Question

1. We are conducting a one-way between groups ANOVA. We have 50 people in each condition. Each person rates how much they like their assigned food (pizza, burger, or taco) on a scale of 1 to 5 (1 = hate this food, 5 = favorite food ever). We run a hypothesis test and find a significant statistic. What does this mean?

1. Calculate all the appropriate HSDs for the following groups:

Pizza Mean: 2.3; Burger Mean: 4.5; Taco Mean: 3.7; Standard Error (s_M): .32

2. If the critical value found in the q table is -6.236, are any comparisons significant? What do your findings mean?

Answer 1

The investigator interested in testing is there any significance difference between food (pizza, burger or taco) with respect to favorite food among people.

By testing the above hypothesis. we found that there is significant. meaning that there is difference between food (pizza, burger or taco) among people. Now one can interesting finding between which two groups are differs the taste (i.e between pizza and burger, burger and  taco or pizza and taco). for this one can use Tukey's HSD test will use.

a) first find absolute difference between means of pizza and burger, burger and taco, pizza and taco

Group 1:pizza and burger 2.3- 4.5 = 2.2 (by ignoring negative sign because absolute difference)

Group 2:burger and Taco 4.5- 3.7 = 0.8

Group 3:pizza and taco 2.3- 3.7 = 1.4

Using the following formula for calculating HSD ,

HSD=      q is table value corresponding to number of groups (3) and error degrees of freedom (147) , n is sample size taken in each group but not total.

HSD = 3.349 * sqrt(0.32/(50))

HSD= 3.349* 0.08

HSD = 0.268. by comparing this value with the above difference of means, if any difference of means more than 0.1515, then we can say that the difference is significant.

Since all groups are more than 0.268, therefore all groups are differ significantly.