# Hypothesis difficulty

#### Cynderella

##### New Member
Let $$Y_{ij}=1$$ if the $$i^{\text{th}}$$ child is classified as obese at the $$j^{\text{th}}$$ occasion, and $$Y_{ij}=0$$ otherwise.

The marginal probability of obesity at each occasion follows the logistic model

$$log\frac{\Pr(Y_{ij}=1)}{\Pr(Y_{ij}=0)}= \beta_1+\beta_2\text{gender}_i+\beta_3\text{age}_{ij}+\beta_4\text{age}_{ij}^2+\beta_5\text{gender}_i\text{age}_{ij}+\beta_6\text{gender}_i\text{age}_{ij}^2.$$

If one construct the hypothesis that changes in the log odds of obesity are the same for boys and girls, then $$H_0:\beta_5=\beta_6=0$$.

But I am not understanding that why it is not $$H_0:\beta_2=0$$ to indicate the hypothesis that changes in the log odds of obesity are the same for boys and girls? Since $$\beta_2$$ indicates changes in log odds of obesity for male than that of female (assuming female is reference category).