is less than 0.05, it indicates a significant interaction effect between the major and the type of puzzle. This means that the puzzle-solving abilities of history majors and mathematics majors differ significantly across the puzzle types. Understanding these interactions can provide valuable insights into the cognitive skills and problem-solving strategies of students in different academic disciplines.