Question

Researchers measure the frequency of feeling of loneliness in samples of several age groups of adolescents. Each age group has an equal number of participants. The researchers use an ANOVA to assess whether age effects the frequency of loneliness. They report F(2,15) = 3.63.

1. How many age groups were in the study?

2. How many participants were in each age group?

3. What conclusion should be drawn? Justify your conclusion by stating the appropriate critical value.

Answer 1

1) The calculated F(2, 15) uses following degrees of freedom

Degrees of freedom for groups = 2

Hence number of groups = 2 + 1 = 3

Number of groups = 3

2) Degress of freedom for within groups = 15

Total degrees of freedom = 15 + 2 = 17

Hence, total observations N = 17 + 1= 18

3 groups and 18 observations

=> number of observations per group = 18/3 = 6

Number pf participants in each group = 66

3) Let level of significance =

0.05

Critical F is found using Excel function f.inv.rt(0.05, 2, 15)

F-crit = 3.682

3.63 < 3.682

Hence, we do not reject the null hypothesis

Conclusion :

At 5% level of significance, we can conclude that age does not effect frequency of loneliness.