null hypothesis for a factorial anova

Null-hypothesis for a Factorial Analysis of Variance (ANOVA)

Conceptual Explanation

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

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

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.

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).

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

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

1st Null Hypothesis – 1st Main EffectThere 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 EffectThere 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 EffectThere 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].

1st Null Hypothesis – 1st Main EffectThere 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 EffectThere 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 EffectThere 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].

1st Null Hypothesis – 1st Main EffectThere 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 EffectThere 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 EffectThere 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].

1st Null Hypothesis – 1st Main EffectThere 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 EffectThere 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 EffectThere 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].

1st Null Hypothesis – 1st Main EffectThere 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 EffectThere 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 EffectThere 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].

1st Null Hypothesis – 1st Main EffectThere 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 EffectThere 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 EffectThere 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].

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.

1st Null Hypothesis – 1st Main Effect

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

1st Null Hypothesis – 1st Main EffectThere 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

1st Null Hypothesis – 1st Main EffectThere 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 EffectThere is no significant difference in the number of pizza slices consumed in one sitting by upper and lower classman.

1st Null Hypothesis – 1st Main EffectThere 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 EffectThere is no significant difference in the number of pizza slices consumed in one sitting by upper and lower classman.3rd Null Hypothesis – Interaction Effect

1st Null Hypothesis – 1st Main EffectThere 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 EffectThere is no significant difference in the number of pizza slices consumed in one sitting by upper and lower classman.3rd Null Hypothesis – Interaction EffectThere is no significant interaction effect between athlete type and classman status on the number of slices consumed in one sitting.

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.

1st Null Hypothesis – 1st Main Effect

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

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

2nd Null Hypothesis – 2nd Main Effect

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

2nd Null Hypothesis – 2nd Main EffectThere is no significant difference in weight loss between those overweight and those not overweight.

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

2nd Null Hypothesis – 2nd Main EffectThere is no significant difference in weight loss between those overweight and those not overweight.

3rd Null Hypothesis – Interaction Effect

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

2nd Null Hypothesis – 2nd Main EffectThere is no significant difference in weight loss between those overweight and those not overweight.

3rd Null Hypothesis – Interaction EffectThere is no significant interaction effect between diet type and weight status on weight loss.