Question

Below are a hypothetical (separate) set of data. The experimenter is interested in the number of errors made by rats in a maze as a function of the kind of reward. Group 1 receives 100% water reward, group 2 receives a solution of 50% water and 50% sugar as the reward; and group 3 receives 100% sugar reward. Perform appropriate analyses to test if the type of reward affects the number of errors; if so, how.

Group	1	2	3
	1	8	6
	3	7	5
	2	5	3
	1	4	3
	3	6	3

Answer 1

We use the Excel Data Analysis Tool for ANOVA single factor with repetition      

The null and alternative hypotheses are :      
Ho : There is no difference in the number of errors for different types of rewards      
Ha : There is a difference in the number of errors for different types of rewards      

ANOVA Table

Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	40	2	20	10.909	0.0019961	3.885
Within Groups	22	12	1.83333
Total	62	14

Test statistic F = 10.909     
p-value = 0.0019961     
     
α = 0.05     
0.0019961 < 0.05     
that is, p-value < 0.05     
Hence, we Reject Ho     

Conclusion :     
At 5% level of significance, there is enough statistical evidence to show that      
there is a difference in the number of errors for different types of rewards     
     
In other words, the type of reward affects the number of errors