Null hypothesis for a Factorial ANOVA

1. Null-hypothesis for a Factorial
Analysis of Variance (ANOVA)
Conceptual Explanation

2. With hypothesis testing we are setting up a null-hypothesis
–

3. With hypothesis testing we are setting up a null-hypothesis
– the probability that there is no effect or
relationship – and

4. With hypothesis testing we are setting up a null-hypothesis
– the probability that there is no effect or
relationship – and then we collect evidence that leads
us to either accept or reject that null hypothesis.

5. As you may recall, a Factorial ANOVA attempts to
compare the influence of at least two independent
variables with at least two levels each (e.g., 1. Player –
Football1, B-Ball2, Soccer3 and 2. Age – Younger1,
Older2) on a dependent variable (e.g., pizza slices
consumed in one sitting).

6. Here is a template for writing a null-hypothesis for a
Factorial ANOVA

7. With a Factorial ANOVA, as is the case with other more
complex statistical methods, there will be more than
one null hypothesis.

8. 1st Null Hypothesis – 1st Main Effect
There is no significant difference on [insert the
Dependent Variable] based on [Insert the 1st
Independent variable with at least two levels].
2nd Null Hypothesis – 2nd Main Effect
There is no significant difference on [insert the
Dependent Variable] based on [Insert the 1st
Independent variable with at least two levels].
3rd Null Hypothesis – The Interaction Effect
There is no significant interaction effect between the
[Insert the 1st Independent variable] and the [Insert the
1st Independent variable] in terms of the [Insert the
Dependent Variable].

9. 1st Null Hypothesis – 1st Main Effect
There is no significant difference on [insert the
Dependent Variable] based on [Insert the 1st
Independent variable with at least two levels].
2nd Null Hypothesis – 2nd Main Effect
There is no significant difference on [insert the
Dependent Variable] based on [Insert the 1st
Independent variable with at least two levels].
3rd Null Hypothesis – The Interaction Effect
There is no significant interaction effect between the
[Insert the 1st Independent variable] and the [Insert the
1st Independent variable] in terms of the [Insert the
Dependent Variable].

10. 1st Null Hypothesis – 1st Main Effect
There is no significant difference on [insert the
Dependent Variable] based on [Insert the 1st
Independent variable with at least two levels].
2nd Null Hypothesis – 2nd Main Effect
There is no significant difference on [insert the
Dependent Variable] based on [Insert the 1st
Independent variable with at least two levels].
3rd Null Hypothesis – The Interaction Effect
There is no significant interaction effect between the
[Insert the 1st Independent variable] and the [Insert the
1st Independent variable] in terms of the [Insert the
Dependent Variable].

11. 1st Null Hypothesis – 1st Main Effect
There is no significant difference on [insert the
Dependent Variable] based on [Insert the 1st
Independent variable with at least two levels].
2nd Null Hypothesis – 2nd Main Effect
There is no significant difference on [insert the
Dependent Variable] based on [Insert the 2nd
Independent variable with at least two levels].
3rd Null Hypothesis – The Interaction Effect
There is no significant interaction effect between the
[Insert the 1st Independent variable] and the [Insert the
1st Independent variable] in terms of the [Insert the
Dependent Variable].

12. 1st Null Hypothesis – 1st Main Effect
There is no significant difference on [insert the
Dependent Variable] based on [Insert the 1st
Independent variable with at least two levels].
2nd Null Hypothesis – 2nd Main Effect
There is no significant difference on [insert the
Dependent Variable] based on [Insert the 2nd
Independent variable with at least two levels].
3rd Null Hypothesis – The Interaction Effect
There is no significant interaction effect between the
[Insert the 1st Independent variable] and the [Insert the
1st Independent variable] in terms of the [Insert the
Dependent Variable].

13. 1st Null Hypothesis – 1st Main Effect
There is no significant difference on [insert the
Dependent Variable] based on [Insert the 1st
Independent variable with at least two levels].
2nd Null Hypothesis – 2nd Main Effect
There is no significant difference on [insert the
Dependent Variable] based on [Insert the 2nd
Independent variable with at least two levels].
3rd Null Hypothesis – The Interaction Effect
There is no significant interaction effect between the
[Insert the 1st Independent variable] and the [Insert the
1st Independent variable] in terms of the [Insert the
Dependent Variable].

14. Problem #1
A pizza café owner wants to know which high school
athletes eat more pizza during their lunch break so she
knows which group to advertise more to. Is it football,
basketball, or soccer players? She further would like to
know if there is a difference between upper (juniors
and seniors) and lower (freshman and sophomores)
classman.

15. 1st Null Hypothesis – 1st Main Effect

16. 1st Null Hypothesis – 1st Main Effect
There is no significant difference on the number of pizza
slices consumed in one sitting by football, basketball,
and soccer players.

17. 1st Null Hypothesis – 1st Main Effect
There is no significant difference on the number of pizza
slices consumed in one sitting by football, basketball,
and soccer players.
2nd Null Hypothesis – 2nd Main Effect

18. 1st Null Hypothesis – 1st Main Effect
There is no significant difference on the number of pizza
slices consumed in one sitting by football, basketball,
and soccer players.
2nd Null Hypothesis – 2nd Main Effect
There is no significant difference in the number of pizza
slices consumed in one sitting by upper and lower
classman.

19. 1st Null Hypothesis – 1st Main Effect
There is no significant difference on the number of pizza
slices consumed in one sitting by football, basketball,
and soccer players.
2nd Null Hypothesis – 2nd Main Effect
There is no significant difference in the number of pizza
slices consumed in one sitting by upper and lower
classman.
3rd Null Hypothesis – Interaction Effect

20. 1st Null Hypothesis – 1st Main Effect
There is no significant difference on the number of pizza
slices consumed in one sitting by football, basketball,
and soccer players.
2nd Null Hypothesis – 2nd Main Effect
There is no significant difference in the number of pizza
slices consumed in one sitting by upper and lower
classman.
3rd Null Hypothesis – Interaction Effect
There is no significant interaction effect between
athlete type and classman status on the number of
slices consumed in one sitting.

21. Problem #2
Imagine you want to compare the effectiveness of 2
different diets (low carb vs. low fat). You also want to
assess whether people lose more weight on either diet
if they are already overweight vs. normal weight. It’s
also possible that the effectiveness of these two
specific diets depends on whether or not participants
are already at a normal weight or are overweight.

22. 1st Null Hypothesis – 1st Main Effect

23. 1st Null Hypothesis – 1st Main Effect
There is no significant difference in weight loss
between those on a low or high carb diet.

24. 1st Null Hypothesis – 1st Main Effect
There is no significant difference in weight loss
between those on a low or high carb diet.
2nd Null Hypothesis – 2nd Main Effect

25. 1st Null Hypothesis – 1st Main Effect
There is no significant difference in weight loss
between those on a low or high carb diet.
2nd Null Hypothesis – 2nd Main Effect
There is no significant difference in weight loss
between those overweight and those not overweight.

26. 1st Null Hypothesis – 1st Main Effect
There is no significant difference in weight loss
between those on a low or high carb diet.
2nd Null Hypothesis – 2nd Main Effect
There is no significant difference in weight loss
between those overweight and those not overweight.
3rd Null Hypothesis – Interaction Effect

27. 1st Null Hypothesis – 1st Main Effect
There is no significant difference in weight loss
between those on a low or high carb diet.
2nd Null Hypothesis – 2nd Main Effect
There is no significant difference in weight loss
between those overweight and those not overweight.
3rd Null Hypothesis – Interaction Effect
There is no significant interaction effect between diet
type and weight status on weight loss.