Scenario
Mrs Dorothy (the School Secretary since 1965) has the task of purchasing coffee for the Staff room. Four large tins, containing four different brands of coffee, currently reside in the cupboard and take up a lot of room. This overcrowding motivates Mrs Dorothy to make a monumental decision – to buy only one brand of coffee rather than four.
The problem is, the four brands appear to be equally popular amongst the 20 staff members of the school who drink coffee. Specifically, 5 staff members prefer “Burned Roast” brand, 5 prefer “Toasted Cinders” brand, 5 prefer “Smooth and Singed” brand and 5 prefer “Scorched!” brand.
As a consequence of this deadlock, a decision cannot be made on popularity alone. Mrs Dorothy has to find another way to choose a single brand for purchase. To do this, she interviews all 20 staff members and asks them to give a rating (between 0 and 20) for how much they actually like their preferred brand of coffee. The higher the rating, the more they like the coffee.
From these data, four average scores can be calculated for the four different coffee brands, and Mrs Dorothy decides that the average highest score will be chosen as Summertown High’s “Official Staff Coffee”.
She has no prediction about which coffee will be favoured by staff, but she will perform post-hoc tests to determine the “order of preference” of coffees
Furthermore, when the data is collated and the raw numbers are examined, Mrs Dorothy believes there may be an issue with meeting the assumptions of a parametric test.
The grouping variable (COFFEE) has four brands:
“Burned Roast”
“Toasted Cinders”
“Smooth and Singed”
“Scorched!”
Task 1: State the null and experimental hypothesis based on the scenario (does the scenario imply direction?) Specify the decision criteria for retaining or rejecting the null hypothesis
Task 2: Before performing any statistical analysis, what type of test would be most appropriate for this design? Why?
Task 3: What is the Independent variable and how many levels does it possess?
Task 4: What is the dependent variable?
Task 5: What are the assumptions of a One-Way Between-groups ANOVA?
Task 6: For each level of the IV, check coffee preference scores for outliers and normal distributions (only use z scores and normality tests)
Task 7: Conduct the Kruskall-Wallis test and provide reasoning for either accepting or rejecting the null hypothesis
Task 8: Using an alpha level of 0.05, write a results section for the hypothetical study.
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