Question

Q1. Researchers were interested in determining whether there were any differences in the tendency to procrastinate based on birth order, i.e. first, second, or third child born. Using the data in the table below, answer the following questions.

1. State the null and alternate hypotheses.
2. What is the total sample size?
3. Identify the independent and dependent variables
4. What is the test statistic value?
5. What is the p value?
6. What is your conclusion (assume α = .05)? Phrase your conclusion based on your hypotheses.
7. Do we need a post hoc analysis? Why or why not?

Descriptive Statistics
Birth_Order	Mean	Std. Deviation	N
1	57.66	23.947	250
2	59.44	23.479	250
3	60.26	23.408	250
Total	59.12	23.606	750

Tests of Between-Subjects Effects
Source	Type III Sum of Squares	df	Mean Square	F	Sig.	Partial Eta Squared
Birth Order	885.048	2	442.524	.794	.453	.002
Error	416490.152	747	557.550
Total	3038756.000	750

Answer 1

Problem: Researchers were interested in determining whether there were any differences in the tendency to procrastinate based on birth order, i.e. first, second, or third child born.

a.
The problem is one-way ANOVA (Analysis of Variance).
Null hypothesis-H0: mu₁=mu₂=mu₃ (Means are all SAME)
where, mu1=mean based on first order; mu2=mean based on second order and mu3=mean based on third order
Alternative Hypothesis-H1: atleast one mu_i is different from remaining ones (Means differ significantly)

b.
Total sample size=N= (250+250+250) = 750

c.
Independent variable:
Since, it is one-way ANOVA it has only one independent variable (or factor). It is typically a categorical variable. It is controlled by the experimenter. Here, Birth level form independent variable with levels ("1","2","3").

Dependent variable:
It is the variable that is the "result" of independent variable.

## From ANOVA table we obtain,

d.
Test statistic value = F-statistic value = F0 = 0.794
[F-value=Mean square of birth order / Mean Square Error]

e.
p-value=0.453
[p-value=P{F(2,747) < F0}=0.453]

f.
assume α = 0.05
Comparison: p-value (0.453) is greater than alpha (0.05).We fail to Reject H0.
Conclusion: There were NO significant differences in the tendency to procrastinate based on birth order, i.e. first, second, or third child born.

g.
NO, we DO NOT need post hoc analysis. Because,only if we Reject H0 in above ANOVA we go for further analysis. Here, we fail to Reject H0.
[post hoc analysis is needed when we have to find out if category is significant, which level of category (or combination of category) is significant.]