Question

The following data summarize the results from an independent-measures study comparing three treatment conditions.

a. Use an ANOVA with α = .05 to determine whether there are any significant differences among the three treatment means. Note: Because the samples are all the same size, MSwithin is the average of the three sample variances.

b. Calculate η2 to measure the effect size for this study.

Answer 1

From the given data we can summarize the following terms: K = Number of treatments = 3 N= total number of observations = 10+10+10= 30 G = Sum of all the T = 20+30+40 = 90 Also we have sample variance s2 and we can calculate SS(Sum of Squares) using following formula. SS = s2 *(n-1) , where n = number of observation in particular sample SS2.67= 2.67*9= 24.03 SS2.00= 2.00 * 9 = 18 SS1.33 = 1.33 * 9 = 11.97 

Step1) Null Hypothesis Alternative hypothesis : HA: Atleast one of the treatment mean is different. Level of significance Step 2) Obtain the ANOVA table and locate the critical region. dfBetween Treatments = K-1 = 3-1 = 2 dfWithin treatments = N - K = 30 - 3 = 27 From the F-Distribution table, we will find the FCritical value for dfBetween Treatments= 2, dfWithin treatments = 27, and alpha = 0.05, and is given by FCritical = 3.354. Now we will obtain the