Question

The heights (cm) in the following table are from Data Set 1 “Body Data” in Appendix B. Results from two-way analysis of variance are also shown. Use the displayed results and use a 0.05 significance level. What do you conclude?

	Female										Male
18-29	161.2	170.2	162.9	155.5	168	153.3	152	154.9	157.4	159.5	172.8	178.7	183.1	175.9	161.8	177.5	170.5	180.1	178.6
30-49	169.1	170.6	171.1	159.6	169.8	169.5	156.5	164	164.8	155	170.1	165.4	178.5	168.5	180.3	178.2	174.4	174.6	162.8
50-80	146.7	160.9	163.3	176.1	163.1	151.6	164.7	153.3	160.3	134.5	181.9	166.6	171.7	170	169.1	182.9	176.3	166.7	166.3

Short answer

The following conclusions can be drawn.

• The interaction between age and gender does not have a significant effect on the heights of the subjects.
• The factor of age does not have a significant effect on the heights of the subjects.
• The factor of gender has a significant effect on the heights of the subjects.

Step-by-step solution

Given information

The ANOVA table is provided for the data given on heights (cm) under two factors: age bracket and gender.

Testing the interaction effect

For the given two-way analysis of variance, the following hypotheses are set up.

Null hypothesis: There is no interaction effect between age and gender on heights.

Alternative hypothesis: There is an interaction effect between age and gender on heights.

The ANOVA output shows that the p-value corresponding to the F-statistic value of 1.7970 (under interaction), that is, the row with the header Age*Gender is equal to 0.1756.

As the p-value is greater than 0.05, the null hypothesis is failed to be rejected.

Thus, it can be concluded at 0.05 that there is no sufficient evidence that there exists an interaction between the factors of age and gender on height.

As the interaction effect is not significant, the individual effects of age and gender will be tested.

Testing the effect of the factor ‘age’

The following hypotheses are set up to test the effect of age on heights.

Null hypothesis: There is no significant effect of age on heights.

Alternative hypothesis: There is a significant effect of age on heights.

The ANOVA output shows that the p-value corresponding to the F-statistic value (under age) of 2.0403 is equal to 0.1399 (from the row header ‘Age’).

As the p-value is greater than 0.05, the null hypothesis is failed to be rejected.

It can be concluded that there is no significant evidence to conclude the effect of age on heights.

Testing the effect of the factor ‘gender’

The following hypotheses are set up to test the effect of gender on heights.

Null hypothesis: There is no significant effect of gender on heights.

Alternative hypothesis: There is a significant effect of gender on heights.

The ANOVA output shows that the p-value corresponding to the F-statistic value (under gender) of 43.4607 is less than 0.0001 (from the row header ‘Gender’).

As the p-value is less than 0.05, the null hypothesis is rejected.

It can be concluded that there is a significant effect of gender on heights.